09:02:58 Alright, let's get started so welcome everybody. Good morning. Good evening. Good night, whatever to wherever you are.
09:03:08 And this is the first meeting of the transport barrier working group, and we'll try to As the old saying goes, cross the river by feeling for stones on the subject of transport barriers.
09:03:25 Before we get into the main event.
09:03:32 And on here.
09:03:34 Let me just say a few generic words I hope everyone can see it so this is meeting number one and the topic loosely speaking is barrier formation.
09:03:49 So today we have three talks, which I hope will stimulate a lot of discussion and sort of mentally have a plan of 15 plus 15 for each. And these are loose.
09:04:05 And we have course talks by familiar names and faces David rituals Abby a Gar Bay and Steve Tobias, and then we'll have a general discussion after that, which could include, where else we go although, given the way things are.
09:04:26 We have some plans and health, you know, to help stir the pot em democrat oea will be a kind of a code discussion leader.
09:04:36 Now, for these things I noticed that there are questions, you're supposed to have questions so what I thought I would do is just read off the questions and, shall we say, put the bees in your bonnet and let them bows around while you're listening to the
09:04:53 talks. So some general questions what exactly is the transport barrier we've had that one in various plasma meetings over the years it gets surprisingly convoluted what mechanisms underlay barrier formation or barriers always accompanied by a drop in
09:05:14 turbulence intensity I think we know the answer.
09:05:19 Probably is no but what exactly is going on. How could we characterize or understand barriers that are partially porous that past say some scale of of Eddie's or fluctuations but not others.
09:05:36 And what determines barrier scale and build up time.
09:05:41 And I have a few maybe a few more here more specialized where do these emerging scales, which seemed to pop up in this in this field at the key moment like the asthma scale or Ryan scale, how do they relate to barriers speed of propagation point made
09:06:02 by Grecia the relation of homogenization and barriers and the relation between barriers and in homogeneous mixing which I suspect David will touch on.
09:06:28 So, maybe, maybe let those ideas rattle around. And with that, I think it's best to get on with the substance so David please I think everybody knows David ritual he's already been introduced.
09:06:38 And he needs no further so go ahead.
09:06:41 Okay, thank you.
09:06:43 I'm trying to get the
09:06:48 screen full screen just second. Hopefully this is it.
09:06:59 Well,
09:07:02 there we go. Can everyone see the full screen. Okay, perfect. So I'm going to, but it's not supposed to be moving.
09:07:09 Let me stop you from moving.
09:07:12 Right.
09:07:18 Try to keep it fairly short talk with just a few slides in it. And mainly used as a platform for discussion.
09:07:28 So this first image is actually from a very early paper of mine in in 1988 where I was looking at what's called the repeated filaments ation of artists the interfaces so this is a touch is already on the first word interface and already what I was looking
09:07:45 at in at this time was the fact that a vortex patch which you could think is is a perfect barrier because it contains one volume for to city and outside another high voltage city that these themselves are actually not completely sure barriers they actually
09:08:06 can filament, they can lead to breaking ways. And so they are indeed partially porous to small scale fermentation. So these kinds of processes are taking place, and can take place when these barriers are subjected to small part of patients, even small
09:08:23 permissions can do this.
09:08:25 So, I would argue that the essential ingredient required for jet formation or, in the case of planetary atmospheres and oceans, it really is a.
09:08:36 The information is associated with PV barriers or PV jumps or near jumps are sharp gradient so guess is probably more appropriate.
09:08:45 With the intentional reading is that your reversible nonlinear was the way breaking.
09:08:50 So these are PV contours of potential for diversity counters are what support roles few ways. And when they break the lead to Jeff formation. Now, depending on how much breaking tape space is I'll come to you later.
09:09:05 You may have sharper were more diffuse barriers or jets, we'll see how that works. but the first thing I wanted to discuss is basically the jet formation cannot, the current linear theory, it's not a linear process.
09:09:19 And it's very simple to understand this from the point of view of how PV contours.
09:09:27 When in linear theory, they, they can no law, they can not overturn. So in linear dynamics mean position because of the fact that all that can happen is also age, these countries can all sleep and moreover by PV conservation, the area, contained between
09:09:43 contours or under a contour is a constant in time consuming it incompressible flow here.
09:09:52 Then, all they can happen is the area stays fixed and if you then think about rearranging PV contours into equipment latitude pictures then, assuming no breaking takes place then the equipment latitude picture on the right here is forever the same.
09:10:08 So I don't know if you can see my, my cursor moving think anyone confirm that they can see a cursor. Yes. Good. Okay, so the point is that the yellow region here this area here is essentially preserved for all time so nothing actually happens in the sense
09:10:25 of equivalent latitude.
09:10:27 So jets don't form and if you don't have any way breaking.
09:10:32 So, this is an example of filament station and what I was looking at here was the fact that here, the interface, although it looks like a bold curve. This is an old picture so I'm afraid that the reproducibility of this is not very good, but I started
09:10:46 with actually a, an interface consisting of four closely spaced vortices the contours.
09:10:54 They actually lie on a circular vortex patch. I've laid out the patch at least half of it here, so that you can see as time advances downwards, the linear oscillations followed by a growing steepening wave and eventually you can see that there's a spreading
09:11:10 of the contours in time, and eventually the start breaking. At one point, and then they break repeatedly so this is the full invitation process. And the point here is that overboard sections of this interface, the area between the countries is actually
09:11:26 shrunk. So this is the way you get steepening at least over parts of, you might call it the jet, in this case.
09:11:36 And how does this happen. Well, it happens through sheer.
09:11:39 So Pat actually explicitly asked me to talk about sheer so this is one of my favorite subjects anyway. And I think this is really the key process that underlies the way the way breaking takes place and the mixing takes place, and I'll finish my talk today
09:11:54 actually with a proposal for how cheer alone can be used to explain the migration of jets and the steeping or formation of jets in these flows without appealing to many of the myriad of the mechanisms that are out there.
09:12:11 I'm currently.
09:12:13 So, first of all sheer induces way breaking waves break into the region of greatest year this is something that's been observed by a number of people over a while and it's it's super simple to see in a circuit of vortex patch where in the interior, all
09:12:28 that can happen is you're in solid body rotation assuming no disturbances. So fluid particles that are next to each other, initially, stay at the same distance, whereas outside in the region strong cheer.
09:12:39 That's not the case there, things are rapidly shared and what you find is that when you induce a small perturbation like we like I illustrated the previous couple pictures that those perturbations always break outward into the strong sheer zone the Regional
09:12:57 Regional High shear outside the, the patch, and the filling stations all occurring on the outside region which is leading to a migration of the mean position of the boundary actually inwardness case so mixing is occurring on the outside of the vortex
09:13:11 in this case.
09:13:14 Here's the more extreme example where, in this case there's a large scale linear shear applied across so this is based the week linear sheer profile is applied which is growing slowly and time.
09:13:28 This causes a Gaussian vortex initially to deform in a quasi at about a way until it reaches a point where they week filament week PV contours here virginity consciousness case, get pulled away stripped away, leaving a sharp much sharper interface which
09:13:47 is then resistant to the sheer so you form a sharp interface here by again here and the way breaking here is all on the outside the vortex and here's being pulled away to infinity in both cases, both directions.
09:14:02 Another example this is an example of that was done by a co author is newly hornik inhale Heifetz back in 2014 we're we're looking at asymmetric pair topic for instability.
09:14:16 And this is another beautiful example of how sheer these huge steeping of interfaces. So when the experiment we we carried out we had a region of four levels of potential for to see in a channel flow.
09:14:32 This is all in the bear tropic participant equation.
09:14:37 We're just see dynamics and we chose the potential for diversity to be negative, or non monotonic so it basically up some value here then it goes down then it continues up a couple levels up into q4 so it's a no more profile, which is designed to be unstable
09:14:57 and you see the early stages this instability here with that he's forming rolling up these black borders he's already he's here, and this is the early time stages and to set the example so this is basically if you can just focus on the solid curve for
09:15:13 the meaning velocity you bar so mean velocity. Then, an issue is this black curve here. And, notably, the shear which is the URDY here is more or less the same magnitude on either side to the north into the south of the main PV jumps in the center of
09:15:33 flow. On the right is the PV distribution showing the non monotonic nature of initially the dash curve show the final or late time state averaged profile here more rounded jet and then the TV distribution is has nearly monotonic at late times.
09:15:53 But the point here is that initially sheer strong cheer exists on both sides of the jet unlike the circular vortex patch that was illustrated at the beginning.
09:16:04 And what happens is that as you go later in time, the instability divorcees get. There's some sharing that are actually affected and tearing way tearing apart the blackboard and sees below interface.
09:16:14 And you can see the the flow the nature the flow in these white arrows in the middle panel here showing the, the actual velocity field arrows that are mine mainly among the, the sharp interface it's developing in the middle of the image on the left.
09:16:32 And you can see the certain recirculating flow here but you can see the strong shear is taking place on both sides interface, and what you notice on the right hand side of the final pictures that the material that was gray initially has essentially vanished
09:16:47 in overlord section of this interface that because the gap. The gap is narrowed here. And this is basically PV countries coming together to form a sharper interface, through nonlinear Crosby way breaking and sheer.
09:17:03 So here's a blow up of that example, this looks very much like what you see in film mentation except now the film mutations occurring on both sides the interface.
09:17:12 Interestingly, there's a whole history of a way breaking your following from the right to left. Here's a wave about to break it's just about to fall over.
09:17:37 Here's the previous broken wave which is falling for me and filament to the self. This was the previous one to that which was breaking to the north. If you follow backwards there's another one going to the south and the north and on and on and on.
09:17:27 We call this a dragon head actually in the.
09:17:37 It's kind of a looks like that into us anyway the, the point is the film is so complicated profile, all the great material here, used to be on the interface here and it's completely.
09:17:49 It's been essentially stripped away, leaving just a very sharp interface.
09:17:54 On the right hand side so you Lisa sharp PV gradients.
09:17:58 This is quantified here which I'm not going to spend any time in about paper basic looking at how the gap, reduces over large parts of interface and how the mean gap changes in time.
09:18:09 But I want to focus mainly on sheer and what we call the positive feedback mechanism what keeps the mixing in homogeneous here. So way breaking occurs preferentially in regions of reducing GPV gradients.
09:18:27 So if you start with a sister, a situation where say the BMP gradients are our uniform throughout like a uniform flow like deja why and then you add some perturbations to it then.
09:18:56 process which I discussed extensively in last talk. And what this does that. So in the early stages you, you do some mixing the mixing leads to some more diffuse gradients the middle of the flow further way breaking then it's easier to accomplish on these
09:19:13 in these reduced, way more regions have reduced PV gradients. And eventually, this leads to sharper gradients.
09:19:23 on either side of a region have produced gradients, so this is not a perfect staircase but this is an example of what happens if you do moderate amount of mixing typically.
09:19:34 But there's a positive feedback mechanism in play here.
09:19:38 Mixing further weakens the ingredients and places, while strengthen them and others, and that strengthening actually causes greater shear to develop near the edges of the strong PV gradients, as well seen a practical example in a moment.
09:19:52 So initially, the shear is all very weak and it's only actually being induced by the eddies that we've added to the main stage, once a week just to develop, then those be jets then apply additional sheer in addition to the at ease.
09:20:09 To cause further mixing. And now, in this final stage here and nearly final state.
09:20:14 We have a situation where significantly greater sheer now exists on the flanks of these high gradient regions. And so any.
09:20:29 So this is what we call the positive feedback mechanism, and the mechanism of the process is only limited by the available perturbations the main flow.
09:20:38 So this is why when you consider a, an unforced flow.
09:20:44 The essentially the eddies transfer their kinetic energy eventually reducing their ability to mix and you're left with a nudie zonal phone at least for large defamation blanks and this was illustrated in the previous talk in this paper with Michael McIntyre
09:21:02 in 2008, where we considered a initial stage with a beetle I mean gradient of tension for TriCity with some fairly large Eddie perturbations throw on top, just so that we can get some significant mixing taking place by time 10.
09:21:21 Looks like we just have a big mess with no kind of real structure, but you can start seeing some emerging things here. And then eventually start seeing these bands appearing a minute late times the flow becomes more social.
09:21:32 And what's happening here is that you form on your PP staircase, so this is shown here with you put them attitude as a function of time where, initially, you have the these would be equally space for Peter why as a profile for potential fertility.
09:21:49 And you see in some regions, you form sharp ingredients in the mixing is occurring in these regions here where the PV gradients are the countries are moving apart.
09:21:58 see in some regions, you form sharp ingredients in the mixing is occurring in these regions here where the PV gradients are the countries are moving apart. So here's the, there's a drift of PV countries moving together to form the sharper green gradients and the sheer exists, close to the shore gradients and this is shown in
09:22:08 the zonal velocity means of loss in the right hand side, strong sheer exist, close to the strong PD gradients.
09:22:15 You have relatively weak here in his back to a region here and the strong shear on either side here.
09:22:24 So, with however when you add forcing, so if you if you have sustained we forcing and you don't have dissipation to put back the the ingredients of PV this mixing process continued can continue perhaps and different, definitely, leading to PV staircases
09:22:41 and associated short jets. So this is shown in this example of topographic forcing from Scott myself within a.
09:22:49 is shown also in at various times here with the PV is a function of of latitude so you can see that increasingly sharp staircase for me in time.
09:23:10 And this shows that in fact the, the flow is very non zonal in this this case but we're looking at the equivalent latitude than an equivalent of two picture you see the shark chats, where he wouldn't necessarily see them in zone averages you see a smeared
09:23:24 out picture of them.
09:23:25 Okay, so I'd like to conclude with this a couple final slides will charge, they're supposed to be the controversial slides, if you like. So I would like to propose that the universal mechanism like underlying the PV staircase formation so specifically
09:23:41 for atmospheric ocean flows I'm not talking about density certified flows or other types of barriers that form. They have similar similarities but they're also important differences.
09:23:52 So let me focus on the PV staircases or the PV jets be like.
09:23:58 So I would argue that fundamentally the sheer induces the way breaking, and to see this you can go back to the simple case of a single passive PV contour, located in Y equals A each of x and zero call that f of x in a linear sheer flow you equals lambda
09:24:16 y. So the passive PV controller is no PV jump across is just a curve in space. Now, the dynamics of the curve satisfies dydt equals, VBV is equal to zero year we're considering just a sheer flow with you equals lambda why.
09:24:33 And then if you expand what d by DC is the material derivative then you find that y equals each satisfies burgers equations which we, we all know lots about.
09:24:43 We know the burgers equations form short shocks. This will happen in finite time, you could write down the explicit solution in terms of initial conditions.
09:24:52 And basically, this interface or this curve will become multi valued after a certain time dependent on the sheer applied and the maximum slope effectively of the interface.
09:25:05 So basically after this time, the way breaks.
09:25:09 Now you might imagine that instead of a passive PV contrary, if I have a very weak PV contour. So that means a small jump that's something similar to this would happen.
09:25:19 And you didn't make imagine that all that's going to protect the contour from sheer is its own Peavy jump. So PV jumping as the units of shears well I propose that basically the PV will country will oscillate protecting yourself a sheet from this year,
09:25:36 at least if the PV jump has a value which is comparable to a bigger than this year. This is the proposed critical criticality condition.
09:25:48 Now, otherwise you suppose the potential versus the jump is less than this year. So then in that case I would say the contract would break and mix. So, when it breaks and mixes, it's been positioned moves towards lower sheer, or towards low another PV
09:26:04 contour. In both cases, so that the effective PV jump, then becomes greater than the sheer. So let's look at this as a sort of a cartoon here. So imagine you have three vv contours representing some sort of gradient here.
09:26:21 This one happens to be a little bit closer to the lower one subway breaking is occurring here. The sheer is a little bit higher, on the right upper side, lower side here so it's breaking to the north here into the higher shear zone.
09:26:33 This breaking basically if it continues pushes the contour for yourself and into actually even further increasing cheer until it reaches a point where, effectively it's combining forces with the country below it, and it's your then begins to reduce so
09:26:51 reaches a point where it can now sustain itself because effectively it's PB jumpers merged with another one nearby.
09:26:59 So the PV Congress closely approach to augment their effective PV, and therefore protect them from sheer.
09:27:07 Now the week jets established early on. So you might say, how does it develop early stages. So if you establish me chats are the only provide only part of typically there's the shows this year the other part is the eddies that were there initially to
09:27:27 start the flow up or perturbations that were being added. Then they strengthen these jets were strengthened by tracking nearby PV controllers which are breaking in the sheer which is then increasing as the PV contours start to merge together to form stronger
09:27:41 jets. So this weekend's PV gradients between the Jets.
09:27:45 Now an exact calculation can be done using adopting some work that Michael McIntyre and I didn't in jazz in 2008, where if you imagine to PB staircases superimposed slightly shifted so here basically are all these red dashed curves here correspond to
09:28:05 Peavy jumps have equal size or these two are closer together, and these two are further apart. And what you're seeing here is the being zonal velocity associated as a function of why, and over on the right hand side is the sheer, do you bar dy, or do
09:28:21 you do one, and between the were the two countries that close together. There is sheer, but this year is weaker than outside in the region where the gap is larger.
09:28:34 So, this is a mechanism that that says that, basically the ways. Any, any countries that are close to here any, any disturbance to this country here would like to break out word, forcing these two countries can even closer together.
09:28:48 So I would argue that the key mechanism that it's a play here is the sheer mechanism. And the nice thing is that this mechanism seems to apply equally well to both zonal jets and ring jets founding causes traffic terminated small was good information
09:29:12 so here's some pictures I showed last time as well. Whereas time event advances, you form. More and more homogenized regions of potential fertility punctuated by strong 40s, but you see the color changes, really correspond to rapid changes potential participate
09:29:23 here, and the associated flow speeds are shown down here on the bottom showing that there are jets associated with the sharp jumps in PV.
09:29:38 So what's happening if you sort of follow the images you see that initially and additionally but earlier times you see a multitude of small jets that are all over the place.
09:29:48 These start merging together into stronger jets, as time develops and then furthermore, they, they continue merging into have a stronger jets with more modernized regions between.
09:30:01 Okay, so I'm not going to. I didn't prepare any conclusions likes and so I figured that instead will be arguing rather than concluding anything in this session so I'll stop there.
09:30:13 All right, thank you David very stimulating talk so any any people want to start arguing.
09:30:26 Well I'll raise my hand to argue a start this this will set off Steve a bit. But, I mean, one immediate reaction as a theorist with to the you know your your statement, I had sort of two reactions off the cuff but as a theorist off the cuff is the wreck
09:30:51 was the requirement of nonlinear wave breaking how do we reconcile that with the massive use of quasi linear theory in this industry.
09:31:03 Okay. Well, first of all, cause the linear theories and linear bad I might agree. Yeah.
09:31:10 And it's a quantitative three gets you part of the way but not all the way as the Laura cope as also illustrating your own talk last week or two weeks ago.
09:31:21 There are some mechanisms there but they're actually the closet in your theory alone, is I think missing the essentials, in terms of the physical things that are taking place I mean, all that's happening in these flows in the simplicity is that peavy's
09:31:39 materially conserved, and all that can happen is that the way you can have way propagation like royalty ways. And for any kind of evolution take place these ways have to break in order to redistribute their potential for diversity now I'm assuming that
09:31:54 forcing indexing are huge and therefore swapping everything is taking place with PV, because otherwise the pictures entirely different. But so long as forcing it damping are very weak.
09:32:06 Then PB and PD dynamics is the is the primary factor here that what we need to be considering, and so way breaking is the, the key mechanism that's that's driving the system to form jets and I argue that therefore the, the way breaking is is essential
09:32:25 and the cheer is also helping to promote form those jets into ever stronger structure so long as Eddie activity rings.
09:32:40 you're looking at, possibly, of course, the thing that a lot of us do, which is a fix up of fuzzy linear theory with a wave breaking model. And then it's the ball to how good the model is but let's see we're starting to get some life so dm then Brian.
09:32:59 I'm battling through to put some live through this.
09:33:05 I had to two questions do use Chris and that's very interesting That sure is is a key player and sheer within us. We're breaking. I'm wondering how much of that picture actually depends on the nature of the waves being was the waves, being backwards waves,
09:33:23 and if you were to have other kinds of waves.
09:33:27 You wouldn't get this because you wouldn't converge momentum and diverged energy in the in the same way so how generate would that be.
09:33:37 I agree, I agree with you that. That's why I said I was very careful to indicate that I was talking about PV dynamics specifically in atmospheric ocean jets I think there are a multitude of other factors that can affect barrier staircase formation and
09:33:53 say density Shutterfly flows.
09:33:56 Michael and I did make the analogy between some certified flows in our view paper in jazz but they're only you can only take that analogy so far.
09:34:06 The nature of the way breaking in for was ways is in some sense, ideal for this because they're the PB itself is it is a highly dynamic tracer which is linked directly to itself.
09:34:22 So, with density certification, density itself is not inducing a flow field, it's through the density creating vortices the perturbations and then feedback on that so it's a way it's one stage further removed and I'm not arguing about that case that's
09:34:38 an interesting problem to its own right, which I could talk about but we're not in the song.
09:34:44 But I think that what I'm talking about really is is very specific to towards be waves, and if you start adding other things to the dynamics, like for instance MHD, and things start get complicated very quickly in fact you start losing the conservation
09:35:02 central density which then can smear out and destroy this process completely.
09:35:09 If I may continue in a little bit better.
09:35:18 Okay. If you were if you were to to add to guess the city Have you looked at how much what's key in, in what I understand is that your PD controls need to move towards regions of Louis year.
09:35:31 If you were to advocate this city, and if you would break that systematic tendency to go to the worst year and mix things up.
09:35:42 How much to kiss the city would actually.
09:35:46 That's a wonderful question because what you're seeing on the screen now is an example of stochastic Lee forced flow, which is building up in time through that forcing we're actually, we're not playing any dissipation this flow, but we're very, very weakly
09:35:59 forcing it as to caustic small scale stochastic small scale forcing of we can put in the, what happens if the stochastic forcing is too big, then you're right that it's basically, causing a break on how close the PB countries can get together.
09:36:15 So what you need to do is you need to make the forcing ever weaker and go for longer integration times. And so the ideal limit to make the perfect staircase is the limit of zero forcing sustained over infinite time.
09:36:30 And then we argue that you would get a perfect staircase and example in that case.
09:36:34 But stochastic forcing yes ease will prevent the PV contours from actually getting very close together.
09:36:42 I mean, just to burst in with a quick quick comment I mean that almost reminds me back to the game of coherent vertices and make Williams 84, where the end where the answer of course that depending on the forcing you wipe out the vertices.
09:37:01 Yeah. The same same bottom line.
09:37:04 Right.
09:37:07 Alright Brian's had his hand up so go ahead, Brian.
09:37:12 So, um, geophysical systems are strongly forced and just spit in all the variables so doing some sort of contour dynamics that has relies on conservation is something doesn't make any sense for for physical problems I mean it may be sense for some sort
09:37:30 of perfect world.
09:37:34 So, if anything is all it a second comment is it all this, the quasi linear theories.
09:37:43 Make exquisitely precise prediction.
09:37:46 We're talking about fixed point structures that are real numbers specific their exact predictions.
09:37:59 The problem with this sort of argumentation is that it's all hand-waving.
09:38:05 It's all saying, Do you believe me that this thing is mixing here it's going to mix more there because you know the gradient is going to be less and then, you know, the arms are flapping around, there's no analytical structure.
09:38:19 You can't take anything like that. You can't show anything you haven't shown anything like the kind of precision that the quasi linear systems get would you just exactly like the jet.
09:38:30 Exactly. and they are fixed point structures.
09:38:34 Compare that to this kind of hand-waving Do you have anything to show that can be compared with observations that if all you're doing is hand waving it there's no way to judge whether your theory is correct or not it's not a theory anyway, it's a it's
09:38:51 a argumentation.
09:38:53 Well, I would argue that a theory in Physical Sciences is only argumentation a theory is not a theorem, a mathematical theory is something you can prove, but we can propose theories net a theory of gravity which then was supplanted by Einstein which will
09:39:08 probably be supplanted by quantum gravity. I mean these are theories only, they're not proven. And people have for a long time, like Commodore have has proposed a surplus theory, and that that is based somewhat on handwaving arguments, based on proposed
09:39:28 self similarity of scales, which makes which is plausible, so I'm arguing on on making a plausible theory based on on accumulated observations, some experience of my own and others that indicate that the role of sheer is that the key feature here with
09:39:47 forms this. And I would argue that if you're really right that you can make exact predictions, then effectively we'd all be out of business. There's really no point studying fluid dynamics because it'd be all solved at this present time, and I don't think
09:40:01 it is. And I would, I would argue that if your theory really is definitive then apply it to the example that's showing on the screen right now, could you actually reproduce these kinds of wavy jets that you're seeing here or do you think this is a fluke.
09:40:19 But let me continue with the Contra damage because these simulations are cheap are done with not country remix but a modification of the method which has Steve Tobias and that time and also know allows for general forcing and dissipation.
09:40:36 We've actually applied to MHD turbulence successfully comparing it to standard simulations using super respectful simulations that outrageous resolutions.
09:40:45 We know it gives you accurate results, even in the case of forced to split it flows.
09:40:50 The flows without forcing anticipation, don't form interesting jets so what I've mostly looked at in this talk, actually are flows like an image is you're seeing our case it was weak forcing week dissipation or no dissipation over very long times, these
09:41:07 take a lot of effort and you need to have a very conservative in America method, like the ones that I'm using which is based on contra nomics but it's called contradiction.
09:41:17 And you have to be able to do things accurately over long times without excessive numerical dissipation. This is something I can give with these methods in which I've been working on for God knows 35 years or so.
09:41:30 It's embarrassing but anyway.
09:41:37 Over that time scale I've been producing these methods and now they got to a point where they're nicely applicable to ideas me can I make that cut in at some point.
09:41:42 I mean, yeah. Yeah, thanks.
09:41:45 A hold it I think this.
09:41:47 Let's not, I mean, let's not have a discussion on the philosophy of science here let's try this stick to the topic okay i mean otherwise we'd bring out the old story about you can't prove anything only disprove it, but I mean if they if there's a continuation
09:42:06 of this discussion on the topic. Go ahead. If not, Steve to buy us has his hand up.
09:42:15 The topic was whether Newton's theory, that's not even though Newton Newton is not fair game here.
09:42:22 Okay.
09:42:26 What are you talking about, We want to stay on the topic is the topic. The topic is whether we have a theory for barrier formation. Ah, that's a fair question, well that's what we're talking about, if you would wait for a second.
09:42:42 You know that.
09:42:44 So, the closing linear theories are closed form analytic theory switch give precise nonlinear fixed point solutions.
09:42:56 There is nothing in the hand-waving arguments that compares with that until they make a prediction that is specific like that, as Einstein's theory does.
09:43:08 Then, what, what can you say about whether they're correct or not.
09:43:12 They're just argumentation, they don't make any predictions that can be tested. So, that's my only question, what, what prediction, for instance, you, we know that in the Jupiter jets we have reversible in gradient of fertility.
09:43:28 How can that happen if it's supposed to be associated with instability, the quasi linear theories exactly explain that the theories that the the crux of the arguments that we've seen would predict that there are no changes inside.
09:43:46 When in fact the observation show changes.
09:43:50 So it can be a correct barrier argument. If it predicts that there's no changes in sign when that observation show changes. Thank you.
09:43:58 I would argue that Jupiter is not the bear topic for this equation are governed by that I think many people here who are much more knowledgeable like Peter Reid would argue, likewise that this is a much more complex system and if if your theory does show
09:44:15 the jets and matches them, then that's remarkable, but I think that most people would argue that Jupiter has very clinic jets that deep flow. It's not equivalent bear tropic repair tropic.
09:44:30 He thought even shallow water, probably.
09:44:34 So, I mean these are very, very gentle.
09:44:39 Gentlemen, please, this, this is good it's lively but we've got two people with their hands up and against my expectations this discussion is running on So Steve was next.
09:44:52 Okay, I wouldn't say very much because I'm going to give a talk on some of this stuff but I think everybody agrees that there are certain limits in which the quasi linear approximation works exactly, and we can, we can all think of limits in which he
09:45:06 does.
09:45:07 And there are certain cases where as Brian said homogeneous isotopic turbulence is a terrible thing to describe using because the linear theory. And that question then is, when, When do you get one.
09:45:19 When do you get the other, and you know for the situation David was was describing.
09:45:27 I think it's a bit much to say, well, it's a, it's a, it's a driven disruptive system, and therefore you can't use you know David's techniques, when in fact he can adapt them, but a strongly driven strongly disruptive system is exactly the type of situation
09:45:44 where the quasi linear theory does break down. And so, you know, you have to be a bit careful shooting arrows, when you know your own theory relies on something being weekly forced and weekly down.
09:45:58 But let me break in, because I wanted to raise this earlier I know DMU.
09:46:05 What about. I mean, the obvious question is the issue of Qubo number.
09:46:11 Right, Steve.
09:46:13 What. Yeah, exactly. Well, in other words, that's I mean, certainly in our beloved one last off quasi linear theory which is relatively low controversy that clearly emerges as at that.
09:46:27 And the underlying chaos of the particle orbits emerges as the criterion and that can all be distilled into Qubo number. Right. I agree 100% pot and this is in my talk that the problem with the Qubo number is it's something that, that it's very hard to
09:46:43 say what it is a priore group on last year in some Asim toxic separation of timescales, in which case, you can say the Qubo number is small.
09:46:53 And, and therefore cause you linear there you can proceed with confidence. Right. And so, in the general situation you don't know what the Qubo number is going to be true.
09:47:03 All right, dm a quick comment and then we have to move on to your boss will do.
09:47:10 Well, the first one is on the exact same topic and it's a bit of shameless advertising, we will be discussing quiz you didn't know and Cuba numbers also in the plasma session.
09:47:24 And what we actually looked into quite carefully.
09:47:28 This past year with a student of ours is that the Cuban numbers in a fully non inner strongly driven Chase, and in the near module case where the we're only in the new emotional does the staircase exists in our system, if you will, numbers are all of
09:47:56 order one.
09:47:49 So you can say much about it.
09:47:52 And the question they are models that we compare to our found to struggle the breakdown new emotionality where the staircase actually occurs. So, so that that's at least maybe we can discuss what questionnaire means in all of the systems, maybe different
09:48:13 things. But certainly, there is a concerns about the closures, that you need to put in, and the question our relations to make it hold at least in plasmas near marginality.
09:48:28 Okay, I think we better move on to your boss dm, so.
09:48:35 So thank you David. Don't go away. We have a general discussion at the end if we don't kill each other in the meantime.
09:48:42 And our next speaker is Xavi a Gar Bay, and I should introduce him since he's not been introduced so Xavi a I guess started out in the a co normal superior.
09:48:56 And he's one of the leading plasma theorists globally and certainly has played a key role in the, in the cataract, and the French and the French and European fusion programs.
09:49:13 He's won several awards for his work and I should add one last item from the beginning. He's been one of the key players in the festival the theory that we hold every two years.
09:49:28 And that's sort of the the the fusion communities, answer to the Hawaii program. So there's a lot more to be said about Xavi a but we're running out of time so go ahead please.
09:49:42 Thank you very much, but for this introduction. Can you can you see the slides there.
09:49:48 Yeah. Okay, good. Okay so so I had to present the plasma physics there.
09:49:59 That's even magnetised student business.
09:50:01 So, so I'm going to tell you about the relationship statuses and transport various which is Adobe.
09:50:14 observations, I can say so in turban and turbans talents and Putin plasmas and ICBM isn't some time ago, nice, nice overview of these results. So you may remember the kind of figure you see here, top right, showing the level of equals zero specie right
09:50:40 so equals be velocity would be just.
09:50:43 Let's take it like this, as a function of the direction here along the Taurus tokamak, so that's the exploration in the talk, and so on.
09:50:55 So so so close here because into regions here functional areas as opposed to a functional right. So you can see that on this year for instance showing the velocity in blue, which is in the so called Polo direction, talking about that will be the y direction
09:51:12 in the talk. This is destiny sex, and the reasons is actually read the spirit and the reason you see here the difference in seeking blue and red correspond to this to this place.
09:51:29 Now, at the same place, usually we see a correlation of temperature. Okay. And usually at the region where the shear rate is very large, not surprisingly, we see an increase of temperature.
09:51:41 Okay, so that's what we call a staircase so staircase here is kind of parodic arrays of sheer layers, and in between, you can see here, for instance, this place here in this place here.
09:51:58 Transport elements of a large distances by large distances I mean distances which are larger than the correlation and Stevens correlation next, which correspond to what we call other lunches, ok so the staircase at this in our community is an area of
09:52:20 as that confined regions where avalanches propagate. Now, this was seen in many many simulations.
09:52:24 Probably my list is not exhaustive here, some some observations to homelessness is one and showing us one.
09:52:33 And they also shoe.
09:52:43 An ethical model for that, and we saw during the meeting capitals. I saw one and of course again, because we're sorry.
09:52:45 And here I'm going to address this problem from a slightly different point of view. So we, as we discussed actually causing necessary and quite a lot.
09:52:55 We see the working he posted I posted this here is that temperature congregations are related to Michael transport various. Okay. And these microphones for various are produced by shillings.
09:53:07 Now of course, as these simulations are done with heavy five dimensional kinetic simulations I'm not going to enter into this.
09:53:16 And we'll try to restate that was much simpler that we, I think you're way off, which is now communities years ago, equations for brief toys in GFD community the model for the Charlotte Motor for for was P waves.
09:53:32 So, so just keep in mind here, because the notations fortunately I switched in between two communities so xe is a direction around the doors as I said in the room the radius of the doors so it's it's for us the regions of density gradients in emerging
09:53:51 80s, and the parenting direction so so no direction is the y direction.
09:53:56 So that's the direction of propagation of our before is.
09:54:00 So the BC which is uniform here is just in the z direction.
09:54:05 So, so ZCHM equation is just reminded here and you know he's very worried that he, he is equals the velocity so five for us is electric potential by place exactly the same word as the same function, and the potential of two cities, as usual, definition,
09:54:25 up to system here you may not have met him before, which is a normal level of the same function.
09:54:33 That's not that important for our discussion today.
09:54:36 Now, this works in many instances of simulations of this equation and, including during the meeting here I'm going to change it into another model, which is a kinetic model and, which is also very common and consistent replacing the descriptions for the
09:54:53 waves.
09:54:55 By by statistical descriptions, which essentially here, awake integration of an action wave action, which essentially is a probability distribution function of voice packets that you make a replacement for instance, if you're talking about lift weights.
09:55:14 So, so the structure of this equation is very much like a kinetic equation plasma physics that's why you like it very much. And it has a long history, by the way, and the part here which is wasn't brackets between an immediate well I mean Tony and the
09:55:31 action, contains the physics of the propagation, that is the group that or city plus the reflection of the way packets buys and all flows.
09:55:44 And, and the path here which is much more complex actually called us the nonlinear way to direction. So, so it's it's how to derive if you assume quasi on them, faces about your your your your wave packets you find it has the best the structure of Bozeman
09:56:01 type collision of great. That's why some time we could it could break the Mediterranean is essentially the drift way of vacancy and and plus the polar where numbers for the webinar and the y direction times the velocity zone for little cities.
09:56:18 So essentially that the structure I have here is the x direction here, which is again the direction. In the modern age is the y direction which is the buried in direction, and essentially the direction of propagation of the, the, the wave packets and
09:56:35 the show as would be stigmatized and you have a boss of waste packets in between that would be essentially your branches. Okay. Of course you can have us awake packets in within the shell yes and then we'll come back to this.
09:56:49 Now of course you need an equation that will describe the wave kinetic equation which just described, but some kind of thermal mass that of work backwards.
09:56:57 It does not describe. Of course the
09:57:12 city. So this one is actually given by momentum and momentum balance equation. So essentially dangling that you want, the velocity equals to some force. Plus dissipation so dissipation essentially in our case, fiction or viscosity, you to conditional
09:57:19 two collisions between charged particles and put on put on the equations.
09:57:23 So the zonal force here essentially minus divergence of event or stress, and it is related to the web actually the same thing all over the web, where you recognize of course the structure of those two SEMKYXKYKXKY structure.
09:57:40 So this gives you to two equations for the wave action and there's no flow below city, which, at least in some cases is much more profitable than the intro book.
09:57:53 Now of course this is being treated the at length, especially in the year, 2000, in 2009 by particular means of stew.
09:58:08 And, and what is known, and this was also mentioned during the meeting as well is that if you if you address this problem causing it. And that was a discussion we just had barely talking about it but if you use if you use a questionnaire Siri by treating
09:58:23 the problem of bath, say, upon the zoom froze. And you get solution, essentially was weight of the new foods which is related to the fact that is anti anti diffusion and saturation because we are knowing it is and IBM scarcities plus friction, If you
09:58:42 put all together you find this kind of equation that is written just there. And the solution which is essentially for some parameters of course, which is of this kind, that is this would be the University of sec extraction.
09:58:56 Okay.
09:58:56 And and you find something that is valuable. Now, this you this is actually a good result in the sense that gives you some prediction for the during the city's young pitcher and stuff like this but this was not what you would call something sufficient
09:59:11 to expand transport various reason being that usually you would expect something sharper more irregular in shape. I may say so.
09:59:20 So the question is can you find something that is still a vigorous buffing of the kind but but with sharp, sharp or fire of the velocity.
09:59:30 Velocity.
09:59:31 So then writing to something that is a bit outside because in your theory, and which is good which consistency introducing the concept of way flapping in the bottom.
09:59:43 So essentially, if you assume a steady arrays of Zola photos, so something quite stationary.
09:59:51 Your wife committed equation sports down to something very simple it's just the person bracket because, according to break them. Okay, Wait wait no interaction and break them.
10:00:00 The an eternity is actually the one you get for.
10:00:14 Okay, so this is this is actually a proportional to the square of the wave number and the x direction.
10:00:14 And this would be the similarity of your frequency with weight number minus ky times velocity of the zoo.
10:00:18 Now, the shape of this of the distribution function here for for small and dissipation. Okay, we just be that way of action has to be some function of the energy.
10:00:28 So this is nothing else and what we call the big key solution, which was used and instantly to predict sweetens for instance, for an acquisitive waiting process.
10:00:38 Now the interesting point here is that in this kind of structure in the, in the face space so this would be the x direction here, or isn't all the why the vertical direction is a web number in either direction.
10:00:52 So waves which are outside here, the island, the typical Island you get you get for the control lines of the million is wait outside are passing so this would correspond to other branches because they propagate as you seen the direction feeling, but then
10:01:23 waves which actually going to bounce back, back and forth, and these are cops within the shell aliens, show you the surely are being here. So essentially for the profile of the city of the zone or legal status is x of the kind. Traveling with activity okay well. Now the
10:01:26 maximum of the floors.
10:01:29 So then the question is, do you get solution indicators of trapping and the answer is yes. In some cases, so essentially you treat the problem that you're actively, that is, as I said, without dissipation.
10:01:44 The way of action is function of the analogy, but you don't know which which function so you need to solve ability constraint and this you get, of course, by introducing it special.
10:01:56 So, essentially it goes like this so this is the way of action passes away.
10:02:17 Now with, with the island. Okay, what is going on is a flattening of your action in between. in the story inside the island and outside yeah and it actually joined smoothly.
10:02:23 The identity of solutions, this is I'm innocent of mixing but in white space, not in the physical space. The width of the island here which is original while we were flattened and get flattened in here, essentially, goes like the square root of the difference
10:02:37 between the maximum value selling zoom.
10:02:40 Now if you have drive that is in study it is inside, and this we get because we do have insecurities everywhere and if you haven't studied it is in this region here.
10:02:51 In fact, you don't get flattening but you get them in the way of action.
10:03:12 Now, the rest is kind of to you once once what is not as he of course is to solve the equation. But this, we know how to do since the BK work essentially so what you get is his own approach is some kind of nonlinear function of the zone or Forbidden City,
10:03:14 or more precisely of the difference between the velocity and the spinning series The first integral in the problem. And what essentially you get that typically zonal force that's just the velocity is negative here so stable and unstable about some value
10:03:29 and the corresponding very serious extraction.
10:03:35 The Bible is something that and as you can see it's much sharper here and flatter now many more. So this is more like something you would like to see for producing a transport barrier constancy of here and so on.
10:03:48 Okay.
10:04:02 So you get the whole thing.
10:04:04 So the main reserves is essentially that in fact this nevertheless depends very much. Unfortunately, it depends very much on the dissipation. That is what you do is equation operator.
10:04:21 If you just put a so called crew Coverity which is just a pure term that is friction down on the distinction on the action sorry. You find no saying, saying if it is a pure this union, so you need both diffusion and some excitation which is not surprising
10:04:33 because we do have instances in the problem so you need both diffusion, and Ross right that is a collision away way of knowing our interaction operator which is this this shape that is diffusion k x plus excited.
10:04:48 If you do this, you find this kind of solutions you know what I showed, and the equivalent, the contour line or the an internal interface base that is x direction kx direction is this guy.
10:05:02 So the trace or the signature of the flattening of the voc here essentially the flood and you can have your cap, I know the exponent.
10:05:14 So this is something that we go first and this one because this is something that, again should just talk at the very end. That's the, what you, you get actually in the nonlinear simulations.
10:05:24 This one is a full community by the simulation, the whole thing, the velocity is actually less is the radius is something you mean by that is kind of offline, and the corresponding shaping the face base wave in space that is again extraction, can you
10:05:55 number here is this kind of stuff so confusion here is not that clear because you see the regular cases where you see the signatures you flattening out the experts, others where you find the experts. So it's, it may actually be doing to the dependence
10:05:58 on the bottom the local parameters.
10:06:01 So, let me arrive to the conclusions.
10:06:07 Essentially, here, what we get is, is very simple model here, so steady mother for staircases, which consists of a dictionary of zoom or Helios plus wave packets and there are solutions provided the human can for wave typing and provider so that is diffusion
10:06:31 in the wave number space and excitation.
10:06:32 And once you have good that you did you do get some prediction for for the period and.
10:06:41 So of course there are many many many draw or witnesses, if I may say so.
10:06:46 First thing that I stopped saying that we want to predict.
10:06:51 Step Tater I think that'd be like a natural creation there was nothing like that. What I showed, of course, because for this, I would need to construct equation, right.
10:07:01 No, it's not very difficult to write a transport equation over the temperature. Since the diffusion equation is actually proportional to the wave action.
10:07:16 Okay, so any modification of the wave action and particular local decrease, which actually leads to decrease of the DVD and an increase of temperature, but this is still speculative.
10:07:23 Then as a point is is wave cropping up it. I mean, it is actually turns out they are experiencing experiments sorry and photonics, which are able to know whether you're aware of this or not that, which I bought to simulate actually the boatman equation
10:07:39 was a realistic way.
10:07:57 And where we're talking was actually was was demonstrated still here. The question is whether there is enough room in between, you know, within the shell as for for with buckets to develops. It has to be bigger than several times the with bucket extent.
10:08:02 another poem is, of course, we like to prizes to total mystery and there is there is in fact the five be genetic simulation so of course there is a big jump in between the ASIC our equation which is a single mother and in this type of further the whole
10:08:22 food form to complete problem.
10:08:23 The complete problem. It turns out, it is possible to do that using essentially to scare and ISIS, so they've been recent work on this. So it doesn't seem to be real objections.
10:08:35 Now that the main partner here of course as you have certainly noticed that there is no dynamics, as it has just said before we are looking for a fixed point here is a steady solution of the of the equations.
10:08:46 So there is no prediction here on the city meandering magic. Okay.
10:08:51 And there is, it's rather easy to extend the model to drifting.
10:08:56 Some of those doesn't change much to conclusions.
10:09:00 But, but there is nothing here about for instance analogy.
10:09:04 Now of course, the link, the one of the question for us infusion is whether by information which is actually something in terms of confinement. Impressive, big jump in the temperature, could be found by the condensation of shearling Yes, it was a staircase
10:09:21 in fact in clear brainwaves can meet the formation of the principal barrier, and therefore, an increase of improvement of environment. So this is Tim to, to be guideline.
10:09:33 And that's what I wanted to show and second Thanks for your attention.
10:09:37 All right, thank you very much Debbie a very interesting questions, comments, return to the philosophy of science.
10:09:51 Very quiet. Well, all right, David and then, then I'm going to get an A in a inning in and then Brian So go ahead, David,
10:10:03 Zambia in the plasma game avalanches seem to be at the heart of it.
10:10:10 And you start off with equations which looked like fluid equations. I mean, it in the, in the fluids.
10:10:19 When people discuss these gaps and things in the fluids literature whatever avalanches and not really mentioned, so much.
10:10:28 And yet, your equations which are kind of fluid the
10:10:43 avalanche of seem to be crucial to this to the cross species and the confinement and everything is they're trying to say is it should they be avalanches in the fluids game, or is it something that you going beyond fluids that will make avalanches in your
10:10:48 system, but not in the fluids that the, like, the equations that David was looking at for example.
10:10:56 Yeah. Well, certainly the avalanches in, let's say plasma food simulations actually I did them was probably one of the first to get them to do that. So you do see you do see avalanches for showing Miss grid simulations provided the.
10:11:16 Well, at least in the case i'm talking about provide you're dealing with touched by medium, in the sense that this I didn't say anything about it but there are so called Western on surfaces.
10:11:29 Natural talking about plasmas. And this is a place more in the, in addition, the food simulations so I don't think that
10:11:39 I don't think that try to answer your question, I don't think that
10:11:46 tweet tweet that's just kinetic if it is your question, it is a problem and I'm pretty sure that when it does the job.
10:11:53 Now, now.
10:11:56 On the maybe another part of your question, the way I understand is, is, is avalanches essential for the status formation rails. Obviously it is not in GFD or what I can see here, this is a debate in between us.
10:12:12 We're not sure that was a yes or no. At an anxious and necessary or a mandatory.
10:12:21 In the process of staircase formation and I'm not sure that that can be but in this model.
10:12:27 They do play a very important one, as well so part of this stuff is for measuring process I say at least the way the one I showed is essentially due to the formation of a boundary layer at the vicinity of the island I showed, which is essentially an interaction
10:12:49 between avalanches that is passing waves and pathways.
10:12:51 Okay, thank you. Alright, so I think I'm next. Let me, let me play devil's advocate a little bit, which is.
10:13:02 Wouldn't it be sufficient to get a staircase, or would it be I to simply to go back to our old way of kinetic models that you mentioned and simply include some feedback on the free energy source.
10:13:21 In other words, and where those were done with treating growth as as a parameter right and if of course the growth is a function of the gradient the gradient is driven by the flux, and the transport process etc so if you bring the feedback.
10:13:41 You could have, you know, little regions of sharpening of the gradients while where the transport is lower.
10:13:56 I know that works for the single barrier right we're back to the S curve and you know Hinton Oh, one more time. So in some sense you don't I would argue, you don't absolutely need any fancy stuff in wave kinetics, to capture the staircase, how would you
10:14:07 react to that. No actually is going to be the next step. Then as well. So, the idea is exactly this one that is the goal space would be something proportional to temperature gradient.
10:14:20 See, that's what I had in mind. And then there will be another equation that would be a transport equation, right, and diffusion would be essentially x wave actions times temperature brilliant.
10:14:31 I mean, I mean, in a sense when you do that, I mean I'll make another shameful advertising to build on GM, your bat you're going to head towards something like the models have a short on and I.
10:14:44 Yeah, I mean that's exactly what we did.
10:14:47 Absolutely. But there is one difference I think you would agree with this but it's so far, the question is was a mystery to introduce by stability as you need is where we didn't, we didn't.
10:15:00 I think if you put it this way you put the feedback you'll get by stability, because the feedback that the feedback is going to give you a region of high transport and low transport or in plasma speak turbulent and neoclassical once you come to that that's
10:15:17 by stability.
10:15:21 Okay.
10:15:21 Yeah. All right, Brian
10:15:26 case of a bear clinic turbulence in the middle attitude atmospheres is very analogous in fact Charney, I guess, was had played a role in both those with his work with von Neumann.
10:15:42 That was his thesis and Princeton, was to calculate the Barrett clinic turbulence of the middle attitude atmosphere
10:15:52 in the usual models it's it's a homogeneous thought to be homogeneous. It is the equation is homogeneous in the pole to equator, in a simple tangent plane model.
10:16:04 So everybody thought you could do homogeneous turbulence just look for flex gradient relationships.
10:16:10 But in fact, when you do the quasi linear analysis of this homogeneous turbulence, you find that in the homogeneous direction, there's a spontaneous symmetry breaking in which the turbulence breaks up into individual jets, each of which is itself stable.
10:16:37 That is stable as as a jet interacting with the turbulence.
10:16:42 And they, they partition up the total temperature gradient, among them. So, in a given size of channel, you may have six jets spontaneous symmetry breaking into six jets, each with one sixth of the temperature gradient inside it.
10:16:52 Those are very clinic equations, fixed point nonlinear solutions.
10:17:19 Okay, what is your question now.
10:17:09 The, the issue is that, because these are almost the same equations. The only difference. One of them is, is the cross be, and the other is v cross omega, the same equation, essentially the same equation.
10:17:27 So, I'm saying, because this problem has been solved.
10:17:30 In the case of the bear clinic turbulence to the middle attitude chat which separates the equatorial hot region from the polar code region.
10:17:40 I mean, it's the same problem. So we know the solution to that problem. Shouldn't.
10:17:46 Shouldn't that give some.
10:17:56 At least insight into how. Yeah.
10:17:53 That's my point. You sent me the paper so we'd be happy to give a look in and better sure that many problems. It's so I agree with you it's awesome you know that, but to show that some of these problems have been solved in the GMZ community.
10:18:10 That's for sure.
10:18:12 So just send me the vapors.
10:18:16 Okay.
10:18:20 The clock is running and Steve is waiting let's give Greg Collier the last question here.
10:18:29 I read your mute.
10:18:32 Sorry, I didn't understand the end, you said you could have obtained the staircase, which or I guess the zone wave number from your theory was that I mean obviously thats related to the drive, is it, you just putting that into the drive or is it somehow
10:18:50 process through the theory and is it can come out with a wider range than that.
10:19:05 Is your question what is it depends. So, have the ability, the city on the broadcast or on the walls right. Yes, I think so.
10:19:08 Yes, I think so, I Well, I think you said that you could get a staircase with from the distance
10:19:26 is essentially goes like this
10:19:25 in depth.
10:19:27 So yes, of course the
10:19:33 pants in the growth rate of the instabilities.
10:19:43 But we didn't going to cross check against. We didn't compare the result of this model with the numerical simulations, if this, the question.
10:19:55 Alright so let's thanks MBA again for a stimulating talk. And
10:20:02 I think we're doing pretty well on active discussion. So, last but not by no means least for the morning we have Steve Tobias, and Steve has not been introduced but I think everyone in this crowd knows him he seems to be in charge of everything between
10:20:23 proper I sock and the, the Friday morning JFN seminars and various other things and he got his PhD from Cambridge and is now professor at Leeds and worked on a wide variety of things.
10:20:40 So go ahead, Steve, thank you. Thanks for the introduction. Can you see my cursor, just so I can check, because I couldn't see that as when he was doing it.
10:20:51 Yeah. Okay, thanks. And so Pat asked me to talk about quasi linear and what you can do to fix up cause a linear theories.
10:21:01 So, Pat knows an awful lot more about this than I do so I suspect he's trying to set me up for something here, but let me, let me carry on.
10:21:09 So I am going to say something about transport barriers perhaps right at the end.
10:21:15 Okay, and I didn't want it.
10:21:21 Okay. So, first of all, I'll explain what is a quasi linear theory, I'll get to that in a minute but one of the questions I think we want to ask you is, when do cause a linear theories, work for turbulence now Brian Pharrell introduced, because the linear
10:21:30 theories by saying, and I agree with them completely here that there's homogeneous isotopic turbulence, that the questions that people are trying to ask, but homogeneous isotopic turbulence are probably completely different to the kind of questions we're
10:21:44 trying to ask in Geophysical Fluid Dynamics, or in plasma turbulence.
10:21:50 They're all interested in the interactions that lead to the cascade and the intermittency so these are fundamentally nonlinear processes which presumably can't be described in any way because a linear theory.
10:22:01 However, if you have something that's dominated by means, be they mean flows or me magnetic fields, or perhaps means stratification we don't quite know, then perhaps a quasi linear theory will help us understand what is going on.
10:22:17 And I think the answer is yes it can really help us understand what's going on.
10:22:20 But the question then is, if it doesn't help you understand what's going on, what can you do about it and path alluded to this a bit, a bit earlier.
10:22:28 So let me just say what is, what do I mean by a quasi linear theory, so I'll start off with, with a set of equations so here Q is a is a state but a vector of state variables.
10:22:43 It can contain all your velocities magnetic fields whatever you're interested in.
10:22:44 And if I was due to a linear part, which is kind of boring, and a nonlinear part.
10:22:49 So going back all the way to Bruce an escort Reynolds you can split up your, your state back turn into a meme, which I'm going to think of as a spatial me, but you don't have to.
10:23:00 You can think of it as an ensemble me, or a temporal mean fluctuation about that mean. And then of course you all turn the handle you derive an equation for the evolution of the mean for the body to Cuba evolves due to a linear bit, and then there's a
10:23:15 mean mean interaction.
10:23:17 And then of course there's a, there's some Fluxus which come in, which is the fluctuation fluctuation interactions. The average of those. Okay.
10:23:26 And the question is what are these fluxes that contribute to the evolution of the meat.
10:23:32 So in order to get that answer. You have to work out the evolution equation for the perturbations. So the perturbation equations, the perturbation evolves, according to a linear piece.
10:23:46 And then of course there are interactions of means with fluctuations and fluctuations with means. And then there's this term here, which is the, essentially, the fluctuation fluctuation going to a fluctuation interaction.
10:24:01 And depending on your community can be called different things is sometimes called the Eddie, Eddie non linearity main field electrodynamics This is sometimes called the pain in the neck term.
10:24:13 There's some debate about who first called it the pain in the neck term.
10:24:17 And so the question then is, it's very hard to make progress on the evolution equation for Q prime, if you keep all the non linearity.
10:24:27 so it's nice to make progress by essentially ignoring that term or saying so dominant.
10:24:34 So the question then is, when can you say that term is sub dominant to the others and it's a subtle point clearly. If these terms are small, but they just they just happen to be smaller than the other terms, you can neglect them and there are certain
10:24:48 cases where that is true. So for example if you're dominated by the sheer or dominated by the means. Then, then those terms will presumably be smaller, but it could be subtle because what you're interested in, is the contribution of this term to Q prime
10:25:03 Q prime he's going to look at the evil is going to contribute to the evolution of the main through some kind of fluctuation fluctuation going to mean interaction.
10:25:15 And that is going to depend on correlations in key prime and correlations in Q prime might depend on the phase two phase information that's coming from this term.
10:25:29 So there may be some situations where this term is not actually formally small but it doesn't contribute very much because somehow the phases of got scrambled, and somehow it just doesn't contribute.
10:25:40 And so it's very interesting to see when does this term contributes a lot, or when does it contribute very lucky one, and this talk is is really just to say, Are there situations where it works in situations where it doesn't.
10:25:54 So just to say. Sometimes these are, these interactions are looked at in terms of these interaction diagrams. So what we're doing here is we're keeping interactions of means with fluctuations to give you fluctuations.
10:26:08 We're keeping interactions of fluctuations with fluctuations to give you means, and you're throwing away the cascade you're throwing away fluctuation with fluctuation to give you fluctuations.
10:26:18 So, in particular, as I said, Don't use this for homogeneous isotopic turbulence because everything that is in the cascade or in the inverse cascade.
10:26:26 And there's a long history of course the linear approximations. I'm very interested in, if people can find earlier papers than these ones I'd be very interested to find out because there's some debate about.
10:26:37 He was the first person to write down, of course your linear approximation.
10:26:56 in time domains as well.
10:26:59 In fact for.
10:27:01 I think it's for some kind of double diffuse of convection problem. Okay.
10:27:06 Okay, so when might the quasi linear approximation, be correct well we know it's absolutely correct. In certain Asim toxic limits, and I'll come back to those in a minute if you have a separation of timescales you can rigorously developed derive cause
10:27:30 linear equations via an authentic procedure and Greg cine did this earlier on in the conference. What's nice about the quality linear approximation is that because you're taking out interactions in pairs.
10:27:38 You can serve global linear and quadratic variants you don't conserve anything materially so you know David he was very interested in moving things around and conserving PV materially, but you do conserve global linear and contrast variants, and as I've
10:28:02 said there's no local cascade or inverse cascade. If you want to do a statistical formulation of across the linear theory then, as Brian said you get statistical state dynamics, or something that's sometimes called CE to the Keeneland expansion second
10:28:18 order. Now then, part kind of teed me up for this because he said it's all down to the Kibo number, whether it works or not. So I think that's right i think the effectiveness of this approximation is often measured by the Cuban number.
10:28:33 And you can think of this as a.
10:28:37 If you like a degree of separation of timescales.
10:28:40 So if you have a turbulent flow, without with the velocity you, you can work out the rms velocity, you are an S. And then you have a correlation time and a correlation so I'm thinking about this is a ratio of either velocities, or, or timescales if you
10:28:59 like. And if this number are really small the Qubo number is small, then you can throw away those higher order terms they don't project back onto the me.
10:29:15 Of course, this is, this is, perhaps not very useful because you know if you're doing an instability problem or a turbulence problem. You don't know a priore, whether what you don't know if I tell you what, you are a message is going to be be what the
10:29:22 AUYURMS is going to be be what the correlation time of the turbulence he's going to be, and see what the correlation length of the ticket and he's going to be.
10:29:35 So that's not really a massively useful number, but you can, of course, there are some cases where, you know, a priore that the Kibo number is going to be small.
10:29:37 So if this approximation works. It's a nice approximation, you can make predictions, you can go to fixed points or whatever, because the main adjust only down to perturbation perturbation interactions and the perturbations only respond to the me.
10:29:54 So this, as I said this there is a statistical format formulation about this, but this can be shown this statistical formulation can be shown to break down as you move away from statistical equilibrium so actually make the Qubo number bigger then you
10:30:09 can't guarantee that that statistical formulation is is going to work. So in the case that has been discussed a lot this in this conference, the case of the formation of zonal jets, the equivalent of the Qubo number which you can get a priori is called
10:30:28 the US and Australia parameter is the measure of how much energy, you're injecting into the system. If there's a landscape associated with that. And then there's a landscape associated with the Rhine scale, the ratio of those two is, is called them so
10:30:45 in Australia parameter and if there's an apostrophe parameter is very large, and then quasi linear theory works very well and that's what David ritual called the weekly force the very weekly sorry the very weekly forced very weekly dissipated system.
10:31:01 And so you can think about there's an Australian parameter, as a measure of the Qubo number that you can import API or i. So, what I'm doing here in this numerical experiment is changing these in Australia parameter the turbulence and I'm comparing a
10:31:15 a quasi linear theory, with the full direct numerical simulation. And for large than Austria parameters which you see here, the two agree very very well indeed.
10:31:26 Now as you move away, so this is more like turbulence in the ocean so if you like rather than turbulence in Jupiter.
10:31:32 quite a lot of the dynamics that you would like to capture.
10:31:47 Okay.
10:31:47 So just a very short. Slide saying, well, when is the Cuban number guaranteed to be small, a priore and.
10:31:56 Well, sometimes you have an acid and toxic separation of timescales, and so Friday boo Shane is collaborators they did an analysis of the, of the stochastic Lee driven jets on a beater plane.
10:32:13 They assumed a separation of timescales, and they derived that not surprisingly across the linear theory, see to exactly when you have the separation of time scales.
10:32:19 And of course you can get quasi linear sets of equations and Edgar talks about some examples of these kinds of acting toxic separation of timescales, which sometimes lead to quasi linear equations.
10:32:36 Okay.
10:32:37 Also, I guess you could just designate or you might know that your turbulence correlates on a fast timescale compared with evolution of the means if you know that's true, then perhaps you can use a quasi linear theory.
10:32:54 And so this is competition between if you like D correlation and sustained interaction, leading to the driving of interactions with the means that I think is important to capture.
10:33:05 If you go away from quality linearity.
10:33:07 And I think phase information is going to be key is going to be key in driving correlations, but it's also going to be key. If you have lots of phase to know how the turbulence is making you lose face.
10:33:21 Okay, so let me just talk about one way in which we've generalize the quasi linear approximation to perhaps make it slightly better.
10:33:31 And this is just to think about your interpretation of a mean and expand it so this is our expanding our understanding of a means to be large spatial scales, so we're splitting the, the flow into large spatial scales and small spatial scales.
10:33:49 And we're thinking about these things in the in the spectral domain. So Laura cope gave a very nice talk last week, maybe the week before about using GQL for a problem.
10:34:01 The problem of jets, on the beta plane and she showed that you could explain the, the translation of the Jets if you if you use the generalized cause a linear approximation rather than the closet linear approximation.
10:34:14 So what we're doing here is, if you think about the interaction diagrams we had before. We're keeping certain interactions we're keeping a large scale with a large scale go into a large scale and by large scale, I mean, all the way you've numbers are
10:34:33 than a certain all his own or wave numbers, smaller than a certain cutoff. We're keeping a large low interacting with high to give you a high.
10:34:40 And we're keeping high interacting with high to give you a low.
10:34:43 And we're not keeping any of the other interactions, and we're not keeping those, essentially, well we're not keeping this one, the high high going too high, to make sure that the evolution equation is linear in the high modes, and we're not keeping these
10:34:59 other sets to make sure that what we're doing is a triad decimation in pairs, so we can, we can keep the conservation laws that we had before.
10:35:09 Now what is key, or what I think is key as to why this approximation does better than a straightforward quasi linear approximation is that energy. If I think about it here can be scattered into sorry that should say hi into high
10:35:28 into high modes by interactions of short with long so let me explain here. So if this is a form or mean, then an M equals 10 mode can only interact with a formal need to give me another m equals 10 mode.
10:35:45 However, if I expand my, my definition of the large scales to be say m equals zero, and m equals one. Then of course, m equals 10 can interact with M equals one.
10:35:57 To give you an M equals 11.
10:36:00 And m equals 11 can interact with M equals one to give me an M equals 12. And all those interactions are allowed.
10:36:06 Now, this allows some form of non local cascade, and that increases the irreversibility of the system, because you can send energy down, and the irreversibility is increased.
10:36:21 So I think that is that is kind of an interesting feature of the generalized was a linear approximation.
10:36:30 So I'm just going to say how well i'm going to give just give one example as to how well this does on a system which does form.
10:36:38 Transport barriers.
10:36:40 And this is a very very simple model and I'm not going to derive it for the generation of jets internally via convection in the planet.
10:36:48 And it's this very simple Buster Angeles it's been looked at by many many offers.
10:36:53 And so what happens is, in this case the beater effect. This is the interaction of convection with rotation, and the sloping animals. You have a beetle effect because the end walls slope.
10:37:06 Okay.
10:37:07 It's two dimensional because it's rapidly rotating, which is quite nice.
10:37:12 And so what happens is convection plus the beach or effect drives his own or share.
10:37:17 And the zonal share will then inhibit the convection.
10:37:20 So these are the equations that you have.
10:37:23 So this is the shortest city. So this is the Baltic city equation so everybody should recognize the terms on the left hand side, we have a thermal driving from the temperature, and then you have some descriptive terms.
10:37:36 And then the temperature is affected around, and also dissipates. So this is a nice couple system, where as I say the temperature gradient drives a flow, the flow interacts with the rotation and the beach effect could drive shares.
10:37:52 And then the shares may up back on the temperature and form of transport barrier.
10:37:56 So there's been lots of work on this, and there's lots of people who, in the audience I think we know about the, the kind of dynamics, you can get I'm just going to talk about one type of dynamics, because this was mentioned in in Lofa Schmitz talk.
10:38:13 And this is predator prey type dynamic so I'll just, I'll play the movie so what you're seeing here is the, the zonal flow.
10:38:20 You're seeing the volatility and you're seeing the temperature field. And what we're going to see here is that we get convection convection drives jets, in this case, it wants to drive three jets that the parameters have just been chosen such that initially
10:38:36 thinks he wants to drive three jets, we're about here in the evolution.
10:38:40 Those three jets actually go and stable to to jet solution. And that to jet solution bursts.
10:38:48 So, I'm not gonna be able to stop this at the right time. So here I've stopped it and here we have a moderately week share, and we have turbulence going on.
10:38:57 Okay.
10:38:59 And, and then
10:39:02 yeah here we go so I've managed to stop a case where there's a strong sheer. The sheer is acted as a transport barrier.
10:39:09 And the heat transport has been blocked, and we have this predator prey system here where we have the thermal gradient, leading to the convection, the turbulence through the beach with at least have a share, to share puts up a transport barrier.
10:39:23 And so switches off the convection, and then the whole process repeats.
10:39:28 Okay, so I'll just finish by saying this process you might expect is very badly described by across a linear theory. Okay, so I'm just showing you now.
10:39:40 This is what happens if you keep this is DNS if you keep all the modes, you do a direct numerical simulation. you get bursting behaviors. This is a half mala plot, showing the mean.
10:39:51 Share against.
10:39:55 Why, and time and you can just about see the births. Here, whoops, sorry, sorry for a quasi linear theory without, without only has my dog commenting on my talk, and we have for the quarterly new theory we not only don't have the bursting but we don't
10:40:11 have the right number of jets.
10:40:15 the right number of jets.
10:40:25 If we set the threshold for the quasi linear, the generalized quality linear approximation of one which is where Laura set her thing to work. It still doesn't quite work.
10:40:25 So by the time we set our threshold to be five we can reproduce the birthday.
10:40:30 So there's something interesting going on here. And that, allowing the, the expansion of your definition of a mean, really helps.
10:40:40 Just to say why, why are we doing this well.
10:40:44 What we would like to do, and what we have done is derive a statistical closure of the generalized causal linear approximation, which I won't go into here again we split everything up into low plus high mode and derive an evolution equation for the essentially
10:41:01 the two point correlation of the high modes and put it back in.
10:41:05 And this works very well and my postdoc, giving University is just finishing a paper on that if anybody's interested.
10:41:12 So I'll finish by putting up some questions for discussion.
10:41:18 Well okay so the quasi linear approximation really can be valid in certain cases. And it's it's valid in cases where the projection of that term that you've thrown away on to the second key million along to the two point correlation function, so it's
10:41:33 like the triple correlations onto the onto the pairwise correlations is small. Okay. But when is this, I don't know, is the answer to the question.
10:41:42 So qL is a minimal model. But what should be added. Well, if you're doing this statistical theory you could add the next term in the expansion.
10:41:51 And so you, this would be an isotopic in a homogeneous form of Ed q amp M, which has been looked at.
10:41:59 You could perhaps use better interaction rules, which is what I tried to explain, using GQL. Perhaps you could use different averages, I don't, I don't know how much well ensemble averages have been explored but it might be worth exploring it.
10:42:14 You could put in models of irreversibility so Pat alluded to that and David, Rachel, saying, you know, minimal model might be qL plus wave breaking or it might be qL plus wave trapping as Abby said, I don't know in certain situations.
10:42:29 how might you know, a priore what is the best thing to add to your qL, and perhaps you might want to put in some kind of model of phase the coherence or some something which makes you irreversible.
10:42:40 And even even even even more basic question is, can we get a, an accurate description of quantifying, how far we are from this local phone number limit.
10:43:06 fact, but can we get some kind of intuition, as to when we're going to be in the local bernama. So these are all things, I think we should be hoping to think about.
10:43:09 So I'll leave it there.
10:43:11 All right, thank you very much, Steve. For a stimulating talk and I'm sure this will stimulate some discussion.
10:43:19 So questions.
10:43:23 All right, let's see Adrian and Zach VA, and then I'll get in line and then again.
10:43:33 Sorry. Yeah.
10:43:33 Thanks, Steve, that was great talk really interesting.
10:43:35 I wondering about systems where you have, you know, multiple fields, contributing to the evolution of the mean, you know, like a maximum stress in addition to a rental stress.
10:43:48 Does it make sense to think about
10:43:51 you having a different parameter for the large scales versus small scales for one field versus the other or do you really have to be sort of consistent in how you order things between the two fields.
10:44:01 This is the question makes sense.
10:44:08 You're muted. I muted myself I don't quite know when I did that. Okay. Yeah, it does make sense and it's a very nice question, I think, I think the answer is too, unless you have any API reason for knowing that one of the contributions is smaller than
10:44:21 the other, then I would treat them on a, on a, on an equal footing so you might be saying the low RMB turbulence where you know the Maxwell stresses are going to be small or something, in which case you can you can perhaps treat them on different footings
10:44:35 but I think, you know, if you don't have any reason for the thinking that I would just treat them.
10:44:40 Treat them the same if they're both contribution to the flocks.
10:44:45 So we did have a look at quasi linear models or statistical models of, say, breaking of of jet formation by saying magnetic fields so Maxwell stresses.
10:45:00 You know opposing the rentals dresses but actually Pat and pat students have looked at.
10:45:04 It's more sophisticated than you might think because magnetic fields can actually mess up the phases as well.
10:45:13 Totally, a shameless advertising. Samantha will give a talk in the plasma applications group on Thursday on that. So, excellent. There you go.
10:45:24 All right, Xavi a next one Hi Steve.
10:45:30 You mentioned in the example you gave you mentioned that fallen cat Of course one student get the right diet and expect for five years. Okay. Is there a way in advance for a given system to new to know what would be the right cut off number.
10:45:47 Now I wish there was, I mean usually actually bizarrely one is enough. Because that allows scattering of of energy off into other high modes. And I think this this dynamics is so complicated with the predator prey and bursting situation that somehow it
10:46:08 just even that's not enough to kick you into that. I mean bursting is quite a funny thing because you've got these two.
10:46:16 If you like attractors, and you're kind of bursting between the two. Right, so you spend some time near one and then you, you get kicked out and go towards the other.
10:46:24 So I think that maybe just, I mean that's that's a system that's very far away from equilibrium. So it doesn't really surprise me. But the, to answer your question is, I don't know if any theory that allows you to do that.
10:46:38 All right, I had sort of two, two comments but they're related.
10:46:45 This business is of course a classic example of the old saying Do as I say, not as I do. Okay. And one is what in your maybe there is no unique answer but what is your view of the best fix up to quasi linear theory I mean in wave kinetics.
10:47:07 It's of course something like a breaking model which is used in ocean waves that's where we got the idea from at least on you know my end. Okay. But do you have other candidates there.
10:47:20 The other thing is somewhat related I mean, where I think this discussion goes, is the theory works for low Qubo number but in fact Qubo is around one for just about anything that's practice.
10:47:37 So we're always sort of dancing around describing Qubo equal one by pushing from below, you know, making some arguments over the replace the thing with the RMS thing and everybody's happy, but it might be useful to push from above, which of course there's
10:47:59 a lot less, you know, things to play with in the, in the large Qubo regime and I'm wondering, do you know or could you comment on sort of to push from above and below to come to the one regime.
10:48:14 Okay, I know why people, I mean obviously pushing from below is very attractive right because here you have it was easier but also I mean you could imagine you do an awesome toxic expansion, you get a quasi linear system say, then I could imagine well
10:48:28 what happens if you keep the next terms in your Asim toxic expansion, just I don't know maybe do a telescoping or, or just cheat and put them in there so that is no longer quite a linear, certainly in some adding toxic limit that might be the thing to
10:48:43 do. That's the next term which comes in in the US in toxic expansion so that might be the next term to try pushing from above.
10:48:50 It's like where do we start.
10:48:53 I guess that's that's that's the question isn't it. I mean, well we need it you need a model right that you can wrap your hands around and it's not so easy.
10:49:02 So, yeah, Yeah, I think, I think that's right.
10:49:06 And what you're saying, as to which is the best thing to add, I mean, you know, if you have a system like the one David described earlier where you know PV is concerned.
10:49:16 And so then you think well what's the next thing I can put in that, you know, stops PvP conserved and wave breaking is an obvious thing to put in, then that's the way to go.
10:49:26 It's clear that that's the next thing to put in if you just have a general general turbulent system where you don't have these materially conserved quantities.
10:49:36 It's not clear to me what is the best thing to put in, sometimes it might be phase, phase mixing or, I don't quite know.
10:49:43 So, all right thank you, GM is next.
10:49:48 You describe that you you need a separation of skills between well short and large timescales short and long way.
10:49:59 Length skills. It's more of a curiosity I found interesting you as an ostrich parameter. So I was wondering, do you have a general way to understand, making connection between, there's an apostrophe parameter and your Rossby defamation rages.
10:50:15 The question being when you go towards weaker call this false. How would your questionnaire approximations, well, why it depends how you're doing, how you're going to that limit because there's a few parameters.
10:50:36 Okay, I'm not sure who parameter. It really, it's really to do with how strongly forced and dumped you are, and is the ratio is essentially of the, of the forcing, you'd be like, and how much energy you're injecting into the system, from which you can
10:50:53 get a London scale to the Rhine scale so if you're changing the Rhine scale, but keeping the other lens scale.
10:51:08 The same, then you can go to a low or high in Austria Futurama parameter limit. But if you're changing the two together, then you know you might be keeping us and Austral fit parameter fixed.
10:51:14 So it's, you know, there's this this. Yeah. You can change the last few parameter by changing one of those things. That's true.
10:51:24 If you hold the other one fixed.
10:51:31 Okay, yeah okay but the point is you're changing booth if you do.
10:51:32 Well it's okay no I guess I'm, I better understand my own question and maybe it's best left for the general discussion because I think it connects more to with
10:51:48 to a point that digital, was it was made, maybe a small large Rosemead information number two question, though yeah so David's got his hand up he can answer your question I'll go in, will give David time Don't worry.
10:52:06 Okay. Brian's next then Dave, David will be the lead the last word for this discussion and then we'll have all of about three minutes for the general but go ahead Brian, and the usual case of closing second order, you're allowed a parameter ization for
10:52:25 the third cumulus. It doesn't make the, it doesn't break the quasi linear it's still quite linear. So, what you do is you go and you look at the third cumulus calculated in a direct numerical simulation you find its Qubo number, you find the you RMS you
10:52:41 find the Tao see.
10:52:43 And then you synthesize a random a random forcing it has that same structure that doesn't change the quasi linearity.
10:52:56 No, I agree 100% you can do that but there are cases where whatever you calculate from a DNS got third key Merlin, but you've calculated will overwhelm the other interactions you've put in.
10:53:09 I'm not saying there aren't there aren't K through cases where it doesn't, but there are cases where it does.
10:53:15 For example, if you did homogeneous isotopic turbulence. That's all you would have.
10:53:24 Yes that's right i mean i that's why I argued for that, of course, but I'm simply saying that, that this coupon number can be synthesized with noise, without to make a closure.
10:53:40 That I has, you can you can even make the right color of the noise. Yeah, I think something very subtle, you're talking about having the nonlinear turn actually be adaptive.
10:53:49 It's not just it's not it's Qubo number of things you're talking about, you're talking about, adaptive feedback. I think that's exactly right and of course you I'm sure you know there are people who look at what color noise should you feed into the linear
10:54:02 operators the best reproduce, you know you have an average, you know these people they look at that. Yes, it has to mean so that that's my point it's a subtle, it's subtle What is this thing that you're feeding in as part says the minimal thing that you
10:54:17 have to add to, to, to get your theory to work and you know if you're starting to have to add call of noise, then it may be that you might want to start thinking about what is the physics behind the Illinois by agree with you, you can certainly do that
10:54:32 and I think that's a very interesting way to go.
10:54:36 Still fuzzy linear.
10:54:38 All right, let's. Okay.
10:54:41 Let's we were really the clock is running ladies and gentlemen that, let's get David Rachel who's been waiting patiently a while, a chance.
10:54:52 The words spoken ways you must radio keep this short.
10:55:12 But I think the case where the Rosebud information length is smaller than the other skills and the system for instance, particularly Ryan's length or the mouth rebellious like that, based on energy injection rate.
10:55:15 This is a much different, much more different system than the typical ones that people know well, where you have one new these zonal jets dominant in a flow.
10:55:28 So, the, you get much more meandering more time dependent motion, there are the interest space before the season and in fact as LD becomes much smaller than all these other links, the idea of a zonal jet breaks down and the flow becomes dominated by closed
10:55:45 bring jets, which are not so dissimilar from what you find the gold stream at ease, etc. in the ocean.
10:55:52 So that's an interesting limit, which isn't, I don't want to claim that Jupiter's is shallow water but Jupiter has a small defamation name, at least be think of the order 140 eighth of the planetary radius.
10:56:06 So, one would expect some significant nonsense ality in the jets and if you look carefully you can see anything you like you can believe that throws Street, or you can actually start believing that there's considerable wiggles and these jets, but that's
10:56:22 a different problem. I'm just saying that the small defamation length case could be hard to analyze and the quasi linear approximation just because it's seems to be forever time dependent with large amplitude excursions of jets merges of merging with
10:56:38 vortices etc. It's more like it's starting to Murray come close again to this homogeneous turbulent limit Toby's limits which is difficult to analyze.
10:56:50 Absolutely.
10:56:52 I can talk to that, I agree.
10:56:58 So let's thank Steve and all the speakers for the morning and we have three whole minutes left for general matters.
10:57:11 A few comments.
10:57:13 Next week, the topic is it's rather related I mean it's mechanisms rather than formation that's a fine distinction.
10:57:24 And just, just to know we have something lined up, we'll hear from wasting glow on a freshman and Yannick Sarah isn't there. Many of the points actually that came up in the discussion today.
10:57:42 So you can look forward to that and let me advertise the plasma applications group on Thursday and force we don't have to. We don't have to advertise David Hughes group tomorrow it's the sort of the centerpiece of things.
10:57:59 So curious.
10:58:04 Anyone have any you know we have to home and it's now, any thoughts and things they want to hear right i mean i have i've given the you know the way these things go I have a plan but no pun intended, there, there is some slack in the plan, even though
10:58:21 there's no plan in the slack. And so just curious on any quick general thoughts.
10:58:31 I'm counting on dm who you know this here so and and anyone else.
10:58:38 Well, since you're hitting on me to to to thoughts then.
10:58:43 One thing that I found interesting that except for Steve we did not hear at all.
10:58:51 The word cascade. So nothing seems to be really requiring a cascade view of things, so that's that's first comment, or at least the the appear as a side effect maybe or, in the end, but not the driving mechanism or the driving force.
10:59:12 The other one is.
10:59:15 Well, a lot has to do with the forcing and and dissipation and
10:59:25 I guess maybe that's a question more directly to I'm sorry to put you on the spot again to to the ritual.
10:59:33 But when you say that.
10:59:36 What's interesting is to be in the limit of Lou forcing and Lou dissipation Do you have a feel as to what which one is more important in the sense is it more important to be to have low forcing or to have new dissipation because if it's low forcing.
10:59:54 Then, there may be a significant difference for instance with with plasmas where we have a threshold in power and all the more you crank out the power.
11:00:05 The more you would get from which barriers to a stronger one.
11:00:10 And if you work try and get it to crank up the power and for instance, your systems for so little bit much.
11:00:17 This system and it would smear out all of that organization, then the staircases or the flows, or maybe quite different from what we would have as a barrier so it was wondering about that limits of forcing versus dissipation.
11:00:37 All right, David is back with the further comment. Okay, again, I'll keep it quick but you're right that it's critical that the dissipation is probably the weaker are the two that we typically look at situations where either the dissipation is proportional
11:00:55 to the forcing or the dissipation is zero, as much as we can arrange it. And in these cases we can get the sharp barriers or staircases for me in the other limit where the dissipation is stronger than the forcing you smear out these barriers and it's
11:01:12 much more diffuse, so it's a completely different problem than.
11:01:21 All right.
11:01:23 It's actually after 11 last call.
11:01:28 You're going once, twice, three times Thank you everyone it exceeded expectations, was very interesting and we'll have plenty we have three more sessions, we'll have plenty of time for general discussions and other things.
11:01:43 So at least for this group See you next week and thank you. Thanks, in particular to our speakers, and everyone for their participation quite lively.