09:03:14 Okay, good morning, everybody.
09:03:17 Welcome to the mechanisms.
09:03:21 Discussion numbers are still going up but I think we should probably start.
09:03:27 So today we're going to have a discussion about current Elliot equation or Camelia dynamics. So those of you that have been with us throughout will know that we've already had been an interesting talk by all the pundits on this and Neil also mentioned
09:03:46 Cornelia dynamics in his talk so it seemed a good topic to discuss it in more depth.
09:03:55 So today we've got three speakers. So we're going to start with Rahul.
09:04:07 And then, with his PhD student Nadia, hurry back and they're going to tell us about binary internally fluids.
09:04:11 And then we're going to have a talk from our fearless leader, Pat.
09:04:17 And we will have a break, somewhere.
09:04:21 So whenever you're ready rebel Please, sir. I'll start sharing my screen just.
09:04:34 So, this is the talk I gave a little few weeks ago, I won't repeat everything but I'll just remind you what the cost of your stokes equations are.
09:04:49 So this work has been done by several former students and john given some mathematical work which I will not talk about today.
09:04:57 The second half of this talk will be handled by Nadia he's done all the work with a ternary fluid mixtures, and our supporters from these agencies, some references which I can give you later if you want.
09:05:13 So Part one is binary fluids and part two is turn to redo it so I had to park God, that you have will have to leave notes.
09:05:24 So, again, motivation, very quickly. Eventually, we would like to understand.
09:05:31 At least warm clouds and find out how raid occurs or forms and for this from such word clouds. So we really should be able to handle multi-phase flows.
09:05:45 So let's see what is the best weekend do today.
09:05:48 I've given other examples of multi-phase flows droplets of boiling water bubbles in a turbulent flow. This exotic object called an anti bubble which I will not talk about today.
09:06:01 So, let me remind you, if you have two fluids. A and B. In a homogeneous mixture.
09:06:09 And we are below the console your point.
09:06:13 I talked about this a bit last week in the interfaces group.
09:06:19 Then, initially, they're all mixed, if you start at high temperatures but you come down to low temperatures after a crunch. And you see it coarsening, and the red face separates from the blue face.
09:06:34 Okay, this is to tell you how a binary fluid face separates and this is the process of course me.
09:06:43 Today we will look at what happens when we go beyond simple to fluids but the include effects of turbulence.
09:06:56 If you were just doing two fluids, or let's say two coexisting phases, which are distinguished by a scalar or the parameter phi at the simplest level you would write down a Landau Ginsberg functional, where this grad fi whole squared term gives you the
09:07:27 cost, the energy cost of free energy cost of having in homogeneity is and phi. And this Wi Fi is typically a double well potential, which tells you about the two coexisting phases.
09:07:36 So here's a plot of the fi a double well.
09:07:41 And in equilibrium. We are below the transition temperature, etc. So you'd be have two coexisting phases. And in the scaling that I have chosen phi is minus one and one of the phases and plus one in the other phase and define precisely at coexistence
09:08:00 and I demand that the variation in fi is only along one direction for y and impose the boundary condition that on the left boundary. I have one phase, and on the right boundary I have another phase, then in between that as an interface in this particular
09:08:24 case, you can actually solve it, it's a tangent hyperbolic interface with a width, which eventually will go to zero if you go up to the critical point.
09:08:35 But that's not what we are discussing today.
09:08:39 Now, if you put in the velocity field of the fluid. You have to generalize the above the Dow Ginsberg or card Hillier treatment to include the velocity fields.
09:08:54 So this is good old Nadia Stokes here up to here this is the viscosity.
09:09:00 This is the effect of gravity, where ro fi is the deviation of the density, from the density of the main density of the two phases that are coexisting general one and grow to this term over here minus alpha UB include when we do two dimensional turbulence
09:09:25 to this is the friction, which is absent in three dimensions.
09:09:30 we will look at low Mark number flows Divergent Series zero.
09:09:35 And the five feet evolves in this fashion.
09:09:40 Here is the new term when you add the defect so you got grad so this is how the fluid affects the scalar field fi.
09:09:51 If you did not have this term, you would have walked in the statistical mechanics literature would be called time dependent Ginsberg look down with a conserved order parameter.
09:10:05 This function here new is the chemical potential at it follows from a functional derivative of f with respect to fi.
09:10:27 The interface with over here is the sky and the surface tension can be related to the gravitas that these are, in my view, a very nice set of equations if you want to study to phase know which doubt actually be turbulent.
09:10:37 The only trouble is that there are many dimension less numbers there's Reynolds aspect lay there is something called a bombs number. Older saga number capillary number con number which is a dimension this measure of the thickness of the interface.
09:10:56 The Wii but number which is a non dimensional number with it's proportional to one over the surface tension and not and do not are characteristic length and velocity skills.
09:11:09 So I'll just give you some examples of the sorts of things we can study. So let's look at one droplet of the blue fluid in the red fluid.
09:11:21 But the flow is turbulence, that is external forces of the Cold War of sorts, which would keep you homogeneous and that's traffic turbulent so this is what it looks like.
09:11:33 The pipeline is the fight equal to zero control.
09:11:38 Now, you can go beyond these pretty pictures and you can actually analyze it.
09:11:44 So, given this fight with zero con two, you can calculate its perimeter in any simulation.
09:11:53 And you can compare it with the perimeter of it, and deform droplet of equal area at time t.
09:11:59 And you call this parameter gamma.
09:12:02 If you plug gamma versus time, especially at low Reynolds, low surface tension that is, I gave a number. It's really spiky.
09:12:17 You can get the property to distribution function for these.
09:12:22 And when you have a high surface tension so you have a model a secular droplet.
09:12:28 It is narrow. But if the surface tension is no this thing gets deformed quite a bit and you get a long tail.
09:12:38 And indeed, this is what I call spiky is the technical word is multi fractal, and you can find the multifactor spectrum by, you know, many means.
09:12:51 Again, as you might expect.
09:12:55 The multifactor ality increases as the surface tension decreases.
09:13:01 So, this we have discussed in this paper here.
09:13:05 That is the effect, if you like, of the turbulence on the droplets.
09:13:12 Now you can ask what is the effect of the droplet on the turbulence. And before the turbulence we can just look at the energy spectrum.
09:13:24 In the absence of the droplet you would have this purple line.
09:13:29 And then you add the droplet, you can see that it grows at small K.
09:13:37 This is reminiscent of what happens when you add polymers, to a nebula Stokes, the way.
09:13:44 And this change in UK can be part of a Christ in a way with a formula that I will not explain in full detail just now, but you can think of it as an effective scale dependent viscosity, which you can actually calculate from here.
09:14:06 You can see in this inset if it is large enough if not I can enlarge it in the discussion session.
09:14:12 And from this scale in dependent viscosity if you extract a dissipation.
09:14:21 Then you actually get the dissipation production exactly as you do in America.
09:14:28 You can also ask for the spectrum of the scalar. That is the field phi, just by k by minus k, and I have plotted it here, if you plot it versus kuc very clear oscillations.
09:14:57 it's more fuzzy when the surface tension is slow and the droplet is it formed.
09:14:58 And you can ask for these oscillations in K. And not surprisingly, they go roughly as two Pi over the droplets diameter.
09:15:08 So you can actually quantify quite well, the statistical properties of such a droplet in this flow and other thing which had mentioned was coarsening arrest I showed you coarsening.
09:15:29 But actually if you do a little more work and analysis which we did in this paper in 2d, and with Brossard director who had also studied it in 3d earlier with Federico Trotsky and David Nelson, Roberto Vinci.
09:15:45 You can look at the spectrum of the scalar field fi.
09:15:51 And from it, you can extract the length by taking this ratio is a bit like the integral scale in turbulence but this is where the five fields are one of those skills.
09:16:07 And, indeed, it's.
09:16:09 We have shown by doing a lot of simulations that this LC scales, as. Forget about the pre factor, but sigma to the three fifths, which is known as the hinge scale.
09:16:22 When you look at the typical sizes of droplets in a turbulent flows.
09:16:29 So you can look at coarsening arrested another way you, this is to the so you can ask at what wave number k does the inverse cascade get cut off.
09:16:44 Just like the course and then gets cut off at this hint scale this energy spectrum inverse cascade also gets cut off at some Casey, which is comparable to two pi over.
09:17:00 Else I'll end with a little bit on multiple droplets and turbulence. So here we start with 49 droplets. And we started running in this particular case the surface tension is quite large.
09:17:19 So, not surprisingly, the droplets all coalesce. And at the end, you don't have.
09:17:21 You know how only a few droplets left.
09:17:25 And you can you can characterize this in many different ways. I will just show you a little bit.
09:17:31 So you can ask what happens to the energy spectrum. Again, the energy spectrum rises at small K.
09:17:41 For the same reason as earlier again more so when the surface tension is small.
09:17:48 And you can also ask how the number of droplets decay with time.
09:17:54 And, you know.
09:17:56 You can also find that the rate of drop that merging increases as the way that number decreases.
09:18:04 You can also characterize the statistical properties of the scalar field by looking at the spectrum of the scalar field. And we also came up with a nice criterion for detecting droplet mergers even though you're running a complicated simulation you don't
09:18:20 want to look at it all the time.
09:18:22 But if you just plot the evil at the ends trophy it's a function of time. Every time there's a drop that merger there's a nice peak, and you can if you match it by it's exactly where there's a profit margin.
09:18:36 This seems to have been missed earlier, there was this mathematical work which I'd already described, so I will not go through it. Now, and neither did really tailor instability.
09:18:50 So now we have done similar studies in ternary fluid mixtures, but for that I will let Nadia take over and I'll stop sharing my screen.
09:19:02 If you have questions you can ask them now.
09:19:06 Or if you like you can ask questions after that yes talk.
09:19:12 David. You decide.
09:19:16 It was fine. Does anyone have any, any questions at this point.
09:19:21 Please raise your hand if you do.
09:19:26 Oh, ok, ok,
09:19:34 Ok pant.
09:19:39 Yeah.
09:19:37 Hi, dBu.
09:19:41 I mean, you mentioned, of course the, I think that we very important element of the hinge scale, which is central Yes, in the physics of these things and I'll talk about some length.
09:19:55 Right at the emergence of though what what you know again polymers are very much on my mind in this story, who as a contrast, you see the emergence of something that could be called an elastic range in other words a differential between a range that's
09:20:14 mainly hydrodynamic and then the range that's mainly elastic.
09:20:19 Exactly. I mean this is it. Can you see my screen this is the energy spectrum versus k over.
09:20:32 Then you see the stale goes up and that's where we calculate the effective of scarcity, we have calculated the analog of this quantity in simulations of Nadia Stokes, plus polymers which we deal with with a sophisticated PDP model which is much better
09:20:49 than already.
09:20:53 And the same effects exactly the same effect the tail comes up in exactly the same way. That is a scale dependent viscosity if you translate that into an energy dissipation the energy dissipation goes down.
09:21:06 So there's dissipation reduction.
09:21:13 Yes, sorry, continue. I'm sorry. Is there any reason you chose to sort of keep score in terms of effective viscosity.
09:21:23 Because when you have an elastic fluid, imagine many other things to to cast the answer in terms of.
09:21:33 Well you could I guess part of it is history. This is what we did when we did polymers and habitual use as a tropic turbulence, and even before that, I think, catchy or Laval have, and collaborators had done something similar in Wall bounded close.
09:21:54 So this is just, we had done polymers that's what we did there that's what we did here, and I mean you can come up with other things too. Absolutely, we'll come to that.
09:22:06 Thank you. Sure.
09:22:08 Thanks, Brian, please see in meteorology the primary usurper application of this result would be in the formation of of raindrops. Now in the formation raindrops The problem is that as two part particles droplets collide, a film of air forms between is
09:22:35 caught between the two impacting drops, and they simply bounce away from each other which makes it a strong, a very low impact parameter for the formation of droplets.
09:22:47 It doesn't matter how high the surface tension is they don't see each other because of the intervening layer of air that they bounce off. Is this in your equations.
09:22:58 Well, I mean, it depends on if it's a warm cloud and your air is code word for water vapor. It is.
09:23:10 To the extent that we have two phases.
09:23:12 So let me tell you what is not in the equations, when we write down the con helium type free energy and keep only up to the fight to the fort.
09:23:25 If you were doing critical phenomena that is expansion that is good.
09:23:30 Near the critical points so that the order parameter changes are not huge.
09:23:36 But here we are using it with impunity quite far away from the critical point.
09:23:42 Now if you really want to put in the full free energy for water water vapor.
09:23:49 I mean that would be a big pain but this smaller question of principle that, strictly speaking, if you have to face blows or three phase flows. This is what's physical mechanics would ask you to do.
09:24:01 What's the problem, the problem is on today's computers or even computers say 20 years down the line.
09:24:10 Strictly speaking, this is not doable calculation that typical cloud is 10 kilometers and typical droplet is micrometers.
09:24:19 So, you know, we're not going to do it on the computer but I think it is important, at least from my point of view. To begin, where we can and see how far we can go.
09:24:31 Otherwise, you have to have all certain parameters were, you know, collision rates of droplets and some, you know, parameters that take care of surface tension and so on.
09:24:41 those are more phenomenal logical.
09:24:44 And you have to measure those parameters and that's one of the things which makes cloud physics.
09:24:50 Okay.
09:24:52 They've come a long way but, right, that that's all I can say.
09:24:58 Thank you.
09:25:02 Okay, thank you.
09:25:04 Thank you. I'll stop sharing my screen so Nadia can take over now. You
09:25:15 Can you see my screen.
09:25:18 Now, yeah.
09:25:22 I'll talk about ternary mixers. And these are my outlines.
09:25:28 So, at the past point, why we should worry about toner refill mixtures.
09:25:34 If you see in nature. The money system contains more than two fluids to a miserable fluid. So here's some examples some experimental setups. So, here, one compound droplet which contains three musical theories and here one is passing through one invisible
09:26:02 liquid liquid interface. And this is one floating droplet. So, at the moment, we have three different fluids. So we have three different interfaces.
09:26:09 So we need to model all these three industrial fluids and three interfaces. So we define three different order parameters which are the concentrations.
09:26:22 And we define something called free energy functional, which content. One is, this is called vault free energy this is coming from the mixing. And this is coming from the interface, feel free energy.
09:26:38 So in this setting we have three different sufficiency and coefficients.
09:26:44 Sigma one two for the interface, one, two, and sigma 13413 interface and sigma 23423 interface and j is the interface in thickness.
09:27:01 So, like in binary fluids, we have double for NCL so what internal employees we have three minima. So we take gifts triangle and project this potential on this gives triangle, where all the three What is his representative your guys's team you see will
09:27:31 and all sides of this triangle represents the minimum three energy pot. So we like the comedian obviously equations for the stoner employees, which is kind of generic extrapolation of the binary one, so here.
09:27:44 Here is the only difference. We can have three different social justice at the plate, and this is incomprehensibility condition. And this is our vocabulary questions so there are two Camilleri questions, we need to solve in our numerical methods for Suwon
09:28:04 and see to water parameters, but the third one we can get easily from this conscience you one plus two plus it equal to one and a music in competence yellow PCs functional derivative of the P energy functional.
09:28:22 And we add something called longer longer and multiply and CEOs discussion constant and gamma is the interface of mobility.
09:28:34 So I want to comment on this digital interface model.
09:28:40 So, one can ask.
09:28:43 In many experiment and measurement.
09:28:46 The individual thicknesses of the order of nanometre, and by certain extremists on the value of mobility is found to be 10 to the minus 17. So, these are very small numbers, and it is very difficult to simulate, and to reach such length skills.
09:29:07 So, in this talk will use physical matter which use. You just interface which is our finest pilot thickness, and we call it the user interface matter.
09:29:23 can converse to watch the actual solutions. The soft interface limit for Jai, and mobility goes to zero. So, these are certain estimations, like if i is less than equal to four times in this dishes land scale which is defined like this, and your mobility
09:29:53 should be
09:29:56 similar to your chi square, then the solution will converge to the staff interface limit. And this pace will matter chameleon average talk method will be easily validated.
09:30:15 For many physical situations.
09:30:18 So we use those that don't matter.
09:30:22 But, solving this CNS equations.
09:30:28 Yeah. So, the corner equation, it does like minimize the free energy.
09:30:37 For example, if you take two different invisible fluids. The blue one is the one droplet sitting at the interface between two different flavors. One, two and three, then eventually at equilibrium, it will take difference if depending upon the saffir Simpson
09:30:57 coefficients, like, in this case, the surface of a lens is looking like a lens. So, this is Kennedy energy, the droplet OSI layers and eventually it reaches to steady state, an equilibrium state, and the geometry is looking like a lens.
09:31:18 So when we talk about team usable fluids. The one thing comes. Always is called awaiting, and we define something called waiting parameter, which is minus of sigma, this sigma i is one of the coefficients.
09:31:40 From the interface LTNSG, and we call when, when this mode, who is positive, we call it total waiting. And for the negative W, we call it faster waiting, like in this case for the lens, this is possible wedding.
09:31:57 And for these three different scenarios. All total waiting here.
09:32:14 The blue phases, with two and three like two other red and green, and likewise ew three is for the deep. And
09:32:14 this is where it's one and this thing.
09:32:21 So, by using this Canada now is true for the ternary fluid so you can study different kind of physical situations, and one of them is compound droplet dynamics in turbulence.
09:32:36 So, what is compound droplet compound or player is droplet is encapsulated by another droplet, and that is one food words, other to fluids.
09:32:47 And here we each call mobile forcing to get homogeneous and I sort of toggle ends, and we call Laconia equations for with this compound of letting sell conditions.
09:33:00 So, these are two content blocks of what is he, but this normal binary droplet, and this is for a compound droplet. So you can see the difference of the chlorophyll of the voting city for the normal case and the compound or of lettuce.
09:33:21 And the RT different snuff sorts for this compound droplet.
09:33:28 And here in this study, what we do, we change the size of the know droplet, and we fix the outer darkness eyes, and we see the deformation of the other interface.
09:33:39 So basically what is the effect of this inner droplet on the outer interface, like in this is kind of people use this model this compound droplet model for the WBC sell in the blood.
09:33:54 So this is nucleus for that WBC sell, and this is the outer thing.
09:34:00 So, here the plot for deformation parameter with time. So, the first parameter is basically measure of the information about interface here. And we can see the long spike here.
09:34:25 Like, when the inner droplet is very small. You can see the long spike which, which includes 34 minutes and this is the cumulative PDF of the difference and.
09:34:30 So, the patience of the inner drop layer leads to more deformation of doubt and face, and the formation gets suppressed for larger in our droplet size.
09:34:42 So, similarly, here, measure the distance between the center mass center of mass between these two droplets, and here also the cumulative PDF of that, and easily the one can so that for the
09:35:03 higher droplet higher rate I radius of the inner droplet, the fluctuations of the outer interface is suppressed.
09:35:16 So, that is another physical study, which is a quite experiment in Asia.
09:35:27 This is called sense of droplet, and then lenses. So, when to drop less common contact if these blows in time, and leads to paralysis.
09:35:39 So the growth of the breeze follows power with different scaling exponents, depending on the flow parameters.
09:35:47 So for spherical droplet Carlson's, which is done extensively in the experimental and the medical simulations, the trees will grow as did the one in the viscosity, and to the half in the inner civilization.
09:36:08 But one decent experimental study reveals that for liquid lands, while since this growth mechanic john for those either one in the risk decision, but people are two by three in the region instead of half.
09:36:22 So, I'm going to so my symbolism results for this lens, while since this is circular plot for the face fields for the landscape and since this is these are two lenses, sitting at the interface between two invisible fluids.
09:36:41 And this is the time for loosen up the control. This is 015. c one equals 01512.
09:36:49 So, the source they will do some of the country. And this is the white component of the velocity field of this interface.
09:37:00 And, at the please. And this is the time evolution of the white component of velocity field.
09:37:10 And the plot is for the breeze growth for different simulations, like, four different answers number.
09:37:18 The data collapse in a single slot, when they exist scale by the resource and length scales, time and land skills. So, therefore from different simulations.
09:37:41 So for this reason there is, there is one clear crossover between two different power regions. This is for two to one and this is 42 or two by three. And this flood content, different size of the lenses.
09:37:47 So, this power law is independent of the size of the lenses which are going to boil since.
09:37:59 These are the presser Laplace tracer. Like, it is visible that this growth mechanism is developed by the curvature, and which is related to love love stressor for this viscous region.
09:38:20 This is a lackluster and for just initially john This is. You can see my small over just coming at the interface at different places.
09:38:28 And this is something comes through something surprising results like for this lens questions. it giving stairs to this nervous to Floyd.
09:38:41 If you see the kinetic energy spectrum here.
09:38:45 This is the time of evolution of the spectra. And one can see it is on can see the color of skin and get to the minus three, at some point.
09:38:57 So, even with. If you see the dance number, it is of the order of one. But even with many small runners number one can see calm.
09:39:16 Like, this is something similar to the elastic turbulence, where at very Lauren someone can get turbulence, like energy at all scale distributed at all skills.
09:39:19 This is another sector for Kyu wave number, and this is for PX webinar.
09:39:29 And similarly, this is Christian space Spector 5151, he.
09:39:46 It is defined in the binary case. So this is for the one or parameter, this is, this scaling is getting the minus two. And this is for second one seat of his field, and this is across 5152.
09:39:57 All scaling circle to manage to.
09:40:01 So, my conclusion. So we are able to simulate different complicated multiple systems using our Canadian average tricky questions. And this car system provides an elegant model for binary and ternary fluid flows and not that we don't have to enforce boundary
09:40:18 condition on the moving droplet boundaries, and even at very low last number we have zero tolerance, it says in the system similar to elastic turbulence, and we need to something.
09:40:32 Studying more in this sense.
09:40:36 Thank you for your attention.
09:40:40 Thank you, Nadia.
09:40:43 Questions anyone.
09:40:46 Can I ask a very basic question.
09:40:49 Yes, when you're choosing your potential.
09:40:53 Do you have a lots of choices you could make for for the mean how can how can strained is your model, I suppose is what I'm getting at is your choice, kind of, chosen to be the simplest or is it chosen from what you know.
09:41:15 The simplicity of, like, when you botched up the tunnel if you is, it is kind of orderly, like extraction from the binary one. So, so when you start from the Turner eating.
09:41:23 And if you switch our switch off, one of the pages, then it should converge to the binary one. That is one criteria. So, yeah, obviously, one has to choose the simplest model for that.
09:41:38 If you see the binary fluids like the free energy is actually if you calculate it is logarithm functions.
09:41:46 But people use wl for 10 sales for simplicity.
09:41:52 So, it's for simplicity we use this potential one can use other other buttons and knobs.
09:42:01 Okay.
09:42:06 What about could ask an even more basic question about the choice, the choice of the current Hillier the equation is the continuity equation chosen because it has no nice properties.
09:42:20 Are there other equation that have no nice properties that you could couple of is the current led equation, the absolutely the right equation.
09:42:29 I know I can see your link on here because when you have invisible fluids, all the fluids conjure, then you should have some equation which is conjure in mass, like another equation.
09:42:52 My comment I think it's perhaps the simplest you could write up.
09:42:56 Of course you could think more complicated equations.
09:43:00 But even with the simple one we have so many parameters and so much to me I'm just going to add kind of the same comment I mean if you think, in, in, you know, a statistical mechanics problem from a mean field theory, what's the simplest thing you can
09:43:19 do for the free energy, the answer is ginsburg oh and down. But then you realize you got to conserve things here conserve mass. So then basically the marriage of conservation and ginsburg lambda equals calm Hilliard is the way to say, the way I look at
09:43:37 it.
09:43:41 Perfect. That's exactly right.
09:43:52 There was some discussion questions that we wanted to put, because some parts of this meeting are also doing things like transport barriers.
09:44:03 I think they have not been explored very well in the content is setting.
09:44:10 In particular, I think, even the direction of the branch in tracers or Harry Potter goes at the level of the next year it got in your liquidations all that says wide open as far as I know, and this could access.
09:44:27 Well I mean I agree in general I mean we have looked at barriers in to DMHD, which is tomorrow, I guess Fridays entertainment in in Pascal's group, but I mean, it's certainly an under explored area.
09:44:53 Okay.
09:44:55 Anyone else night to ask anything.
09:45:05 So obviously very early in the morning, late at night.
09:45:14 Okay, then we'll, we'll move on to
09:45:20 to perhaps talk.
09:45:26 So, Nadia, if you would, unfair so I can share. thank you.
09:45:38 And
09:45:38 I have a few inflammatory comments at the request of our maximum leader at the end. So, can everybody see.
09:45:50 So let's all right good so this is, there's a lot of you graphs, but I'm, you know, although I live in San Diego I'm hard to fast talking New Yorker.
09:46:02 So this is about ch ns turbulence and the bulk of the work was done by Shang fan a student of mine, and like so many times we've heard in this meeting, meeting he's gone off from science to the pursuit.
09:46:17 The pursuit of riches but I keep in touch with him so on we chat so I hope when he makes it I can send him a grant proposal and acknowledgments to I think many of the usual suspects here.
09:46:32 And let me say you know it's like when you go to the doctor, they say that you ask for a specialist they give you three names, so I'll give you three papers if you're interested in this and ours are at the end.
09:46:57 A classic old paper along the lines of what I talk about is the famous paper of Ricardo Ruiz and David Nelson now 40 years old, facade pearly car and else, his red letter which was mentioned is another good one helped help trigger our interest.
09:47:05 And I also recommend you who rules over the view or review article in physics of fluids which captures a lot of this stuff and relates it to other systems.
09:47:17 We've heard the Khan Hilliard equation described I think I counted three times now.
09:47:24 I'm just going to write it down and so I'm going to write down the two dimensional ch ns and to DMHD equations and here's the CHNS and here's the two DMHD and you'll note the obvious similarity.
09:47:39 I tried to highlight the differences. Why am I doing 2d The answer is not because I've been absorbed into zoom worlds but because there are good reasons for I'm thinking about 2d, in the world of fusion physics and other words to D captures all the nonlinear
09:48:00 physics of 3d reduce them HD which is sort of the most basic reduced model so the point of the 2d is the it's it's good when you have a severe constraint on the third dimension like a strong magnetic field and I have backup slides on this.
09:48:19 So you can see immediately see you have infection of a scalar field which is the density contrast.
09:48:26 The the con Hill your structure on the right sort of in place of the simple resist of diffusion. And in both equations, the kind of a Lawrence for structure Lawrence for a slight structure, which is due to the, the effect of the chemical potential gradient
09:48:45 on the vortices it right so BB sigh here is the cross grad sighs so the similarity is obvious and by the way Ruiz and Nelson picked up on this 40 years ago.
09:49:00 And in particular, if you look at the high magnetic Reynolds number or high pack claim number where you have, in some sense a nearly ideal system, the shopping list of conserved quantities is similar energy.
09:49:15 concentration is the counterpart, and even something like a cross Felicity in each case I won't talk about the cross Felicity at all here.
09:49:28 The other thing is that if you have a system where you have a density contrast in other words different phases, you immediately see that the CHNS system supports a linear elastic wave.
09:49:45 And this linear elastic wave which can be weekly or daily or weekly damped or growing depending on the K but it.
09:50:03 But, you know, is dominant Lee a real frequency for a strong density contrast, B is like the density contrast. This looks awfully like our dear friend the alpha brainwave, it's more accurately like a capillary wave at the phase interface propagating only
09:50:14 along the interface of two fluids, where the gradient inside is non zero. It's the analog of the alpha brain wave and important differences, It's a large only in the interface or region.
09:50:29 So the elastic wave activity does not fill space. So, CHNS definitely qualifies and as an elastic fluid.
09:50:40 And I was out a little meeting on elastic fluids before this one at in a zoom sense and it was depressing to me to see not a peep about CHMS, they will come back to elastic fluids later.
09:50:54 So the first thing I think someone in this crowd my think of what have a single Eddie, which brings us to the homogenization problem.
09:51:04 And in the spirit of magnetic fields the simplest to marginalization problem is flux expulsion pioneered by the late Nigel lice in 1966 in which our distinguished chairman is one of the experts and the idea is you wind up the flux into the boundary of
09:51:22 the Eddie so in a sense the flux is expelled from the Eddie, ultimately back reaction can assert itself, some references here I think both owls are here and this point but we won't get into back reaction, simple way to expand to understand MHD flux expulsion
09:51:42 is this little grunt and hand gesture argument.
09:51:46 You gotta conserve the flux through the Eddie while you stretch the field and wind it up so little be is bigger than big be and little owl is less than the size of the Eddie.
09:51:58 And then you have a raid balance between wind up and dissipation of the stretched field and you get the expulsion time. And the key point is that scales is magnetic rentals number to the one third, and my the plasma people should know that it's one third
09:52:15 and not one half like you get in sweet Parker there's a story behind that. But there's no time for that now.
09:52:23 So if you undertake the same exercise with the con Hillier now VA Stokes, you get an interesting contrast you have a three stage evolution, which I call the jelly rolls stage, a winding up.
09:52:42 There is a topological or evolution or reconnection stage where you go from, from a spiral structure to kind of a layered or target structure, and then the slowly evolving target pattern which exhibits coarsening right so the point of this and on the
09:53:02 last stages sigh is ultimately homogenized on a slow timescale, but meta stable targets patterns form and courses, and in the end you're back pretty much to homogenization.
09:53:16 The key timescale is little different than the Weiss classic, because of course, the here the dissipation is hyper diffusion rather than diffusion. So you get scaling with pack play to the minus one fifth and the con number to the minus two fifths, and
09:53:33 the con number really helps you to separate the timescales.
09:53:39 And if you look at the evolution in time you see the three stages here not too surprising. What is interesting is the third the coarsening stage I mean in the classic paper of rhymes and young, on, on homogenization they present the kind of a two, a two
09:53:59 timescale argument where the first scale is your dispersion on the Reynolds number two the one third and then there's a slow viscous Missy mixing stage of Reynolds just with Reynolds number in ch en su get rather a more complicated story which is a kind
09:54:18 a kind of punctuated evolution, and the punctuated evolution is of course the process of band merger and we've heard about you know how to say it bubble mergers, etc.
09:54:46 merger. And by the way, note that they, the x axis here The T is logarithmic helps understand that. And then I compare of course the, the band mergers to the bubble mergers in one of our,
09:54:54 sort of, it's a ballsy model applied to drift waves just, you'll hear more about that next week, but that sort of brings out the similarity.
09:55:05 So now we come to the main event, some aspects of CHNS turbulence and it's a very much a comparison and contrast.
09:55:14 So a quick primer on MHD turbulence of course and stuffy conservation is broken.
09:55:23 What, what differentiates MHD from ordinary fluids is you have both Eddie's an alpha brainwaves and so CHMS will have these elastic waves and Eddie's Okay, you get a dual cascade very important forward and energy and inverse in a squared, and an absolutely
09:55:44 fascinating conjecture due to a neat bouquet at a coffee break in a meeting in po Hong we were at some years ago, kind of triggered some of this.
09:55:55 And we were it was about a meeting on MHD and she said, you know, the conventional wisdom is we got to get the the the energy, right, what's the correction to Commodore off and as many or most of you know, the Wars of religion have been fought over that
09:56:12 and they're still going on. And you know we need a Treaty of Westphalia, but in fact is that the right thing to fight over, you know, conservation of a squared is more related to the freezing in law in 3d conservation of magnetic Felicity is the critical
09:56:30 thing right that's what goes into Taylor relaxation and all these general principles. So in some senses the inverse cascade of a squared or the magnetic Felicity really the important process with energy dragged off the small scale by the fluid and have
09:56:49 we missed the boat and what we're thinking.
09:56:52 So I call this the bouquet conjecture. And, well, the CHNS illuminates this nicely so you know the conserved quantities.
09:57:03 So then we come to scales and ranges.
09:57:07 And you can see the difference between unforced and forced for look real you know fluids here at CHNS systems. And the fourth system of course produces blobs a finite scale structure the unforced system it just goes to a phase separation.
09:57:27 And those blogs are in a scale called the hidden scale which we heard mentioned, which is one of these very important emergent scales it's the counterpart in this problem to asthma of rhymes and beta scale, etc.
09:57:43 And, and it loosely is where turbulence training is comparable to the elastic restoring force if you would in a simple terms if you wanted to understand what the hint scale is.
09:57:56 Think of a little problem for the order of order of magnitude physics class you might teach and you ask the students. What's the size of a raindrop in a turbulent air flow and you might balance turbulence training versus capillary it, and that'll set
09:58:13 a scale and that's the hinge scale, and it just a little bit of bells and whistles a little difference from the, what you saw before because this is 2d.
09:58:23 OK, so the consequences of things is you get the emergence of a new range which we call the elastic range which extends roughly from the hinge scale down to the dissipation scale.
09:58:40 And the, the, the requirement for the emergence of a clear elastic range is this quantity of course be large, and they you know there's not much play except the viscosity.
09:58:53 Okay.
09:58:54 And it's in this elastic range that the interesting things happen right and this of course is somewhat related to the idea of an elastic range and the polymers, but here the elastic range as much larger something will come to at the end.
09:59:11 Okay.
09:59:21 So the key physics of this elastic range is blob coalescence so a simple well known scaling argument you can do gives you the blob size increases as key to the two thirds in 2d if you want to see where it comes from.
09:59:28 Just balance Reynolds, you know, vv with the restoring force and that gives you the scale.
09:59:36 If you have forcing the blob coalescence will be arrested at the hinge scale so you'll see four different strengths of the forcing you ask them to the two thirds power law here in the cut off, who is the blog growth is saturating at a scale that tracks
09:59:54 the human scale. So the blob coalescence really suggest the inverse cascade of size squared is fundamental here.
10:00:02 And if you look at the pretty pictures, right, of course, you see, the CHNS is somewhat somewhat coarser than the MHD, but otherwise okay you have an analogy between the inverse cascade of magnetic potential and the inverse cascade of size square.
10:00:22 So you might think Aha, we just we're going to go off to a duel cascade, and things are going to be like MHD. All right.
10:00:32 Well notice I right, once, one might think.
10:00:37 And at first, it looks good, if you look at the spectral flux of a squared and the spectral flux of size squared, they look sort of similar and I should fess up and say for the spectral flux of a squared we inserted a week, forcing have a small scale
10:00:58 level the playing field with the CH ns, which is in some sense weekly unstable going from, you know, from small to large due to the con Hilliard structure.
10:01:11 But you see in both cases very clearly a negative power transfer. Okay.
10:01:19 The point is the CH ns is on force so it aggregates naturally, you have to pump the magnetic potential a little bit to see it but when you do it's really a small pumping.
10:01:32 You see very clearly an inverse cascade of a squared.
10:01:37 And if you like spectral plots you get them both here I mean they're not the RRCHMS is better it's clearly shows the seven thirds, the a squared is a little sloppy but people have done a better job than us like Jonah and Joe and collaborators for example
10:01:55 in the seven thirds is quite clear in a squared and MHD.
10:02:01 So I'm not going to talk about where the the the seven thirds comes from and any but we can come back to that if you want them to know.
10:02:10 Now the fun part is, however, more power loss, so then you go all it's just going to be boring it's just going to be like MHD.
10:02:19 And then you make the plot of the kinetic energy expecting the old Craig men special of K to the minus three hats.
10:02:28 Well in to DC HNS you get something lighter we got at least more something closer to K to the minus three.
10:02:36 And this was a bit of a problem, I mean by the difference is big enough it couldn't be due to computing we spend some time on that.
10:02:45 And you'll notice the K to the minus three immediately triggers the memory of the entropy cascade rage and pure to the hydro.
10:02:55 So you might think why is this thing with the scalar field in the back reaction behaving like pure to the hydro where there is no back reaction. And why does the ch NSMHD correspondence hold so well yet break for size squared, yet breakdown for energy
10:03:16 and watch physics underpins this surprise.
10:03:19 Well the answer is the interface packing matters. So you got to understand the differences, little bit of a departure from Ruiz and Nelson, as well as the similarities in 2d MHD the fields pervade the system into DCHNS the elastic back reaction is limited
10:03:41 to regions of sharp density contrast where grad size zero and other words interfaces, everything is the interfaces.
10:03:51 As the blobs are coalescing, the interface or region is diminished. So the active region of the elasticity is decayed I mean you just compare the two pictures.
10:04:03 You can do a little better than drawing a pretty picture you can define an interface packing fraction, which is the number of grid points where the magnitude of be beats be RMS were divided by the total number of grid points and you can put a multiplier
10:04:21 there as long as it's not ridiculous. Either way it doesn't matter much, and you get the punch line here, the packing fraction is roughly constant in MHD but the hate decays precipitously in time for to DCHNS.
10:04:41 So what that is saying is the inter the in a sense of the volume fraction of interfaces are decaying. So at the same time the volume fraction where you can have a significant back reaction is decaying so maybe it's not so surprising that the behavior
10:05:00 of the kinetic energy at long time is looking more like to de hydro, and this of course is just a consequence of coarsening due to Bob to blob coalescence right it's simply courses the interface network.
10:05:15 So what are the lessons of this little story. Well, they are to avoid tunnel power law a tunnel vision, like I said, the real space realization of the flow is necessary to understand key dynamics.
10:05:31 And we found it very useful here and it was I was pleased to see in Rahul and Nadia was talk kind of the same thinking that it's important to track interfaces and they're packing fraction.
10:05:45 It seems one player in a potential dual cascade can modify or constrain the dynamics of the other.
10:05:53 and against the conventional wisdom size squared inverse cascade do to blog coalescence is the robust nonlinear transferring to DC HMS that's the important process.
10:06:05 So at least receive HNSQK and her conjecture we're clearly right there's just no doubt about it.
10:06:12 And it begs more attention to thinking more carefully. I mean, about things like magnetic Felicity and 3d MHD I mean maybe they're not an afterthought to two other things.
10:06:27 Now, David asked me to be inflammatory and this is my last real slide so I'll honor the request from our fearless leader so what else couldn't come to mind.
10:06:41 So we have a really wacky one.
10:06:44 Well we have beta plane MHD of Tobias at all. At the speaking and all is the chairman.
10:06:53 Why not have beta plane ch ns, and this is not because we have visions of CHNS to mitigate global warming or something but one could imagine, say an experiment where the PV gradient is produced by something like a slope bottom, or something, it's not
10:07:13 as wacky as its as it sounds, and one could imagine say a physical experiment which is quasi two dimensional swear you would actually could actually play with a to DC HNS system.
10:07:28 I haven't worked the numbers out about that but I think it's not unthinkable.
10:07:33 And the point here is from a theoretical standpoint beta playing CHNS just points immediately at the interplay of these two emerging scales rhymes and Hinz right i mean that's just begging to be looked at and would be a very interesting challenge to the
10:07:52 cases where you have only one emergent scale.
10:07:56 Now drag reduction which Rahul has mentioned a few times is also comes to mind it's it's slightly less wacky.
10:08:05 Let me just say in a pipe, which I think is kind of the gold standard problem of drag reduction.
10:08:14 Drag reduction is really a transport barrier problem just think of Lumley's buffer layer handle all that. So the question is how does CHMS that stack up against the gold standard of polymers which might be described by old Roy be or an infinite variations
10:08:32 there up.
10:08:34 One thing all these models have is the point that there's a linear damping term the zoom relaxation damping which is scale independent. So really only a small part of the inertial range where the straining rate beats the zoom damping rate is in some sense
10:08:53 active CHNS looks to me to not have that problem right in other words activity will occur when the straining raid beats the hyper diffusion rate, which gives you a little more leeway for a significant active range and what gives you a handle.
10:09:16 By the way, I'm controlling the hyper diffusion is the con number, which you you know you could try to drive small that's just the ratio of the thickness to the scale.
10:09:28 D is the same diffuse activity that goes into the pack play number. So in some sense ch ns actually to me looks more promising for drag reduction than polymers, and it's something that ought to be followed up and so I think something with, you know, like
10:09:46 a physical boundary, it seems perfect as a transport barrier problem, and therefore papers on this and here they are. And there's one more on the issue of transport barriers in this for looking at to DMHD but inspired by that work, and that's this one
10:10:07 up here and that's sort of tomorrow's talk in the interfaces group. So with that, I'm sorry for running over and thank you for your attention.
10:10:21 Thank you, Pat some very interesting
10:10:25 questions, comments,
10:10:33 comments that actually can helium, Nadia Stokes Lloyd might be better at track production that polymers, it's a very interesting suggestion.
10:10:44 even without going to vote counted flows.
10:10:48 Do you think we could just look at dissipation reduction and try to see that.
10:10:56 Yeah, I would, I mean, the answer is, I think, yes, I mean I think would be interesting just to do at same Reynolds number and here you really got to mean Reynolds number rigorously just do a head to head comparison of the polymers, and the and and the
10:11:35 And also look at the comparative size of the elastic range or equal Reynolds number, my suspicion Rahul is you've already got that data. Right.
10:11:47 And so, so.
10:11:51 Yeah. Okay, thank you. Good. But I mean, my I mean not to be to not to poop the party but whenever whenever I deal with to, to bring memories of KITPS past you know real drag, producers, I get hit over the head with the, with the pipe.
10:12:10 You know you're not you're not, you're not going to get, you're not going to sell these guys until you face the paid flow problem, you know your apps, if you're right I've been hit by the pipes and.
10:12:22 And I think there you've really got an advantage because what's happening with polymers is you want more of an active range you want a wider buffer layer which is a wider transport barrier.
10:12:35 So that drives you to big polymers to lower the zoom frequency and big polymers are very susceptible to breaking just being stretched and fracturing in a turbulent flow, and the sponsors for drag reduction you can guess who that is don't like that.
10:12:54 And so now can heal your system will have a disadvantage and it might involve bubbles and the sponsor for drag reduction.
10:13:05 Well for surface ships, that's fine for other kinds of ships bubbles make noise and that's not fine.
10:13:14 But I, you know, there's a, there's an.
10:13:16 It reminds me of the fusion program, honestly, there are these trade offs between scientific reality and engineering desires in both cases but I think the con Hilliard should be explored it hasn't been for drag reduction, except for your work raffle.
10:13:37 Sir, will push it some more. Thank you for the ideas.
10:13:42 Adrian.
10:13:45 Hey, thanks. This was a helpful talk as somebody who's unfamiliar with Khan Hilliard, as well as the other ones today, by the way. Thanks everybody.
10:13:54 So, so forgive me if this is a dumb question because I'm new to this kind of related stuff, and this is about. I think the battles that you described as religious appropriately that HD conflicts, which occurred before I entered the field as well so maybe
10:14:09 there's going on now they're not over right I agree, I agree, but but still I missed some of the stuff that I'm alluding to, so forgive me if I got it wrong but I believe that the conflict of the slope in the inertial range, kind of, part of the reason
10:14:25 why it's important is that it speaks to a difference in interpretation of how the eddies interact with each other right sort of sharing versus advocating.
10:14:33 And I'm wondering if the, the slope that you found to be surprisingly different here similarly says anything about sort of the interaction of Eddie's in con Hillier it as opposed to an HD, because the question makes sense.
10:14:44 Well it does. I mean on the bed.
10:14:57 I think there's fights over details which by the way are really fights over priority but,
10:15:04 but they, you know, one thing I think most sane people have converged on and it's of course due to Craig min and a Russian kickoff is the point that you no longer just have ABS you have alpha brainwaves right and you have to you have to understand the
10:15:24 inter the progression of the Eddie in the presence of alpha brain waves and the key point is, you know, things only happen when you have to counter propagating alpha brainwaves that in some sense, beats to a low frequency mode and drive and Eddie it's
10:15:43 very much like me a plasma physicist looks like nonlinear Landau damping, right in other words waves are reversible. And the only way you get irreversibility is when you beat it to low frequency.
10:15:57 Okay, and in some sense resonates with the fluid.
10:16:01 So that's why there's a difference of MHD and and Eddie's, and the the key, then they're all kinds of fights in the bookkeeping and accounting of that which I mean we'll be here all night.
10:16:19 Now CHMS certainly has the same property, it has elastic waves but what's different is the elastic waves or pinned to an interface which courses.
10:16:32 So it says the waves are getting weaker and weaker and weaker as the bob coalescence progresses. So that's why you get back to to the Hydra dynamics type trends in the end.
10:16:47 I don't know if that helps you. So the, the effects of MHD, that makes it different from hydro basically sort of going away in time. Well I'm on the th en s.
10:17:01 That makes it different from MHD is coarsening, which makes the back reaction decay in MHD it does not course it. Okay, and the back reaction does not decay.
10:17:14 That's the point.
10:17:15 Okay.
10:17:18 Got it. Appreciate I've got a follow up question. If no one else has questions but I'll wait to see if anybody else as well go ahead Adrian You're right.
10:17:40 Well, you also may not follow this slightly and really you were put on the subject of comparing to HD I think you cited that Mac paper on on flux expulsion and vortex disruption.
10:17:31 Yeah, well there's the criminal is right above you on my zoom he Right, right.
10:17:41 But I, in the spirit of comparisons between MHD and CHMS.
10:17:53 You know that that paper had this like scaling of like alpha and Mach number and the magnetic number. And does that extend also the CNS stuff I mean can you set up a system where you can officer I take the scaling Where do you get for text disruption
10:18:00 in staging areas we wanted to look at that that the student graduated so our flux. Our expulsion studies did not include the back reaction.
10:18:11 We should have, of course, let the great man above you comment on the bed, let me just say the point of that in my mind is that identifies a criterion in which you get a back reaction.
10:18:28 And you will see that criteria and appearing through a different route in my talk, I guess it's Friday for Pascal's group.
10:18:38 On the subject of clinching of the diffusion, or transport of magnetic potential.
10:18:44 Okay, so that's why that is not it disrupts vertices, but it is also a very physical perspective on the onset of clinching clinching of diffusion of magnetic potential which is an absolutely critical problem, because then that starts poking the finger
10:19:03 in the eye of the kinematic Dynamo, and I we should of course turn it off, turn it over to all of my Mac at all to comment further here.
10:19:18 All no particular comment on that.
10:19:23 Well, I have a comment, it's sort of related maybe about the two systems.
10:19:28 So, In the flux expulsion game.
10:19:35 You will recall there was a great lot not a great, there was a disagreement between two of the greats between Nigel vice and keep them off at on timescales, right.
10:19:49 And
10:19:49 in between Keats first book, he gets it wrong, right, and then he right and then there's paper can call and off it gets it right was Nigel gets it right.
10:19:59 So the interesting thing about why Nigel get got it right, is because he used the induction equation in its before, even though he was doing to the MHD.
10:20:08 If you know easily use the induction equation and it's a form, you get it wrong. And then that, which is kind of puzzling in a way and you have to, and then Keith kind of reconcile this by saying, if you had matter over the whole history and this kind
10:20:24 of thing.
10:20:25 Now you you evoked the Niger scale.
10:20:31 But in the current period you don't have another equation in the induction in the magnetic problem the equation really is to be equation, as it were. Yeah, but in this room.
10:20:41 In this one, you don't have a be equation. Typical observant of you, David.
10:20:48 You know, do it, you know, we do different things, this was for pedagogy right I rather than bring out Moffat and cam car but i i thought it. Well I was reusing a slide for a different audience where I thought a grunt in hand gesture would go over well
10:21:06 and you're right this is from me. But this thing down here which I just blasted through this we got from a Moffitt and cam car time card.
10:21:18 Okay.
10:21:19 As usual, you're good at catching all the little swindles.
10:21:25 So, in that MHD disruption, business, I mean there's there's
10:21:34 your student has given talks on this I haven't read the paper admittedly so forgive me if again I have a dumb question but it seems like there's a distinct difference between the action of small scale fields, you know, Mac through the maximal stress versus
10:21:50 a sort of the coherence of parental stress. Do you expect the same thing would emerge in the CH ns system, I mean is there is there like a maximal stress equivalent and then we talked about the phases around stress versus.
10:22:03 I mean, like I say I wanted to do that and by the way I wanted to do drag reduction that the student had enough Sean had enough for two PhDs and, you know, he.
10:22:19 I think justifiably demanded release from captivity right I don't want to be tried in The Hague court for human rights abuses. But I mean, here it is there's, there's the Maxwell stress.
10:22:33 Okay, or you can convert it's an equivalent there up. Yes.
10:22:37 And we won't do that today Pat was.
10:22:40 You didn't have that gluten at all, in anything use that today not not I did have the blue term and the turbulence I did not have it in the flux expulsion bit.
10:22:49 Okay, okay.
10:23:03 So I mean one thing to do is to revisit Mac at all and then in this system but i think you know you're going to get very similar results with some factors of see running around and stuff like that, that not sure, you know, I would bet that the sort of
10:23:09 here into the mental stress to be very different. I think that the, the added damping terms are going to make it so that you. Oh yeah, I mean the one of the points okay yeah that's certainly true I mean, the point is that magical ratio.
10:23:27 The way I look at that magical ratio which is Friday's talk is comes from his elbow which balance, which is a dissipation of magnetic energy, a contract in competing against a transport or flux of magnetic potential.
10:23:45 Now here in the con Hillier the dominant player in the dissipation is going to be the hyper diffusion rather than the diffusion so there's, there's going to be some difference.
10:23:56 Yes, it's going to be different whether whether it's really a conceptual difference or not I don't know yet. Okay, that makes sense, good problem to do.
10:24:07 Okay.
10:24:08 Thanks for humoring the random questions.
10:24:18 Okay. Does anyone else have things to add.
10:24:25 Um, David. Can I make a comment in the interest of historical accuracy.
10:24:32 Please, and that is that I believe that the, the RM to the one third timescale for flux expulsion was actually first found in a paper by Jean Parker.
10:24:46 Oh, okay.
10:24:52 But others may know better.
10:24:58 Oh, yeah, but there was that other part as well right there's Bob Parker, he did stuff on block sex potion as well didn't me.
10:25:08 Well, I'm in the 60s as well. Yes. No comment.
10:25:19 Yeah.
10:25:21 Thank you.
10:25:32 Right.
10:25:33 In what you said about MHD turbulence and stuff that you didn't mention Catania and Feinstein I thought you would.
10:25:43 Should I bring the fall I can bring the slides back if you need it.
10:25:47 I think that was simply.
10:25:50 I think that was simply Oi, that was simply because I tried to at least to stay within 1520 minutes, and I have no way I could, but again Sorry to keep advertising so made shameful advertising but that's Friday.
10:26:07 Right. In other words, the question that Rahul asked about transport barriers even, you know, forget the pipe right even in the simple systems that arises out of, you know, we started to look at exactly this point that Adrian raised of comparing you know
10:26:29 the suppression of transport of Psy with the the qatanani of Einstein and but then we started doing the Cortana of Einstein without an externally input be zero, right and then that led down the road to the idea that the interfaces are that form, and you
10:26:52 know you have blobs of magnetic flux interleaved by little regions of high field, which are the barriers for that.
10:27:15 there's, you'll see your comrade in arms names plastered all over that talk on Friday. Okay,
10:27:26 wonderful, I should look forward to it.
10:27:31 Okay.
10:27:33 I sent, say, I've got more questions that we have time but I don't know if you want to break into a different subject or different phase of this No, no.
10:27:42 Today's subject is this one, so you know, feel free Adrian, if you've got the energy to ask questions, go ahead. I hope I'm not derailing other people someone feel free to raise their hand, so that the only other place, the other place and they may see
10:27:55 that I've seen the sort of hyper resist diversity show up which, if I remember that sort of, you know, an analogous term that you had in the CHNS equation.
10:28:05 I think that when people try to construct reverse models of, I don't know if it's plasma Boyd are carrying driven turbulence where they sometimes get hyper receptivity there right.
10:28:16 And so maybe this is a naive question but is there is there some analogy to like plasma driven turbulence going on in this system Yeah Well the answer is come back on Friday again But look, I mean, that very simply.
10:28:30 I mean that your request this question is very important and it what what we should be talking about and the reason why it's important is, I mean, I think we're dancing around the fundamental question in this program of what physical systems might have
10:28:51 a mean field theory that could be cast as a con Hilliard because the con Hillier it is an excellent blaring paradigm right it. It gives you know we've heard David and other say many times you want the negative viscosity with the regularization right bingo
10:29:10 bingo that's con Hilliard right in. So the answer is in 2d MHD and in 3d reduced MHD. You do get the possibility of a negative resist it now if you have a negative resist diversity you know that there's gotta be something regular rising it.
10:29:32 And what comes out of that is a hyper resisted okay if I'm just cranking the perturbation theory and that appears in the plasma literature.
10:29:42 Oh you get names like Hank Strauss and all but it actually just comes out of doing a proper conservation theory that conserves A squared properly so you get a negative resist devotee and a positive hyper resisted at the hype so the answer is yes but I
10:30:02 The hype so the answer is yes but I mean that's not in that problem it's not an externally prescribed input. It is in some sense a way of looking at the nonlinear transfer process.
10:30:16 If you see what I mean.
10:30:16 Do you have to make sense.
10:30:18 And it's very by the way it's exceedingly important in plasma and fusion physics it underlies the process of Kaler different you know JB tail or relaxation, which is a critical, critical process for us which is flattening the current profile it's a diffusion
10:30:35 of current. And that's a hyper resist devotee.
10:30:39 And as we go now in token max that are not so tied to, you know, the balance of resist devotee in the electric field where there's transport of current, the hyper diffusion becomes very important
10:30:58 right and you got a question.
10:31:00 Yes, picking up on that point, the
10:31:07 land out term, finding the other side of the scarcity.
10:31:28 In order to get an equilibrium, turns out not to be the mechanism that's operating, either in the beta plane turbulence Jupiter jet kind of problems or an MHD, the mechanism of the calibration is completely different.
10:31:30 It is in fact of feedback. It's a kind, it's actually a feedback regulator regulation and the regulation is between the perturbations, which grow up, and the main flow.
10:31:45 What happens is that the perturbations macroscopic Lee, change the being flow to bring the system back to a fixed point equilibrium.
10:31:55 This is totally opposite at odds with an equilibrium, produced by land argument.
10:32:07 Sounds like predator prey to me.
10:32:20 predator prey is a,
10:32:25 widget, say, a fairy tale kind of a you making up a story. I mean this isn't predator prey we're talking about here. This is the knob stokes equations, this is the attractions HD.
10:32:40 The fact that you can look at them and say, well it looks something like this, ecological model I have over here. I mean, that's a very weak analogy. Well, I find it a conceptually useful analogy to understand these, these feedback loops, which is a fair
10:32:57 point, and in particularly understanding them in in situations that are highly transients which is what we have to deal with.
10:33:10 Okay.
10:33:15 You think you
10:33:24 still cannot raise my hand.
10:33:28 I can hear you.
10:33:30 I wanted to ask you a question if you can make a comparison between.
10:33:34 Come here.
10:33:36 And grandmother solutions k equation which equation which also has negative.
10:33:42 Oh, can I can I, I mean, I can't do it off the top of my head I haven't thought about Ks in several years but so maybe I'll pass, I'm sure someone maybe Rahul I could pass that one to two or we have done a lot of chaos.
10:34:04 But it's not exactly like calm Hilliard.
10:34:07 We've done it mainly in two dimensions, and yes it's nice. It doesn't have to be forced, but to get real turbulence it can hear you have to force it.
10:34:19 So, the chaos. Go right there is the diffusion with the wrong side.
10:34:26 And then there's a hyper viscosity which saves today.
10:34:32 Yeah.
10:34:33 I'm not sure that the direct analogy.
10:34:37 If you do two dimensional cares, which we have also done.
10:34:41 You do get cells of a given size and roughly speaking, the size of the cells is inversely related to the point at which you get to the peak in the case spectrum.
10:34:59 So, but that's about it I mean there are no two fields, there's only one field
10:35:09 of two dimension provenance was karma ski, and it has a tendency to to go unstable. So for to prevent it, you need to have a condition is negative acquisitive vicious inverse of censorship says have an answer for those lives as condition goes small and
10:35:31 vice versa. When you do this, and instead of licenses system and liquidity produce. Come over of turbulence for infinite time there's no edges so it does work for two dimensional terminals I don't know how it works for other situations.
10:35:47 Okay, I'm sorry, I'd have to look at your papers, but the last time I wrote a paper and put up a situation ski in two dimensions.
10:35:55 We made a strong argument for it, giving the same next boat and says the Kp said equation.
10:36:02 In fact, turbulence in the gravity selection ski equation, certainly in one D in great detail, I can send you a recent paper and then today also, as far as we can tell belong in the Kp said universality class.
10:36:21 And as far as we can tell, there is no multi scaling. So again it's different for tournaments.
10:36:28 Okay I send you my papers and then you, we can have a discussion offline.
10:36:43 Okay.
10:36:49 Would anyone else like to contribute.
10:36:53 Please,
10:36:53 Just raise your hand.
10:36:57 Or if not, if you want to chat informally then of course there's the gather town facility where you, you know, you can bump into people and chat to them there, which is quite good.
10:37:16 Otherwise, since we didn't have a break, I think we'll call it, call it quits for the day I think we've, we've bombarded path for sure with a lot of questions, so thank you everyone for contributing speakers and question is today.
10:37:32 And we kick off again tomorrow.
10:37:36 plasmas, is it. Yes, if it's Thursdays plasmas it's.
10:37:43 It may be a little hard core but I think the the non plasma people shouldn't be afraid, there's some lessons there.