09:03:40 Good morning. Good evening. Good afternoon, whatever everybody and welcome to the grand finale of wave of staircase 21, they all sound the same after a while.
09:03:55 And you're going to get short reports 15 minutes, maybe with five for discussion but I mean if if it takes a little longer it comes out of the five.
09:04:08 The five working groups and these will act, more or less, as a summary of what's going on here. So, for better for worse so in that spirit Off we go with the transport, we're at barrier Working Group summary.
09:04:28 Okay, so often running so the transport barrier working group was.
09:04:40 Things are.
09:04:40 Why can't I advance my slides
09:04:49 are actually activities, had we had four sessions, we're focusing on formation mechanisms symmetry breaking and momentum transport with contributions from the people listed here we had three contributions per session which fill the entire session and
09:05:08 run and ran over with a ton of questions so thanks to all participants for stimulated stimulating and spirited discussions. So, I'll talk about why we're doing this, then how barriers form and various levels models and scales methods which was sort of
09:05:31 the heart of it. That's the, you know, it's the center Institute for theoretical physics how you calculate things is is really the name of the game dynamics and then a little long time perspective which I thought was useful.
09:05:47 So in case you haven't figured out by now a barrier is a region in the system of a width that by necessarily has to be noticeable so large compared to some underlying correlation length of turbulence or waves were wave turbulence or transport is markedly
09:06:07 reduced.
09:06:08 It is usually accompanied by profile steepening.
09:06:12 And the fact that you speak of both barrier and base states suggest two states of normal and the barrier which smells by stability and you get from one to the other.
09:06:24 The transport bifurcation.
09:06:27 An example of a barrier is the steep gradient that forms in the edge it and Lh transition and a mat in a token Mac and for those of you like numbers that gives an increment in temperature over a scale of a centimeter have about a kilovolt in round numbers.
09:06:44 numbers. So that's quite a barrier when you think about it, and barriers are an essential very key element of layering right in other words they're, they're like the sheets of pasta in the lasagna that separate the layers of the good stuff right so it's
09:07:01 element barriers are usually associated with a rollover in the flux of something the order parameter or relevant quantity so the flux would roll over in the forum like this, which is indicative of a negative incremental the few 70 in some cases it could
09:07:20 be the rollover could priests age a jump to a higher branch, like we saw here.
09:07:27 And how does the rollover occur it occurs through feedback of of self, the self sharpened to order parameter on the flux in other words the D if you will in simple terms dropping is the gradient increases the classic form of this problem in this is called
09:07:46 zGs traffic or drift wave turbulence in the jet, and it leads down the road to the predator prey type of structure with multiple fixed points and transitions between, and I don't know why I'm having trouble advancing here, so how.
09:08:04 So, in discussions of fundamentals we had contributions from retro freshmen Sarazen and us mostly on jets ritual and then you know both his general talk and he and his contribution emphasized the, the critical nature of irreversible nonlinear Rossby wave
09:08:26 making breaking as the key to in homogeneous PV mixing that everyone chance like a mantra and this business, and bass shear is what induces the wave breaking and you can think of this by contour roll up because sharing is a kind of a universal mechanism
09:08:46 this leads to self sharpening and berries barrier formation and the feedback is wave breaking leads to bunching of constant PV contours which leads to sharper gradients then which may make breaking easier.
09:09:03 And we also associated that PV, we also learn that PV gradients are a natural consequence of expulsion as you know from the parental bachelor theorem and that's strong PV gradients can protect the system against sheer erosion, and this is the fabled mechanism
09:09:22 of Rossby wave of elasticity. In other words, it drives up the Rossby wave frequency. So in some sense the the rate at which you can nibble or diffuse away at the interface goes down the processes involved appear in both scale and space so there's more
09:09:41 going on than the inverse cascade This was shown by on a freshman you know you can write the angular momentum balance and energy balance of stirring to fluctuations to mean to dissipation of the flow, and the critical jump in the step in the fluctuations
09:10:01 is of course the Reynolds work of the fluctuations on the mean which you can relate to the angular momentum.
09:10:08 But in.
09:10:12 In addition to that there is a spatial flux of energy going on right where you look at the essentially the spatial the VP car later, the cubic which is in essence the spreading effect and the, the work done on the mean flow, you can drop the flux of fluctuation
09:10:32 energy in a quasi linear perspective which says then if you have rentals work. There must be a spatial flux of energy here so in other words it's a little bit interesting that, that it's not simply the inverse cascade that there's a flux and rent spatial
09:10:50 flux of energy that's concomitant with the rentals work, critical to flux is is of course it both intensity and cross phase, right so barriers can occur also at constant intensity by phase D correlation it fixed fluctuation level.
09:11:10 So this connects the story to the thriving industry of phase dynamics.
09:11:16 E cross be flow for example, can, can lead to read rentals forces that are consequence purely a phase curvature which trigger can initiate barriers and turbulence in turbulence with homogeneous intensity and this was observed in a device, a small plasma
09:11:38 device and was this the theory was discussed by Yannick Sarazen.
09:11:57 Another interesting topic, who was beta plane MHD in other words what happens to when you you bring instead of the usual jet problem enter the magnetic field so then you're coupling jets to the field and you have this, you have the momentum transport
09:12:03 problem and MHD the infamous or famous elbow which parameter are sub MVA in the mean field over the main square fluid energy emerges as the key parameter and, and the messages that magnetic field effects of course can have a big effect on the jet, then
09:12:25 this was shown by Tobias at all and Chen and diamond in the past. An interesting contribution from David Hughes was the observation that when the magnetic parental number exceeds the critical level for small scale Dynamo this being in 3d rentals stresses
09:12:45 tend to decode here and no large scale vortex forms. So the message was that some small scale Dynamo can suppress a larger scale jet, which was an interesting result in terms of models and scales right the poster child for this program surely was the
09:13:03 con Helier the equation, which reconciled negative diffusion regularization and the conserved order parameter. And it's, it was developed to describe face separation and this is a natural for layering.
09:13:20 Okay, if we were meeting in person I would have suggested we order con Hillier the equation t shirts for the program.
09:13:28 An interesting sort of alternative perspective as introduced by Edgar who pointed out the the similarity of binary fluid convection to double diffuse of convection and the key point in the, in the binary fluid, convection was the cross diffusion right,
09:13:47 the fact that that flux driven by the temperature gradient can affect the concentration and this is very similar to what we infusion referred to as an upgrade in pinch it's not a suppression effects.
09:14:03 And this cross diffusion. By the way, can arrive in some systems out of the nonlinear interactions. So, the gist of all this was a rich variety of dynamic patterns that exhibited face separation and the more general observation that the famous Swiss Hillenburg
09:14:21 model which is possibly applicable to double diffuse of convection even though it lacks double diffuse of effects and it does have the property that it's very emotional, and is by stable.
09:14:35 So that's a kind of an interesting alternative here.
09:14:40 The other and sort of general point was the critical nature of emerging scales the Rhines for the jet the asthma dogs are mixing and the Hinz for ch ns.
09:15:00 And, you know, they compliment the input scale for the two to mixing scales that go into the theory and I would point out, they also exhibit nonlinear gradient dependency so and if you're looking for the origin of the non linearity that gives the flow
09:15:11 of the rollover in those fluxes. They're a good candidate.
09:15:16 So how do we calculate something, and this was Tobias garb a glow gherkin and Hainan in.
09:15:25 Well, you know, everybody's favorite is quasi linear theory which is derivative from Velux of veteran of and segue day of and 61 second day of being the key author So, and you know it's a trick where you forget about the whole story of the cascade and
09:15:43 you look in the mean field by plugging in the linear linear or nearly linear response and the devil is in the details of the linear, the near the near linearity, the linear response or even the near linear requires small Qubo number by the way something
09:16:02 that's very difficult to predict it's an outcome not a control parameter and except for toy models.
09:16:09 This is achieved in the last off plasma by Hamiltonian chaos, basically appealing to the overlap of wave particle resonances there, the physics of the irreversibility is clear and it underpins resident diffusion, the Fokker plonk equation, the key question
09:16:25 in all of this, you should ask is, where does irreversibility come from.
09:16:33 In the jet problem absence a critical layer interaction with waves which we didn't hear much about the irreversibility is less clear, and the and the bottom line say in Steve story was the uniqueness takes up and Matt fix up is essentially related to
09:17:05 breaking which we heard about earlier so the a breaking model is required and then there's the question what is it and he you know he he addressed it by looking at classes of interactions. So Xavi a Gar Bay took a little bit of a different approach looking
09:17:10 at wave action density retreating as quasi particles, a kind of a, but like what using wave kinetics which treated the wave action density is a concerned face based density.
09:17:23 And this is exploits the long appreciated wave kinetic of last of duality.
09:17:30 It was used extensively for prior work on the drift wave Ross zonal flow system and the key point there of speaking of irreversibility is Ray chaos save the day.
09:18:01 So here it was a somewhat different tactic of looking at the staircase as a BG Hey solution. So in these kind of a stationary exact nonlinear solution exploiting the integrals of the motion as in BG Hey solutions have a glass of equation so is essentially
09:18:02 BG Hey solution of wave kinetics.
09:18:06 It requires ultimately chorus greening and this was buried in a little codicil that you need some kind of induced diffusion in case space, which makes the whole thing, written in a very reminiscent of the homogenous ation process right we all know that
09:18:23 for PV homogenization you need some kind of diffuse of like structure and you need that also, like in the Shapiro O'Neill problem for the large amplitude plasma wave, the critical issues or time evolution and mergers and interesting future direction might
09:18:44 be to bring out since we're basically doing riffs on the glass of equation. Bring out Linden bells ideas and look at the most probable BG k state as an interesting way to go.
09:18:58 There was a lot in this meeting on July, 4 Llewellyn Smith in young there which is a base stable mixing length model in the k epsilon style. This was also a quasi particle game and the inequality particles are slugs of intensity here it was applied to
09:19:16 drift wave problem by way to blow the two scales where the stirring scale and the Rhine scale, there's the at the emergent one and you have, we, she evolved density vortices it and potential and stuffy of the fluctuations.
09:19:35 There were two regimes of strong and weak mixing in this recovered staircases barriers etc Rossby wave elasticity which defines effectively the Rhine scale, was the key effect, and also recovered aspects of mergers including aspects of time development
09:19:54 including mergers and barrier development.
09:19:57 The issues were of course the competition between self sharpening external sharpening interesting observation of staircases symmetry. The fact that Rossby way the plasticity seem the more promising mechanism than here was a bit puzzling, and one wonders
09:20:17 if you could connect this to wave kinetics by parcel kinetics is advocated in ancient times by golf and Spiegel.
09:20:27 We heard when we are there, as gherkin gave us a discussion of envelope theory which is basically I can all plus diffraction that's a typo sorry diffraction method leads down the road to the usual MLS stat genre structure.
09:20:47 And we see she earlier formation as a 2d cell focusing phenomena and he gave some interesting insight into the physics of streamers are and mixing.
09:20:57 We had an interesting talk of a different variety from Robin Hainan it right who said To hell with all this theoretical methods I'll let my computer Tell me what's going on so the idea was to Deuce to deduce the mean field structure by what amounts to
09:21:14 a glorified regression us from simulation data using machine learning, which he describes as an art form. It's the art is in tuning the neural net and the results were very interesting for two DS ago a walk autonomy the con heal your structure in vortices
09:21:34 it for density a diffusion turbulent diffusion plus interestingly vortices the gradient driven pinch which is a cross the fusion if you want to call it that, the ladder the vortices the pinch gradient pinch seem to be more significant in that application
09:21:52 than the conventional wisdom of sharing. And there was little or no sign of them often vote turbulent spreading. This is very promising like to see more in a somewhat less more complicated problem where the answer wasn't already sort of partly cooked
09:22:13 it we had talks on dynamics by cope Galperin and another group by balmforth I'll just very briefly, balmforth pointed out very important that there are two types of mergers one where two guys eat the guy in between by moving toward him and gobbling him
09:22:34 up. And one where they just suck the life out of him and Leave him. Leave his space vacant and they get bigger.
09:22:43 We had an interesting discussion by Laura cope on migration. So the point here is that jet motion or drift is occurring and how do you describe it and this is very relevance to turbulence spreading that we face as a problem in fusion turbulence spreading
09:23:03 being the same as entrainment. And the point was that migration was only contained in the generalized quasi linear theory if the cut off or large enough to include the zone on in the resolved mode they highly nonlinear wave.
09:23:17 Why is that that's because the zone on breaks the symmetry in an important way to facilitate the drift and it acts as a mediator for nonlinear interaction, the migration velocity scale with the drag times the Ryan's length.
09:23:33 So it's like you know you're coming up in 20 minutes, yeah okay I'm almost done two, and Boris, all told us about more on mixing and particular discuss the the mixing jet problem do ality and also pointed out the role of zone ons and mixing.
09:23:51 So let me a little bit of perspective comparing way flows 14 to Burstow aka ably organized by Pascal, and staircase 21, I think I find this amusing interest in citation of Bly, which was published in 98 is rising 23 years on we heard we had staircases
09:24:17 in 14 but we didn't hear much about it.
09:24:21 Not too much and we'll haka and a hell of a lot this time so that tells you something.
09:24:27 The role of emergent scales seems to be more highly appreciated their role is gradient scale, giving a transport bifurcation.
09:24:37 There's been a resurgence in the ancient art of mixing length theory. I notice in the climate group was using simple mixing length models to So somewhere Ed Spiegel is smiling staircases have become more interesting we talked about drift with mediators
09:24:56 we talked about a variety of mergers, and we talked about their resilience in the face of avalanches and con Hillier now VA Stokes was identified as an instructive dynamical model and joining you know it's got an acronym now right it joins Charney has
09:25:15 a yellow and Nina and DDC.
09:25:17 The eternal discussion of mean field theory continues with kind of a focus on the need for a good way of breaking model and finally Arctic oceanography offers a plethora of fascinating and opportunities that we want to hear more about in the future.
09:25:36 And that's all folks.
09:25:38 Great, thanks a lot, but since since we're already 20 minutes and I'm just going to ask people to hold off. Questions or comments or put them in the chat if you'd like, but let's have a scalper a PR talk.
09:25:52 Everyone.
09:25:54 Let me share my screen.
09:25:57 So, I've been asked to talk about these interface group meeting sessions that we had. And just as a caveat, this is I propose an interface group meeting because I knew very little about interfaces and I felt like I needed to understand them better.
09:26:13 So right now I'm being asked to summarize a bunch of things I didn't quite understand in the best of cases. So, anyway, I'm going to try my best to summarize what happened in these interface group summary but just as, please.
09:26:27 Apologies to anyone who's working misrepresenting.
09:26:31 So the point is, I'm thinking of a layered system in which the layers are already formed and the evolution of that layer interface system is going to depend on the interface itself on individual structure into facial flexes.
09:26:44 And so the whole point of the sessions to understand what's going on a little better.
09:26:49 So we had four sessions. The first session was dedicated to just find a list of the types of interfaces they exist. The second one was on interface on motion.
09:26:58 The third one was on the interface will transport IE flex through the interface on the forefront ended up being able to wrap up session.
09:27:06 So in the first session we looked at types of interfaces and we had a large number of short talks on different kinds of interfaces that happened in different systems and starting with interfaces and come he didn't have his talks equation interfaces instructor
09:27:23 structure formation in rotating convection by Edgar interfaces in partially partially missable systems and porous media flow by Eckert my work, density interfaces in stratified share turbulence by Cheadle diffuse if circuits interfaces in share flows
09:27:38 by Justin Brown turbulent interfaces and magnetic layering by David Hughes, and I gave a brief summary of interfaces in law parental number double diffusion.
09:27:50 And one of the questions that I asked everybody is so what is an interface in the first place. And I one definition that came out is that it's the same region connecting or separating to physically distinct extended regions of space and sort of the poster
09:28:05 child of that would be the interfaces that occur in the Navy strokes equations, in which you basically have a binary fluid and the interface of separating the two phases of the fluid.
09:28:17 And so there was this nice exploration of that topic by role and by Eckhart, who both use these equations in which you have an equation for the evolution of the phases of the fluid, and in here The interface is the interstitial structure basically depends
09:28:32 both on an infection diffusion process, as well as the potential from which you determine which phase the flu is in so the structure is mathematically well defined the structure of the interface in this context.
09:28:46 A little bit more blurry.
09:28:50 Mathematically, our interfaces in singly stratified and W stratified fluids, where we don't have a face change but we just have to two sides of the interface with different properties either different densities in the work of ci or different temperatures
09:29:07 celebrities and the work of Justin Brown, and in these cases the interfaces are typically slightly turbulent. And so the question of the definition of the interface what it is exactly becomes a little bit more difficult.
09:29:20 And that's exacerbated when you start looking at even more turbulent interfaces are pretty common in law parental number systems.
09:29:28 And so this was illustrated and David you stalking magnetic layering. And in the law parental number interfaces that we see. So in these cases interfaces are extremely turbulent.
09:29:40 And again, their definition of what an interface is it becomes a little bit more blurry just as the interfaces more blurry.
09:29:57 Now, and then came this thing out of left field, for me at least something I had never considered is that an interface could be determined, defined as a transition between two dynamically distinct regions, rather than physically distinct.
09:30:05 And that was illustrated in Edgar's talk for example where he discussed rotating collection systems and the presence of convict ons where you had regions that are convective, separated by these dynamical interfaces, in some sense, from regions that are
09:30:23 non conductive, and another, and that was brought up by Gilliam, I believe, talking about here and interface perhaps in fingering systems or at least I interpreted his comments as meaning an interface between to dynamically distinct regions.
09:30:42 In the past I was thinking of an interface in fingering regions of the ocean as something separating to fully connected layers with a fingers in the middle.
09:30:50 But of course another possibility of considering that interface would be one where if you zoom in here you have the region that fingering and stable, Jason to a region that is collectively unstable.
09:31:01 And this here in the middle would be the interfacing question.
09:31:06 So there was really a new to me at least a new definition of what an interface might be that I need to process in moving forward.
09:31:15 And some comments that came up.
09:31:18 One of the comments I still remember is, how thick can indeed face be and still be called an interface I think that's a very good question.
09:31:26 Not that we didn't come up with an answer but that's certainly something to think about.
09:31:31 And in the future I think it would have been very nice to have a more competitive quantitative discussion of comparative interface structures in these different fields.
09:31:42 And I think there's still a lot to be learned in that.
09:31:47 And calendula also suggesting a classification of interfaces into families, the kind of interfaces are coincidental that just happened to be there because of some formation I can discern or because of initial conditions, and then self made interfaces
09:32:01 that actively participate in their own maintenance which are pretty common in number of fluids. And I think this is an idea that needs to be looked at in more detail.
09:32:11 What is it that distinguishes mathematically self made interfaces versus coincidental interface. And of course a lot of what Pat discussed in the previous session addresses that question.
09:32:23 But personally, I'd like to understand that better.
09:32:26 So then we moved on to session two which was an interface in motion. Now, we had four presentations, so packs talked about interfaces in 2d MHD David ritual talks about contour dynamics and contraction for 2d Qg Neil talked about interface motion in defensive
09:32:45 systems and I presented a little bit of the radicals 2007 model for staircase evolution.
09:32:52 And really this session, I think can be summarized in.
09:32:56 If you have an interface between two fluids have characterized by be one and b2b as a consumer of quantity. So think about density, think about magnetic flux think about anything that's conserved potential volatility.
09:33:12 There's really two types of interface motion, there's the adaptive reversible transport, that just deforms the interface.
09:33:19 And then there's the usually reversible transport associated with a flux through the interface. So that could be diffuse a flux could be turbulent flux.
09:33:28 And that one, both moves the interface and changes the characteristics of the flow on either side.
09:33:36 Now, in the models that Neil and I discussed. The interface is considered where one spatial dimension one time dimension. So, the objective model was not present there was no adaptive flux directly.
09:33:52 And so that allows us to just focus on the second part which is motion of the interface associated with flux through the interface. On the other hand, in the models discuss my pattern David.
09:34:05 You had necessarily both because there are multidimensional problems. And so one of the big questions is how to deal with that and I'll get back to that in a moment.
09:34:14 So for the one time one spatial dimension so these interstitial flexes I reminded the audience that right Cole has a theory that classifies interface motion and merger into two categories depending on what controls the interface or flux and loosely speaking,
09:34:32 and it's very nice theory, if the interface of flux is controlled by the height of the layers adjacent to the interface.
09:34:42 Then effectively flux through an interface is associated with interface emotion, and often leads to layer merger interface mergers and therefore layer mergers associated with colliding interfaces which is this picture here so in black here these are say
09:35:02 interfaces and they move to one one another and eventually collide. On the other hand, if the interface will flux depends more on the Delta be so the junk in the quantity be across the interface, then the way layers merge is by weakening of the interface,
09:35:16 and the eventually the interface disappears.
09:35:19 And so that's shown here. So again, the dark colors are density gradient say and you can see that some interfaces just disappear.
09:35:26 Now, Neil talked about interface motion and merger in the equation in particular, and what really struck me in his talk was the distinction made between systems where you start with symmetric initial conditions in which, in that case, the region's on
09:35:53 side of the interface can either take the value plus one or minus one. There's no other possibility. And in that, in that case, the, the, the delta d across an interface is necessarily constant so the flux cannot depend on that.
09:36:02 And so the interface merger in this case simply from this physical argument can only proceed by mergers and that's exactly what happens.
09:36:10 On the other hand for, and that was a very nice demonstration if you have asymmetric initial conditions, the quantities, the field and question on either side of the interface can take any value initially.
09:36:23 And so the flux across an interface will depend both on the thickness of the layers and on the jumping be, and in that case you can have different kinds of mergers, where you have the interface disappearing, for example, so that's an illustration of how
09:36:38 you can only have disappearance of interfaces if the flex 3d interface depends on the jump.
09:36:44 And of course in the y slot model which has much richer dynamics in terms and possible interface structures, you can have both types of mergers and I thought that was really interesting to tie all this together.
09:36:57 Nine multiple dimensions which were the topic of tats and David's talk. The problem is, and I think is the first time I really realized how difficult that problem was, maybe I was naive before in there you have to not only take into account the multi
09:37:10 dimensional entity of the problem that the fact that interstitial transport is integration motion is both due to reversible and irreversible dynamics, so that makes it hard.
09:37:22 And secondly, the interfaces in both of these systems is really passive and plays an active role in the dynamics themselves.
09:37:30 And so for example David talked about problems in QDQG turbulence, where frequently, we observe systems that have a reasonably uniform potential 40 cities separated by these interfaces.
09:37:44 And what happens is that diversity within the interface affects the interface and that's this nonlinear connection between the two. And you can develop very complex shapes in the system by doing that.
09:37:56 So David talked about control dynamics method to resolve that problem, and in particular presented, what's called a clam algorithm for control reduction which is type of control them and mix.
09:38:07 So there was a long discussion about the applicability of the method. I mean the applicability of method for elective dynamics is obvious. And there was a long discussion on the applicability for non-conservative mixing across interfaces, if it's possible
09:38:19 and if it's accurate.
09:38:24 Pass talked about interfaces in 2d MHD and again I gained an appreciation for exactly how complex the problem was through these very nice talk. So they're good way of looking at the problem is to think about the system as considering the magnetic flux,
09:38:39 a, and the system develops these large regions of almost uniform, a separated by very thin interfaces. And again, it's one of these cases where the interfaces themselves which are the gradients of a are actually the magnetic field, which has a strong
09:38:53 dynamical effect on the interface on motion.
09:38:56 And furthermore, these interfaces become transport barriers as Pat discussed, which prevented diffuse the flux.
09:39:03 And so all of that together leads to a really complex system will specially temporarily and also dynamically.
09:39:12 And if I had any things to suggest for future meetings, I think, because the multi dimensional problems discuss my pattern David was so complicated.
09:39:22 And the other ones were so simple. I think it would be nice to meet in the middle and talk about the one diversion of the two DQG and to the MHD by focusing on these other topics so we briefly mentioned which are these be staircases in plasmas and the
09:39:38 Jets talks about that this, the local discussed and looking at their migration into facial flexes in the systems which would be a really good way of having the two come together.
09:39:51 So in session three.
09:39:53 We looked more specifically about the transport across an interface. And so we had three talks. I gave a very brief review of selected interface transport models and a few sister cases and Alan Christine talked about one de simulations of layering interface
09:40:06 transport and and Alexi talked about flux and entrainment in cross single component stratified interfaces, in, in Stratford share flows.
09:40:20 And here.
09:40:30 The key was to try to find common points between these different interstitial flex models. So the one that is commonly used in double different interfaces is old model by Linden and Shurtleff, and they're tied back to what we saw earlier, basically the
09:40:37 the transport through an interface or through a layer, and the heat flux initial number is proportional to the really number two the third which is the one on results in whether really number is given here in depends on the layer height.
09:40:50 So, this is one example with the flux depends on the layer height.
09:40:54 But on the other hand, the ratio of salt to temperature flux is proportional to the facility ratio and that's controlled and. And also, there's a week dependence on the density ratio.
09:41:05 So that gives you an idea of the transport across any one of these diffuse of interfaces.
09:41:14 The, and this is validated experimentally with a ratio of the sort of the heat flux is indeed tending to a constant, as a function of the jump across the interface in in these experiments by Turner.
09:41:27 Now, so that was just a recap and then, and then Alan demonstrated that you can construct a one D model for mixing and stratified flows that has the diffuse of transport model, exactly, but the adaptive transport in the turbulent transport model using
09:41:45 a stochastic approach, where you have certain physically motivated role for the mixing controlling the rate and the size of the overturns in this flow.
09:41:56 And with that, he can reproduce staircases and more even more interesting if he can quantitatively reproduce the flex ratio for example through the interfaces.
09:42:07 And I thought that was very interesting.
09:42:11 Alexi then went on to give an excellent review of what is known on transport through shared density stratified interfaces. So the sort of general view is that you have a fluid with two different densities.
09:42:25 And then there's share flow across the interface and everything is characterized by this buoyancy Richardson number, which is given here and there exists different mixing regimes, so either mixing by large scale, Kevin Helens pillows, or mixing by scouring
09:42:43 by humble modes. And one of the things that really came out of her talk was the fact that although generally people agree about the distinction between the two regimes on a practical level, different experiments, different model setup for numerical versus
09:43:01 experimental different types of experiments setup vastly disagree on the magnitude of the effect. And that's something that both interesting and really calls for further study, and something to think about.
09:43:16 In the future, I think, would be to look more at these interstitial flux flows in other systems. So, these more complicated to DQG or to the MHD system focusing at these irreversible transport.
09:43:31 In another one it would be to start using some of these cage slash humble mixing models to look at transport to double defensive interfaces and, and Justin Brown when partly there in his talk earlier.
09:43:43 And then for these mixing models to predict what the flux laws to see what the predict for layer mergers comparing with data. And of course, some of the.
09:44:05 would be interesting to do. And then to finish up we had the full session which was wrapped up where we had sort of more random topics but nonetheless very interesting.
09:44:14 So Petrus your new talks about the statistical studies statistical see dynamics of resistive turbulence and Brian talked about statistical state dynamics for modeling the bear clinic turbulence in the middle, it was fear, and I think Pat said that there
09:44:29 there was a lot to unpack in these talks, which I'm not going to attempt to present broadly but just to see. So the general message of course for statistical state dynamics is that you have a layer interface system is the quality steady state of evolution
09:44:47 equation for adequately chosen moments of the system. And the big takeaway messages that selected closure matters and in this topic, but two items that I thought were particularly interesting in Petrus his talk, he discussed the existence of hidden stable
09:45:06 state that can be that can be hidden in the turbulent flow but if you initialize the system in the right conditions or if you just force the system adequately you can suddenly reveal the existence of that state so this is a turbulent system which were
09:45:21 enforced at this time.
09:45:24 forced at this time. Suddenly transition into a layered state. And that's very reminiscent of what happens in double diffuse of systems where you can have a fingering convection system, which is happily fingering without any staircases, and then you put a staircase in
09:45:38 there and then it continues to live as a stable system. So there's some analogies there that could be interesting to study.
09:45:45 It's 20 minutes past.
09:45:49 Okay, this is one of my last slide. So the.
09:45:51 The second talk was by Brian.
09:45:53 So he actually focused on this aspect of statistical see dynamics in which the system naturally adjust itself to a state of marginal stability.
09:46:03 And he made a strong point that even though the system is close to say the marginal stability is still contains the possibility for strong non normal growth or perturbations, which then have large transit and certifications.
09:46:15 And I think one of the most memorable sentences of this series of workshop was something that Brian said, which is, you can't predict the weather by doing linear stability calculation you predict the weather by looking for optimal perturbations are about
09:46:28 to explode, meaning that the.
09:46:34 I mean, I let me not interpret it since we're running out of time, but I thought that was really insightful and can be applicable to lots of different systems.
09:46:45 So yeah, that was it. So I would like to thank all the speakers in my sessions for a lot of these really nice discussions.
09:46:53 Thank you very much Pascal that's terrific.
09:46:56 Okay, so I think we're just going to move on, straight away to the next talk by David cheese.
09:47:07 Around David, you are.
09:47:13 Yeah, I'm around
09:47:23 limps.
09:47:26 Good.
09:47:27 Yep.
09:47:28 Yep.
09:47:30 Okay.
09:47:33 Right, so this.
09:47:35 This is a summary of the, the mechanism. Working Group, as you will know most of you have been to lots of these things there was lots of overlap.
09:47:43 Certainly between the three kind of
09:47:50 than what you would call them theoretical groups, I mean not not the applications group the climate and the plasma which will bit more well defined so there's lots of overlap between the barrier group the interface group, and the mechanisms group so I'm
09:48:05 not sure I'm going to mention really anything that pat or Pascal has not already mentioned, but it'll be a fairly low density presentation anyway.
09:48:19 So this is what we discussed
09:48:23 in the four meetings, we had.
09:48:28 First one was on con honey now via Stokes, where Rahul panitan Nadia pattern talked about binary and ternary fluids and pack talked about, essentially flux expulsion in that system.
09:48:46 Then we had a session on variations of the blind model for the cross be staircases in plasmas, and that will diffuse of connection from wasting quote from Pat and Paul parishioner.
09:49:02 Then we had a more of beat session.
09:49:08 The talk on zombie vortices from from Joe Branco new take on the has the co worker Tanya equation on the phone and work on MHD share photos from Adrian Fraser, and then just, whenever it was two days ago, we had double diffuse it connection on gamma and
09:49:28 beyond gamma from Pascal from Eugene law and Francesco popper going to say something about some of these what we didn't have, for example was we there was nothing in here about stratified sheer flow mechanisms, because, for whatever reason they, they
09:49:45 were somewhere else, but they could have been. of course.
09:49:49 I'm really going to stick to what we talked about in these sessions.
09:49:55 So I would say we discussed the formation of layers.
09:50:01 More or less in these four systems.
09:50:04 So Peavy staircases, leading to certain objects, particularly with respect to Jupiter.
09:50:14 By staircases in for stratified turbulence I essentially mean the Phillips problem.
09:50:21 Then we spoke quite a lot about equals be staircases in plasmas, and the analogy between the governing equation, becoming simplest governing equation for plasma drift quote turbulence and Qg equations.
09:50:36 And of course we discussed double diffuse of staircases, mainly in a sort of thermal headline manner, rather than getting into the very interesting question really of what what happens in double diffuse it staircases when you're out of the reach of computers.
09:50:57 You know, parameters in stellar interiors, for example, and that's certainly not an exhaustive list Wheatland the talk on zombie policies was particularly interesting they, the.
09:51:10 There were staircases really
09:51:13 commensurate with the critical layers in rotating stratified sheer flow. So, the moment that doesn't seem to fit so well into all of these others.
09:51:25 Anyway, at some level of course these are very different.
09:51:29 And I suppose, what we were the question behind all of this, mechanisms, working was, although they're all very different, is there at heart, something in common.
09:51:41 Okay, so that was, at least to me that was the question that I was that I had in mind, we shall see.
09:51:53 So this is my take on it, which might not be everybody's take on it.
09:51:59 So I would say that the most well understood of those cases, is the is the PV staircase so why would I say that because I think we know a lot about it.
09:52:12 I mean we understand it
09:52:16 away turbulence interaction problem, where the turbulence dominates it's more scales, and the Rossby waves dominate at large scale so there's a,
09:52:26 there's an obvious transition between the two of those, which is given by it so good Ryan scale,
09:52:37 which is the square root of view over, Peter beaches of the beat to play parameter you he's going to emerge so you don't really know you in advance.
09:52:49 Oh, in a way, this is a better way of writing it this is how I'm Jeff Alice writes it alternatively cuz this epsilon over BTQ to the fifth power is something you know from the off okay episodes the energy input.
09:53:08 So the dynamics is can these government essentially least into the by one equation, the PV equation.
09:53:17 And what happens is, so if you look at this this is the
09:53:26 last by way diagram, okay so inside the KXNKY inside you're going to get lost the waves and outside you're going to get turbulence and meet the turbulence essentially seeks the greatest mode.
09:53:37 And so moves towards k x equals naught which is a zone or flow. Okay, so this is also this is taken from Jeff Allison's book. This is an ideal I just.
09:53:51 This is the, this is an optimal calculation. This is just a drawing of how our staircase NPV would look like in terms of the zone a wind. But we also know about self sharpening.
09:54:06 You know if you, If you stir the fluid.
09:54:11 Okay then.
09:54:12 The recipe waves radiate away, but the momentum the zona momentum radiates inwards. So there's a natural shot self sharpening mechanism, the BBB staircases.
09:54:25 So I would say all of that, we know quite a lot about this system we don't know everything is not straightforward to predict the, the scale of the Jets on Jupiter, for example, but we do know quite a lot and we can kind of see why there might be a staircase
09:54:41 and why it's should stay sharp.
09:54:45 Okay.
09:54:56 Oh, okay. So then again this is my take on it and I believe appreciate it might not be everybody's. So this is what I would say, nice to me is the least out of those ones that I put at the beginning the least well understood case, in a way, certainly
09:55:08 well studied.
09:55:10 So why would I say that, why do I think double diffuse of convention is not particularly well understood. What do we know about it. So what we know about it
09:55:20 is that there is a well studied and indeed present instability of a mixed state.
09:55:27 So typically you would start off let's say with us. So thing that state
09:55:34 Something has become unstable you gets a kind of homogeneous turbulent state. And out of that stationary state if you regarded as a stationary state you can look for an instability as they're dependent depth dependent instability.
09:55:52 Related to this gamma which is a ratio of the fluxes discovered by by Ratko and indeed there is that instability Does, does indeed occur, whether it's my own take is that it's that's that's the start of the process, but it's not the end of the process.
09:56:18 Because, and if it doesn't fix the wave number either because was discussed at length is instability of course as a so called ultraviolet catastrophe.
09:56:31 So if you know the wave number, the theory fits well, but the theory doesn't tell you the wave number.
09:56:38 And even if the theory told you the wave number it wouldn't tell you why these things lead to layers, in my view, and I don't think we do know what leads to layers in double diffusing convention, I don't think it's obvious quiet what this what the self
09:56:51 sharpening mechanism is.
09:56:55 I also don't think it's obvious even though layering occurs in both salt thing is, soap thinking regime and the diffuse in regime, you know, one is, which way around, hot on top of hot and hot and salty on top of cold impression the others the other way
09:57:12 around.
09:57:14 They both lead to layering but we don't really understand at least I didn't understand what the major differences are between those two.
09:57:23 They're both susceptible to this gamma instability, for example,
09:57:30 and just stepping outside of what we actually discussed in our group I thought there was a very interesting discussions in the climate group about double diffuser convection, both in a sort of global sense but particularly in, in the Arctic, when there
09:57:47 seems to be a double diffuse if convection hotspot, and possibly a cold spot, okay this is just a gratuitous pretty picture to show you what what it really looks like in this is
09:58:04 diffuse of layering in a magnetic system, okay with these very turbulent layers that Pascal was interfaces that Pascal was mentioning so as, Pat, as mentioned in his talk.
09:58:17 We spent a lot of time thinking and talking about what you might think of as caps and our models
09:58:30 are these yes so the the earliest these the simplest of these was put forward in the paper by Phillips in 1972 was interested in stirred stratified turbulence.
09:58:41 And he suggested. This is his points the equation this is the only equation really that he wrote down. He said that,
09:58:50 and explain why the buoyancy flux function, maybe non monotonic flux versus gradient and this is, this would correspond to this dash nine this lower line here, this is just lifted out of Neil's paper.
09:59:07 So it suggests, it goes parts of the way it suggests why you might get sharpening but of course it's an anti diffusers equation and that's all it is. And so, even, even on mathematical grounds so on physical grounds, you need to regularize it somehow.
09:59:24 And to
09:59:28 at least two means have been proposed to regularize This one is time delays I think in the.
09:59:37 In response to Phillips I mean this was first dealt with by Baron Blatt back in the 90s.
09:59:46 Pat has looked at this, as well, with you soon. Okay.
09:59:51 And it's a nice problem it's a nice mathematical problem there are certainly analogies with the problem of traffic jams, going back to the work of Witten, for example in traffic modeling.
10:00:01 Or you might, an alternative is that you might say this is, this is not a complete description.
10:00:07 And of course, and that's what we've been discussing so this is the blind model as we might call it gets called other things.
10:00:17 And this is, this is the model and it's a very nice model it consists of two this essentially is what Phillips had for the buoyancy. And this is an energy equation.
10:00:30 And it says, you know it's not produced from me stokes equations it's phenomenal logical.
10:00:40 But it has lots of things which are in some sense, hard to argue with you might say,
10:00:49 and and so there's a sort of diffusion between both this bit is the flux one to the other and that's non negotiable once you've decided that that lives here.
10:00:59 This is negotiable and this is a dumping term and this is absolutely negotiable This is this in this problem this is this during term. Okay.
10:01:09 But the key, the key aspects of this really written like this it's called a mixing length l and the, the crucial element of all of this, all of these games is that our can change.
10:01:23 And so typically, there might be an L to begin with and in the stirring problem, that of course is the amplitude of the stirring the radius of this knowing if you like the steering mechanism, the rods.
10:01:39 And as the gradients intensify, then a new scale comes into play and the new scale in this case is essentially the ultimate of scale here.
10:01:48 And so you'd like this L, to be able to go between the two. Okay, and obviously there's an infinite number of ways it can go between the two this is the simplest in some sense, and you can see that once you put this out into this equation then it becomes
10:02:03 quite a complicated equation. Okay.
10:02:06 And this is just take him. Sorry I didn't put an acknowledgement This is taken from the play paper at eight, this is, This is the gradient of be different times.
10:02:18 So a spike in B is a staircase. Okay.
10:02:43 And you get quite a regular array to begin with but then they they merge and as
10:02:33 Pascal said they, they obey something which looks like.
10:02:43 Current helium dynamics. Okay.
10:02:42 And so the question that is exercised us to a certain extent, is
10:02:49 How far can you take the blind model.
10:02:52 Okay,
10:02:55 so here's a couple of places you could take it.
10:03:00 So one is back to the, to the PV problem.
10:03:06 Pat and Michelle Crawford looked at this, and it's a, it's a two component model like Bly.
10:03:15 And it has some differences and has some similarities in the sense that this is the emergent scale, Q is that mean potential artists at this is again it's it's a one day.
10:03:26 The notation always changes if you're doing stratification the independent variable is coordinate he said if you're doing PVHY and if you're doing plasma, it's hex.
10:03:38 So this is the emergent scale.
10:03:42 Well I guess this is the emergent scale this is the hybrid scale.
10:03:46 And
10:03:49 it's been the blind model have been taken into, into the drift way problem in a three component way by various people.
10:03:59 And again, there is a sort of mines scale here.
10:04:05 And this is, this is the real thing in some sense, this is from one games calculations, child kinetic calculations to show the equals be shared eight.
10:04:23 The real thing in a plant in a taco Mac i think is harder to measure.
10:04:32 So in the other major thing we we discussed. Besides Bly was the course name and the merging described described in the current heavier now via stokes equations, this has already been mentioned by Pascal so it's a very nice system.
10:04:47 And we had nice talks on binary fluids IV fluids, looking.
10:04:54 Based on this model, these are, these, these are just the final states of the con helium system you get broadening into these different phases regions have different phases.
10:05:08 Okay.
10:05:09 and we heard from pat
10:05:13 on a very nice problem of what what is extensively is only my now blue is gone, bizarre. Anyway, you know what it should be. There should be some nebulous obviously, you might think you.
10:05:26 Yeah. So, look just at this equation in a way. So the analogies with the.
10:05:35 The problem of flux expulsion looked at first by Nigel Vyas back in 66. Of course this is a, this is a more involved problem than that because it's, it's, it's more complicated.
10:05:47 Okay, it's not just double squared of the unlimited potential, and you get this nice pattern, the time goes down and back up and down and back up and down to follow the time evolution.
10:06:00 And so the final state here is like the.
10:06:03 Well this is not quite the final state. This is a long lasting target state in the final stages expelled.
10:06:10 Right.
10:06:11 So in my view what is what's the reason, out of all of all of this.
10:06:16 So the important points that I would say is, what we need we need some sort of negative diffusion process which which has to be stopped at some stage.
10:06:25 We need some sort of.
10:06:29 I should have said more than that maybe n shape flux gradient relation. So going back to this.
10:06:36 Oh sorry, this thing I've been to a meal paper.
10:06:41 So this is, this is Phillips okay and you'll just keep them forever You really need your floods gradient, to take this and shape. Okay.
10:06:50 And whether it doesn't matter. It doesn't in the blind model also, it depends on the form of this is P. Okay, so it's not immediately clear in advance that you'll get this, you need to scales, I would say to him, Typically, one of them is prescribed,
10:07:08 and one of them will emerge.
10:07:11 and the other important thing I think is the, the nice models for integration of dynamics such as such as chameleon Nadia Stokes, we possibly interesting links to other studies, not fluid dynamics studies other stuff in studies of like competing species,
10:07:29 described by such equations. What would I say is still up in the air.
10:07:37 So the blind model is up, precisely that they are models of a youthful models.
10:07:44 Whether you can go beyond them.
10:07:46 You can certainly go, you can certainly apply them to other systems we've seen that, that has been done.
10:07:53 Can you actually go systematically in any sense from the governing equations to such models that I think is still not clear, even, even under this kind of phenomenal logical approach can you can all staircases that we've seen Can you shoot on all of them
10:08:10 into this framework.
10:08:13 You can certainly do it for the Rossby ways you can certainly do it for the cross be staircase Can you do it for double diffusion, that's not clear.
10:08:22 We heard an interesting talk just the other day.
10:08:28 From Francesco pepper Allah who is trying to do.
10:08:31 Well he's thinking along those lines, I guess, as these poor pushing up.
10:08:40 And what Francesca was talking about was what is what is this doing what are the steering roads of double diffuse convection. So what is the, you know, in the blind model you start off stirring and you generate a smart, and then you generate an atomic
10:08:54 scale. What is this stirring in in double diffuse of convection. If you wanted to put it into this framework. He had a, he had an idea of what it was that the homogeneous turbulence grew into clusters of a certain size and they were this domain rooms.
10:09:12 So there's a possibility of putting the double diffusion problem in that framework.
10:09:19 And it's very important, this this double diffusion problem which I say is not so well understood. Not just because it's so interesting but because
10:09:29 it's important to know the transport of these things it's important to know the transport obviously in Ocean at oceanic models. It's also important to know if you're going to try and work out transport in Stella interiors where WP fusion can be important
10:09:44 important as well so it's a very interesting problem with with lot still to be done, I would say, okay, that's me. Thank you.
10:09:53 Excellent David.
10:09:54 Yeah. So again, but 20 minutes in and I think at this point, it would probably good to just take a break that's been a lot to absorb.
10:10:04 Yeah. So again, but 20 minutes in and I think at this point, it would probably good to just take a break that's been a lot to absorb. I'll make sure I keep my final talk short enough so that we still have time to have a discussion about moving forward at the end. So let's take a break
10:10:14 until quarter past the hour, and we'll reconvene them with the, with the talk on classmates.
10:15:05 All right, let's get started again so now we are going to talk about two different working groups and applications, beginning with Deanna talking about plasma, go ahead.
10:15:14 Yeah.
10:15:15 Okay, well, we had four four topics, involving also as you can see, nonplussed by experts that were assured very stimulating experiments and DNS that can be useful for comparison to our observation in plasma plasma actually mainly dealt with the token
10:15:37 that class mass.
10:15:39 And so thanks to all the participants to the speakers and my apologize if I misrepresented any of these.
10:15:48 So I start with the first.
10:15:51 Here, the first session that's the dealt with the impact of external field by external field actually it's essentially meant stochastic magnetic field.
10:16:03 We have three speakers Oban Dinah first from CA, and basically deals with the token like Best Buy where you have the meal, guiding magnetic field essentially a treadle one plus the political one and then you end up with a few lines which are helical on
10:16:23 to try magnet teacher faces. But this well behaved magnetic field, kind of have actually is not exactly a tissue matric first and one reason is the the presence of those coins here, which I in a finite number, and this creates ripple, but as we will see
10:16:46 in the other talks all the kinds of human Gini Ji, and non actually symmetry of the magnetic field were accounted for and discussion went on on the impact of this stochastic few lines that were generated by this nice symmetry.
10:17:06 But, on the layering. And on the generation of the.
10:17:13 Here, the tutorial videos at the point that the terminal velocity is good for the confinement in taking my class class so it's worth focusing on these this issue.
10:17:28 And what Diana showed was the fact that different depending on the number of treadle coins here, and also on the conditionality of the plasma then we can enter different treadle regimes diff three different regimes, where the treadle friction, you to
10:17:47 report
10:17:51 has different magnitudes. And since the defect is complicated.
10:17:57 He went to nonlinear simulations.
10:18:01 And he showed that the, actually this triple and this friction, the magnet YouTube magnet, lead to magnetic bracketing that modify the flows and that was shown to other calm the trouble and stress so in the end you end up with this kind of equation where
10:18:18 the mind at breaking comes from this expression is in this expression you to the, the ripple that balances or even overcome the stress coming from the turbulence.
10:18:32 Now, on the same kind of perspective.
10:18:36 Samantha Chen looked at the dynamics of this strain of stress in the presence of more complex structure of the magnetic field where we had many, many different mode not only breaking the access symmetry but for kind of most turbulent modes for instance,
10:19:00 and focusing on the dynamics of the rain on stress it was shown that actually the stochastic field interferes with the shooting tilting feedback loop, meaning that if you would only have a guiding magnetic field, without fluctuation then you would end
10:19:22 up with the first term here, linking the rain or stress to the main flow. and this relationship leads to some stability was up leading to share layers.
10:19:36 of the magnetic field fluctuation leading software stochastic defacing two important points, it appears much below the, what is called the alphabet ization which is the regime the lot high beater regime where the magnetic stress balances the rain on stress,
10:20:05 And the second point was that the the strength of the sarcastic defacing was found to be proportional to the inverse of the square of the normalized llama rages this dimension as parameter Eurostar which tends to be small in large machine like teachers
10:20:24 it's a kind of busy mystic mystic mystic why because by defacing we reduce the strength of the rain on stress, and then we ultimately reduce but to me the, the magnitude of the sheer layer, which is beneficial to access improved improved confinement animals.
10:20:47 So we expect larger power threshold which was recovered with a 1d model, and part time on then show that, actually.
10:20:59 The, the relationship, the impact story of this turbulence magnetic turbulence on the rain of stress. How did you problem was kind of your problem of the following.
10:21:14 If you can see or rephrase turbulence.
10:21:17 then you can wonder what is the impact of the fluctuation of the better Citi Field coming from this turbulence on the kinetic stress and the kinetic stress is, the more general expression to the one which we discussed here, that was discussed by you have
10:21:35 Mr Hannah in the simple case of ripple it takes the this simple feature and expression in the more general condition where you have the turbulence turbulence popping in the air, then it takes this form.
10:21:52 So, it was found that it was Steven an explicit expression for this kinetic stress, which is given here and especially in the relevant.
10:22:14 Before the transition to improve confinement in the relevant regime where you have strong electricity tablets.
10:22:13 Then you expect this kinetic stress to scale like the gradient of the mean below city trivial little city with the magnetic scattering being set by the electrostatic turbulence in this case, it was not so so that.
10:22:32 So you see that the diffusion coefficient scales like the square of the fluctuating magnetic field here. It was not just that there was an infrared divergence, it's still an open issue but it was assumed that it would like it should be lightly cured by
10:22:47 the local turf of the magnitude turbulence spectrum.
10:22:53 So the second session dealt with the impact of the boundaries forces and dissipation on layering. And we, we first had a nice overview of the layering in turbulence stratified through it and to not in class bye bye whole field.
10:23:14 impact of the type of forcing and the stability of the shoe layers and there are the two different kind of regime that you can achieve either a well defined transition layer here is called scoring scoring or diffused layer where the interface tend to
10:23:36 disappear, due to a overturning, and the critical numbers that were shown, where the current numbers so the disclosure to her that she teaches EDT and reshot some number, which cannot also be seen as the inverse of the square of the fruit number, which
10:23:56 see the potential energy divided by the kinetic energy of the turbulent flow.
10:24:02 So to to kind of flows where show vertical sheer flows.
10:24:08 In this case, high current number leads to interface instabilities, which can have actually different effects, scoring or returning depending on whether it's Kevin animals or homeboy instability.
10:24:24 But, either for force for different forcing either force, a boundary, or relaxation who are the prescribed flow here at large resorts non number.
10:24:39 It was found that it led to a scoring so well defined interface for horizontal sheer flow with strong stratification.
10:24:51 It was observed that spatial temporal intermittency of the sheer layers with some instability that could occur at IR reshot on number.
10:25:07 Okay, so I think that here the, the different behaviors of the end the robustness of the dish. The, the interface. Regarding the values dimension this numbers is something which is interesting in the framework of the plasma physics also so we should look
10:25:28 into the correspondence with this dimension is parameters, and the impact of the forces and boundaries on how and plasma was shown from the experimental side by low touch meat, and especially looking at the dynamics of the edge transport buyer.
10:25:52 First it was shown that when a different kind of heating in the core was applied injecting talk into the plasma, then the plasma rotation was modified internal fight also the mean.
10:26:10 Radio electric field which is involved in the transition to see improved confinement, eh mode, through radio correspondence. And so it resulted in the, an inward motion of the edge transport buyer, that it was the first observation.
10:26:30 That was the first observation. The second one was another way of generating non FCC Mitch free magnetic field at the edge is via current coins here that you can see
10:26:44 in the boundary of the tech of my classmates so they can lead to so called resonant magnetic perturbations and stochastic magnetic field.
10:26:53 So it was shown actually that it led to a reduced in radio language you sorry the, the prime here relates to the sheer, it should be both the regular record field, and the each year are reduced.
10:27:10 And so it was shown to lead to a lower to a larger three Lh transition power. And it seems to be consistent with the proposal the results presented by Samantha Chen previously the stochastic defacing, and also with the fact that you to these stochastic
10:27:30 magnetic field, which heat material binary there are electron losses, which also result in the same kind of physics.
10:27:41 again on this edge transport barrier and that was already addressed in the previous talk by David use a simple model was revived by Misha my calls. At least, I mean, simple in one field in one few using a wonderful model with here, an S curve or an N
10:28:06 Kirby, depending on the way you look at it with a bifurcation you can be either in our mode or in H four depending on the magnitude of the heat flux, you put it in.
10:28:16 But in this work.
10:28:21 Misha my cough reported the fact that they took into account two fields, because this bifurcation here does not only depend on the density gradient but also on the pressure gradient and even on the pressure, have a true.
10:28:35 So taking to account, only the pressure gradient and pressure and density gradient, then the transition was found to be always at the maximal effects, the Maxwell first corresponding to the facts at which the area here are the same.
10:28:55 But when taking into account the pressure curvature, which is actually the case in the forced balance, and we expect the curvature to play a huge role, at least in the back transition when the buyer has already formed with shoulders, well defined, then
10:29:17 in this case it was found that the transition was not at the micro flex it was expected to be at the lowest flex here, a disposition.
10:29:29 Moving to the third session then you see that there's these open question of the in interplay between the avalanches and the state cases. And it was looked at the end this.
10:29:46 This problem in the point of view of the avalanches, whether they can themselves, be kind of responsible of the state cases, and not. So the stage would be the consequence of the dynamics of the avalanches.
10:30:01 So, you Suki for sugar reminded the main results of that she presented during the general session and showing that if you, you take into account.
10:30:16 Typical relationship between the flex and the gradient.
10:30:21 So the flex is related to the temperature gradient, plus aquatic john coming from the, the turbulence intensity.
10:30:32 And if you take into account the fact that the flex might have some time delay the time response. Before going to the security group stage, then depending on this typical time here.
10:30:45 So, first of all, you, you end up with a, what is called a tick off equation, which is kind of extended burger equation to the burger 10, leading to the database or burger he's here with the diffusers terms here.
10:31:03 And depending on the, the, this critical time this response time here if it's long enough. If saw the effects does not relax too fast, then john conform.
10:31:16 And by John's, you can then have push up creation. And it was also mentioned that, depending on the forcing a view the forcing is good. I mean is, has good properties, then you can end up with the jumper aggregation.
10:31:35 And if you continue the pumping has to be continuous and this may be relates to the competitive nature of Broadway the instability that was addressed.
10:31:48 Next by
10:31:51 a bank fourth roadways as physical avalanches, which are unique you choose in flowing through it.
10:32:00 And there it was to kind of roadways were addressed either turbulence, or laminar and it was shown that in each case the drag is very important. It takes a different role in determining case where the drag is mostly governed by turbulence escaped like
10:32:17 this prayer, the kinetic energy divided by the, the length, the hate of the, the flow.
10:32:29 And so the roadways appear in this case when the fruit number is largely Done, done to end the dynamics was also interesting in the sense that short waves, was shown were shown to to lead coarsening.
10:32:48 And conversely if you look at waves which are well separated, then they can lead to new creation of of new role waves in the la mina case then in this case the Nadia stocks equation imposes the drag which is simply the diversity divided by the square
10:33:13 of the depth. And in this case, we observe la mina roadways. Also in non Newton, who eats although the physics is there not fully understood and traffic jams that were addressed by Yusuke equals who, in the previous slide, are part of this kind of dynamics,
10:33:34 possibly also relating to a firewall. Sorry to
10:33:40 to fire.
10:33:43 fire. Breaking or spilling.
10:33:46 And then in this avalanche business.
10:33:49 It was for the first time shown that actually the the avalanches might not be only, I mean that the physics of the spreading of the, and the dynamics of the avalanche might not be local, but might be non local and explicitly by explicit women that actually
10:34:11 it's the nonlocality does not come from some time response or some finite time response due to a fast propagation of France for instance, that really explicit.
10:34:29 And so the framework.
10:34:31 Here was three dimensional in the kinetic space, mobile for Trump in turbulence or real.
10:34:39 Although simple but true equation for this kind of turbulence in taking back plasma or man magnetosphere this key steps are integrated here and they really rely on the put conservation of potential or TCT and linking the potential spectrum to the potential
10:35:00 for TCP correlations, and to get the spectrum, then you have to invert the potential, but what TCT and the inversion scales, as leads to the scale of the explicit nonlocality.
10:35:17 And in this case, the continued model, dealing with trauma and turbulence, then this game was governed by the, what is called the banana with, here you have an example of the trajectory of the truck particle with the banana with between being here the
10:35:36 the width of these banana light shape.
10:35:40 It's fairly small for terminal particles that it can it can become fairly large actually for energetic particle, because the banana which case like the square root of the temperature, and also a dh because, because of other dimensional less
10:35:58 dependencies parameter dependencies through Yannick your 20 minutes in right now.
10:36:04 Okay, so I have to hurry up.
10:36:08 otherwise you won't have time to the chat.
10:36:12 So the last point, the last session was about what happens to my GG, we had a nice talk by again The following year, which was shown that actually in the modeling.
10:36:29 That is proposed here in for for token Mac to predict the flex. some key assumptions are broken.
10:36:39 Especially the fact that there is this kid separation between the, the equilibrium, and the fluctuations.
10:36:47 And this skate separation is broken actually close to the marginality the marginality being the region.
10:36:57 In gradient, where the flex starts increasing the turbulent flex start increasing.
10:37:04 So I don't have to go much into the detail.
10:37:07 The, the way forward to cure the, the models, would be to take into account, other than spreading and fro pardoning and push up by solving a dynamic or equation for the spectrum of the turbulence intensity via KFC on model, and other nice paper, all paper
10:37:31 that was revisited by parts pushy.
10:37:50 Important trust to Neo marginality of Rosen good, and train and in 87 for the fact that if you have an array of convective sales, with the small overlap, then they are boundary layers, which are sarcastic, and then you you end up with a system where you
10:37:57 you have two types of transport a fast transport in the sales that homogenized The, the system and a slow diffuse of transport in between. and the resulting effective transport is geometry mean the square root of the minute when it cannot be fusion and
10:38:14 the one in the cell and the pointed that you can in this kind of regime, you can end up with the corrugated profile that was actually noticed in the paper by verse and route.
10:38:26 Early on, so it has a possible relevance to say case. And last, wanted to mention a nice overview of key to read on experiments on rotating water tanks, where he should actually that the key ingredients for the appearance of sheer layers, were certain
10:38:50 numbers of key ingredients and a speech, and he discussed the key length k hierarchy to have strong staircase and especially, you need to be Ryan scales much larger than the beta skills which measure the anisotropy.
10:39:20 So the.
10:39:13 There was some evidence of way, breaking and PVC lamentation in the industry themes that were addressed and maybe I can just finish there by just leaving the, the last slide, for discussion.
10:39:31 Thanks a lot.
10:39:32 Thanks a lot Yannick.
10:39:34 So, let's have a little look at what Jana cousin the screen well that's up, I'll point out that I've put on the chat. A link to Dropbox, and there I've uploaded the summaries of the working of the four different working group meetings and climate.
10:39:52 So that way, I will speak quickly but you can refer to those documents if you want to get more information.
10:40:04 Okay.
10:40:07 So let me talk about what happened in the climate applications group, this is what terribly named group, because we didn't really talk about climate until right at the end really this is a observational motivated research looking at observations of staircases
10:40:23 in the atmosphere and ocean.
10:40:26 Whoops, that's the wrong mode.
10:40:30 There we go. Hang on a sec. Okay so, um, yeah so these are the things we discussed so we looked at PV star cases on Jupiter again really focusing on from the observations and the modeling.
10:40:43 What can we understand about what's going on. The other talks are all looking at the ocean is social interactions ocean staircases influenced by turbulence and finally we did touch upon the issue of climate what's the impact of ocean staircases upon the
10:40:58 general circulation the ocean. I list here all the speakers of those sessions and I put in bold, the leads of each of those sessions.
10:41:07 And I'm very grateful to delete a particular for their feedback in preparing the summaries and helping me with this presentation.
10:41:15 Okay, so every time we met, we always start off with these questions. What are the pressing outstanding problems what's needed to make progress, and how can our working group work together to make progress.
10:41:29 So what I'm going to do is just in pairs of slides, I'll just address the first two of these questions. I said this is my show my notes. So I'm going to just the first two of these questions and then I'll just leave the last question right to the end.
10:41:44 And there I go again putting on the wrong thing.
10:41:51 So annoying.
10:41:54 Okay.
10:41:56 Just try it this way. Okay, so these were the pressing outstanding questions first of all when Jupiter, the spirit, the PV staircases are very stable I mean they have hardly changed and variation and magnitude or with over decades, if not centuries.
10:42:13 And so why are they so stable.
10:42:17 Also, we do now have observations what's going on in the weather layer, but what's going on in the deep layer is only beginning to become understood but there's a lot of unknowns there and the question of how the weather layer connects to the deep layer,
10:42:32 still something outstanding.
10:42:34 We still don't know what the energetic sources are for these jets, whether it's due to convection or instability, and we don't know how the energy is even dissipated whether it's turbulence stamping gravity waves or magnetic braking.
10:42:46 And so it to make progress as this is a common theme we need more and better observations. Now the good news is the Juno mission has been going around Jupiter for quite a while.
10:42:58 And so there are a lot of observations and for my money, the low hanging fruit of the gravity measurements as emphasized by john or know the gravity measurements that have been taken up only rudimentary been analyzed and we could probably learn a lot
10:43:12 more about the interior by diving deep into that aspect in America modeling that there have been effectively two separate approaches whether you use a shallow water model to look at the weather layer.
10:43:25 And, and then you don't know what's going on at the base of the weather layer so you have to put in better boundary conditions. And then there's the deep conviction models that's really looking below the weather layer, thinking of sort of tailor column
10:43:36 like structures. And there you have to work out what's happening, how does that connect to the overlying shallow weather layer. So really the progress that needs to be made there is in coupling the deep end the shelter models together.
10:43:51 Now, going to the ocean. We look first of all, ice ocean interactions, the oceans actually really exciting because there's all these new observations that have been coming out just in the last.
10:44:02 I'll say five years or so, and these ones in around Antarctica are very new. And so here we're looking at staircases under the Antarctic ice shelf, or under the sea ice floating sea ice in the in the Antarctic Circumpolar Current, and in some cases staircases
10:44:18 are formed.
10:44:20 But these unlike the Arctic are very transient they're localized, they might appear and disappear, they can actually be seen to evolve in time. And so there's, there's so limited observations right now.
10:44:33 We really don't yet know what sets, their prevalence what sets their duration, and also what is their influence upon the melting and freezing of sea ice above or conversely, what's the influence of the melting and freezing of sea ice upon the staircases.
10:44:49 So, again, observations are needed, and particularly when you deal with ice there's the issue of boundaries. If you're under an ice shelf like an article that's predominantly horizontal.
10:45:04 And that's very different from say a marine Terminator glacier in Greenland where the ice face is vertical. And that's different again from having an iceberg were really have very complex shape.
10:45:16 So, these are probably going to give rise to different effects for creation and influence of staircases modeling is also an issue because you tend to have shear associated with this convective mixing and it's still unclear how the shear couples, or how
10:45:33 this year influences the conduct of mixing, perhaps even being so strong as to shut it off. So there is some progress being made, also progress is being made, and beginning to look at how the morphology of that ice ocean boundary changes due to melting
10:45:47 and freezing.
10:45:51 Now, we also looked at staircases and turbulence. So, if you have strong turbulence for example in your boundaries, you will not see staircases but if you're in the middle of the Arctic Ocean, you have these very robust and stable staircases that extend
10:46:07 for hundreds of kilometers and really don't involve much in time. So somewhere in between that you have some effects where these the turbulence can break up or at least influence the staircases, but that idea of how, how much trillions Do you need to
10:46:24 actually break apart the staircase isn't unknown, or what is the influence of moderate tremulous that doesn't break it up but how does moderate turbulence affect the fluxes.
10:46:35 So, we also in particular I'm showing these three images of a warm core Eddie in the Arctic that showed wonderfully. Both double diffuse of end can diffuse of convection taking place within the Eddie, which evolved to break up that this is a relatively
10:46:53 This is a relatively new observation and can have very important consequences for the evolution of Eddie's.
10:47:00 So, again, we need observations. And here I'll just focus on the modeling aspect of it. One thing that came out is the influence of sheer influencing the interface for example between one warm salty layer and colder fresher layer.
10:47:20 And, and that doesn't seem to have been considered in detail, even buy these idealized models such as the cordon Hilliard, and you choose your acronym I chose ballsy, and so on.
10:47:33 And also there's the issue of time dependence the background here so I think these observations could also motivate a lot of fundamental theory.
10:47:42 Finally, we looked at the impact of ocean staircases upon climate.
10:47:48 The idea is specifically in the Arctic Ocean which is a very climate sensitive area.
10:47:54 Because if you have more melting of sea ice.
10:47:57 Then you explore more open ocean, which then enhances more heat up being absorbed by the ocean and you have a positive feedback. So the question is, do these do staircases actually have effects on the global ocean circulation.
10:48:15 And so, How significant to the influence of transport and mixing and crucially, if this is important. How can we even take existing general circulation models and parameter effects.
10:48:30 And so here I'm actually doing a bit more discussion in progress, but there is a wonderful talk given by Vandenberg very recent analysis of lots of our go float dangerous.
10:48:44 Almost 500,000 of them, and looking at. Where have all these profiles taken by all these floats. Where do you actually see staircase formation, and then estimating what's the flex is due to them.
10:48:59 Well it turns out not many of them have staircases 6.4% for diffuse the convection at 8.1% for salt fingers. And when you evaluate the flux is it actually, it almost seems to be below the noise level of what matters for the ocean, something on the order
10:49:17 of one gigawatt compared with 20 values that would be 20 times higher. If you're looking for example a boundary there turbulence mixing or gravity wave mixing and so on.
10:49:29 So that might say well this is actually important to tall, except then you spot this hot spots or, as David said cold spot up in the Arctic Ocean, where you really do have a strong currents of diffuse of connection and soul fingering.
10:49:44 I'll point out that these floats only had one meter vertical resolution. So they actually wouldn't capture the salt finger.
10:49:53 Salt fingering staircases. And so it may also be that this particular study underestimated the number of staircases out there but certainly we would need a lot more fine and scale measurements in the Arctic Ocean to evaluate the impact of staircases.
10:50:11 As for modeling all say there is there is actually a parameter ization scheme that was developed for double diffusion in the oceans. It was developed in 1994 and hasn't changed since.
10:50:23 Despite the plethora of observations that we've been getting in the last 510 years. So certainly, that could be adapted and improved upon. So, last comment.
10:50:34 I'm not going to see who should be doing what I will just put down this diagram to say here is how all these connections can take place between observations numerical modeling laboratory experiments, all connected through theory.
10:50:50 And so I hope the participants and people even who weren't taking part in the climate group might be inspired by some of these problems that are emerging from observations and see how they can apply their skills and interact with other people here.
10:51:05 That's my presentation. Thank you.
10:51:11 Okay.
10:51:14 Fast and Furious so I know that went quickly but again you can download the documents from the web part I'll pass it on to you. All right, thank you. Hi.
10:51:23 I'll pass it on to you. All right, thank you. Hi. I have a few lighter concluding comments, but I think maybe in a little bit of time we should discuss, maybe where we go from here, I think many of us are interested.
10:51:40 One item is the several, some of the groups I know have sort of
10:51:49 put together an idea or floated an idea of a and not too frequent gathering, maybe a seminar once a month maybe embedded in another seminar series.
10:52:05 And if you're interested in something like that i think you know the best way to do that is just to post the leader of your group, and how after we get these things organized we can put together a web page where or something, where all this is laid out
10:52:25 so people who weren't in Group A can see what's going on there and so forth that you know that obviously has to be at a modest level I don't think anyone has the time that we spent in the last two months but on the other hand it's a way of keeping things
10:52:44 moving forward and I know of at least two of these cooking Now, second item.
10:52:53 After a discussion with Mark Baloch.
10:53:08 KITP offers or has been offering follow ons, and follow ons are, where a group of people and the catch is the group is like a border six or seven maximum can go to KTP and you know get there at least the housing covered for two weeks the the idea is you
10:53:20 work on something related to the program.
10:53:23 And I pointed out that given the fact that we had a program in the living room as it were that these might be very popular, and that there would be more than one group might want to have a follow on.
10:53:39 And, at least in principle, he said many fall you know several follow ups are possible I did not get an upper bound on the number of follow ups but it's more than one.
10:53:49 Okay.
10:53:51 A few of us after wave flows 2014 had a follow on and it was very useful in fact that was the first time I read the blind paper was actually in that, in that follow on.
10:54:09 So, you know, these would be basically no talks apart from gathering in a little conference room and actually doing work together, which is the thing we didn't get a chance to do in this meeting.
10:54:23 Let's see.
10:54:24 Interestingly, I hesitate to bring all of this out, but I got you know Mark asked me, well you guys going to reapply for a KITP program anytime soon, which was a surprising, and it was entirely from him I mean I automatically thought that our names were
10:54:47 mud for about five years you know sort of the cycle of things.
10:54:52 And I suppose, you know, we may have gotten some brownie points for, you know, running an active and dynamic program during the pandemic.
10:55:03 So that's something to think about. Obviously, it would have to be different but we all know from looking at the KITP site that you see sort of the same groups re reinventing themselves in a cycle right over over a period of time and the name changes
10:55:25 but the fundamental problems in the set of people stay the same.
10:55:31 And there may be chances for such enterprises elsewhere. Okay, so that's that's something else to keep in mind. So those were a few things I want. Does anyone want to add to that or comment on that.
10:55:49 I noticed the the the climate group was particularly dynamic.
10:55:56 And for those of you who found the plasma side interesting there is the BI annual festival the theory we're on in exon Provence, it should be this summer it's not going to be for the obvious reason but hopefully when Madonna Pfizer Pfizer and Astros Annika
10:56:22 have saved Christmas for it will be restarted next summer. So that's a, that's another vehicle for staying in touch and there will be an online lecture series related to that this summer, sort of what not a, not an online program like this but there will
10:56:36 be some series of lectures and that's something we might be looking to involve some of you in
10:56:46 any any comments from anyone else. Boris.
10:56:56 Yes,
10:56:55 it is.
10:56:57 This is coming to the angles, it was a really long workshop so it has positives and negatives. What I noticed that there is a relatively new direction of research in all those areas which we discussed.
10:57:13 And this is related to the stages of triad interactions. There is a photo papers, which subdivide the interactions in four different groups, and they pay particular attention to hit the city.
10:57:28 So when you have extra strains, they can affect eliciting socialism some groups, become more important than others.
10:57:36 And for example, what is it, so there's a patient that the patient was cautious the dimensionality of the flow and the behave like turbulence in dimension dimension bigger than two but smaller than three.
10:57:49 It's not two dimension to wouldn't it's not three dimensional turbulence. And there is an example of this in a hurry comes to do some studies found.
10:57:59 If you go under
10:58:02 the lens of the vortex for example, and then you find it to some lamps, the direction of cascade changes from direct to inverse.
10:58:12 Could you please get to a point on activities right the time for invite boxes is kind of past. All right.
10:58:28 Okay, so this is something we should look good today I think it's a new direction which is important for all areas, which we consider them this research was not touched upon.
10:58:33 And you were talking about the different venues, there is a venue in International Institute of space stages and burn, we can do that like, like you know you know so so we come up with another proposal and expanded to do it and Burma things that will
10:58:50 be there.
10:58:50 All right, good let 1000 flowers or Hundred Flowers bloom. Good.
10:58:56 Any other comments.
10:59:04 All right, well I thought I prepared a small bit for closing then so anyway I think there are many many chances to move forward and you know this workshop is about self organization.
10:59:20 So, self organize so you know usually at this point, there are some, some nice reminiscences and you know pictures and so forth. Well,
10:59:34 you know, so I was thinking you know you may have noticed in my talk, I made a comparison of wave flows 14 which would technically classic example of what I said a nominally different topic, but really the same group of people that you know the crime
10:59:54 scene, the crime changes but the criminals stayed the same. and then while haka. I have some pictures of some of our key people wearing you know Mexican hats from that.
11:00:06 And then here, and I was looking for some pictures from 2014, and you know they they had been deleted I guess in my system it's a pity but all pictures from Santa Barbara look the same they're boring the beautiful so I just lifted lifted lifted these
11:00:25 the website right these this is what we missed, there's their typical desk views from from KITP. And so when you you know you're thinking about these follow on programs are possibilities for things in the future.
11:00:44 Keep that in mind as motivation.
11:00:48 Now this for this program I at least had a rather different desk view. You know I thought this this is my memory photograph of the program, and it's it's a typical desk view I think for many of us.
11:01:05 And you can see my distinguished colleague is eagerly listening I'm, I think it was a discussion of ice and he heard mice.
11:01:14 You notice that one of our key coordinators is holding forth here and you see some other distinguished participants.
11:01:24 But in spite of all that it was I think a very good program, and very dynamic and i a lot of long and,
11:01:37 you know, energetic back and forth and I at least learned a great deal. And I hope we can maintain the program and the momentum of all this, and profit from it scientifically in a number of ways in the future.
11:01:56 And that's about it I might ask my other my three co coordinators to comment as well at this point and then we'll pack it in.
11:02:07 Pascal.
11:02:11 Um, I'm not sure I have much to answer, I was very pleased with the way the program went and I wanted to thank all the participants for really making an effort for pedagogical talks I learned a huge amount, and I just realized how much I don't know and
11:02:24 how much I still have to learn so it's obviously time for another program that maybe don't just now.
11:02:30 I think we're all a bit too busy, but looking forward to seeing you all again very soon.
11:02:37 David.
11:02:39 I can only repeat what you've already said thank you to everyone that came many of you have come religiously almost every day.
11:02:48 And you weren't organizers so you didn't have to. So for those of you that have come so often and ask questions and give talks and talks and everything it's been fantastic.
11:02:58 So thank you very much for that and let's hope we have a proper one someday somewhere. Okay. Indeed, Bruce.
11:03:09 I got a I want to thank everyone as well. I actually haven't worked much in staircases at all so I learned an awful lot so this has been great for me.
11:03:17 So I'd like to thank David Pascal and patch in particular for bringing me in on the organization of this.
11:03:24 The only other thing I think we should probably let the participants know that we will be doing a feedback follow up thing.
11:03:33 I think so. And that's hopefully through that medium we'll see if we can organize seminars or whatever people like depending on the feedback weekend. So thanks again everyone.
11:03:44 All right, I think once again as Bugs Bunny said that's all folks.