09:00:19 Yes. Okay, great. So, um, we're having this first Working Group. It's obviously a little bit. Oh actually can you record this does it record it. 09:00:31 It's currently recording currently recording. Okay, so this is the first of these working group discussions, I have no experience running any of these things so we'll see how this goes. 09:00:42 I actually had some nightmares last night of this going terribly wrong so the only way is up from here. 09:00:48 So the plan I thought for today would be to first look at. 09:00:55 All right, let's try and see if I can. 09:00:59 I wanted to give a brief definition of what I thought was an interface and this was sent to me by Maxwell's. 09:01:06 He said he looked it up on the dictionary and sees it. 09:01:10 And the dictionary definition was both as a connection between two things as an a boundary between two things. So the two notions of something separating, and something connecting was quite interesting. 09:01:25 So these are the two modern meanings of interfaces. 09:01:30 And in my mind and interfaces also something that is relatively thin compared with the bodies that surrounds it. And so in the selection of what I thought people should talk about I've selected. 09:01:43 Things that describes in objects between two other bodies. 09:01:47 But we can revisit that definition later. 09:01:51 And so with that in mind, I looked at the interfaces that were described in the various talks, all the way from the first three or four weeks of this program. 09:02:03 And what was missing was basically the discussions that we're going to have today so I've invited a few people and there are a few contributions to talk about interfaces with haven't yet discussed in the meeting. 09:02:19 And so we'll have short presentations by some people about these interfaces in particular, then we'll have a break and then we'll have a discussion and just after the presentations, what I'm going to do is I'm going to provide maybe a few questions that 09:02:34 we might want to bring up during the discussions and during the break, if you have more items that you want to discuss and please put them in the chat, and then we can bring them up as well in the discussion. 09:02:46 So we'll start the presentations with Rahul pendants from the Indian Institute of Science, own interfaces in the can kill your nervous talks equation. 09:02:58 So I'm going to stop sharing and roll please go ahead. Sure. 09:03:03 I'll just share my screen. 09:03:16 Okay. Can you see my screen now. 09:03:18 Yes. 09:03:20 Alright, so this will be a short presentation of convoluted tabular strokes interfaces. 09:03:33 And 09:03:33 I already got acknowledgments and everything in my restaurant so I wouldn't spend time with that. 09:03:38 So here's a, an outline for my mini presentation today. 09:03:44 First I'll talk about face coexistence in the sense that we use it in statistical mechanics, then define interface with free energy which is the same as the surface tension. 09:03:56 Then I'll talk of interfaces and conduct of your steps interfaces, and some conclusions I'll do it pretty fast even though I might have a few more slides that you thought I should. 09:04:07 So, let me recall. Here is a binary fluid phase diagram that is fluid of Type A and B. 09:04:16 This is plotted normally temperature and the vertical axis, and set percentage of one of the components on the other axis. In this particular case, this is water and phenol. 09:04:31 So, this side is water rich, and this side is phenol rich, as long as you are below this temperature. 09:04:40 And in this so called two phase regime, you will see an interface between the two phases, you can see it very well here, the shaded region is the water the non shaded region as phenol. 09:04:54 And whenever in the lab, there's always gravity so the dancer face that was to the bottom. 09:05:00 On the right hand side you can see on this panel, a you see this meniscus. And that is the interface. 09:05:18 Now in such systems as you raise the temperature, the interface eventually goes away when you go into the single phase region which is only one liquid phase where the two phases, x. 09:05:21 And precisely the point at which the mix is the critical point where there's a lot of scattering, and then you get critical of lessons so this is the critical or consolidate point. 09:05:31 So this is a very well defined interface. It is thin so long as you are away from the critical point. Here are some simulations and an amazing model which I will not go through just now. 09:05:45 Now suppose you're doing equilibrium statistical mechanics, how do you characterize the interface. So first let's, in principle, I can always calculate the petition functions Zed have a system for which I know the Hamiltonian, so it's some overall the 09:06:02 state's exponential by the speaker he was specificity, that's considered a D dimensional hype the cubicle system of volume, L to the deep. 09:06:12 And let's use periodic boundary conditions and d minus one spatial dimensions. 09:06:18 And in the remaining dimension on let's say the left boundary. 09:06:23 We place phase one. 09:06:27 And on the right boundary phase two. So, a rich on the left and be rich on the right. 09:06:34 Now if you wanted to study such a system. 09:06:38 You can look at one one by one one I mean there is both phases are the same on both sides so there will obviously be no interface. That's minus kbT logs, ed. 09:06:51 And if I take this limit, l going to plus infinity. Just f7 one one divided by L to the DI get the intensive bulk free energy. 09:07:03 And you can get all the equilibrium server in that mix of the system from that bulk free energy. 09:07:11 If you would like to study, an interface, then you have to calculate the integration free energy, which is EFSA by what you do is you take again to seven and limit L to the going to infinity f one to. 09:07:42 It scales is there to the D minus one because the interface, at least for the systems that I'm talking about today is a D minus one dimensional object. 09:07:53 And actually this is the precise definition of an integration free energy, which in common parlance is called the surface tension. 09:08:10 This is normally a very hard quantity to calculate if you want to do it exactly, but at the simplest level we use what's called the bean field description which is the Lindau Ginsberg, or Cornelia description. 09:08:19 I'll come back to this if I have time later, and let me know. I'll just show you that if you have the two phases and be that as I said that is a free energy, which tells you which phase you're in. 09:08:34 You have an order parameter file that distinguishes between phase A and Phase B. The two minute mark correspond to the two bulk phases. And this interface in between them you can actually calculate exactly within this simple theory. 09:08:48 But, of course, when we have turbulence, we will want to couple it with an obvious job situation and this is something I discussed briefly in my talk, and I can discuss again, if people want more details in the discussion session on the 17th. 09:09:07 And then you know you can do many calculations with them but this way of defining an interface makes it completely precise, at least in the limit where you have complete equilibrium. 09:09:18 If you want references I can give you more of and here's the classic reference of Orenburg and Halperin, which discuss this Cornelia Nadia Stokes model. 09:09:29 So, I should put some caveats. So, these are the interfaces that we talk about when we talk about multi-phase flows. 09:09:38 And so long as we are in the two phase three phase regime. The interface is that completely well defined, especially in equilibrium, we can calculate the official free energy. 09:09:52 Now just two caveats for the Super experts in the audience. 09:09:56 Such fluid interfaces which I showed you here from current Elliot's theory, looking pretty smooth actually are rough, insofar as their route Mean Square fluctuations diverged. 09:10:10 If you are below three dimensions. But these are controlled by finite size and gravity and I think it is with that understanding that we use them in the candidate Nadia stokes equations. 09:10:23 Strictly speaking, you should also have noise in the Candela Nadia stokes equation which near equilibrium would be fluctuation dissipation relation respecting noise. 09:10:34 But in most turbulent flows this noise is much less than what is generated dynamically so we ignore it. In those cases, so I hope I've given you a precise enough definition of the sorts of interfaces that arise when we have multi-phase flows, and I'd 09:10:51 be happy to take questions perhaps in the discussion session. Should I stop sharing my screen again. and yes please unless we have time for a couple of questions for each of these Sure, sure, fine, that's fine. 09:11:11 Question. I don't know if I can see anybody raising their hands. 09:11:15 So, I have a question. Sorry, can you hear me. 09:11:18 Yes, I can hear you. So, so because you're talking about interfaces, is there a definition about how thick or thin it has to be for it to be called an interface, because I think, in the context of multi multi phase flows. 09:11:34 Of course, if they are like just like material, the whole material changes right. 09:11:51 What you're saying so I would take the point of view, that if you're happy with my content yet Nadia Stokes description. The interface is sharp. I mean, is not on the scale of the system. 09:11:57 So long as I don't go near the critical point, the scale, these Can you see my screen the, 09:12:06 you know, you can fit this to a tangent hyperbolic actually just attention hyperbolic that sets the scale. 09:12:12 But that's scale, which is the rest of the interface diverges. As you approach the critical point. So when the two phases mix that that stage it will be a very large interface and it will have very large and violent fluctuations, even more so than the 09:12:29 ones I alluded to, but that's in the equations, at least at the level of mean field theory. 09:12:35 So here I don't need to. So long as my f survive in equilibrium is non zero, so long as I'm below the critical point, then it's a well defined thing and what turbulence does to it, we can see in the simulations. 09:12:51 But, strictly speaking, there is no this interface is very sharp only in the limit of zero temperature. 09:12:58 By the way, temperatures hiding somewhere in some coefficient of the court quadratic, which has all been so scaled out in the, we have written it that we are away from the critical points, but at the critical point there's double well we'll actually disappear, 09:13:13 you will get aquatic minimum first, followed by a single quadratic minimum when there will be no interface because that will be a one phase regime. 09:13:24 Thank you for the question. It's useful clarification. 09:13:28 Okay, we're gonna move to Edgar's talk. So I'll stop sharing. Thank you. Thank you very much. 09:13:35 Thank you. 09:13:47 not sure who's coming 09:13:52 able to, is that your screen. Yes. Okay, go ahead. We can, I'm not sure we're seeing your presentation though you're not seeing it. We're seeing the UC Santa Barbara. 09:14:03 Zoom thing. 09:14:06 Why would that be. So you might be sharing the wrong window. 09:14:11 So it helps if you joined for your browser, 09:14:18 yet yeah just share it and reshare it. 09:14:35 Yeah. Very good. I'm sorry I press the wrong. 09:14:39 So, okay, so I want to say a few words about things called connect on so that's these these structures which are spatial localized constructively driven, and the formation of staircase like structures, and I'm going to do this on a very simple example, 09:14:57 which is on the next slide. 09:15:08 And so this goes back to some work that was done by George for owners many many years ago. So he was interested in looking at rotating convection with gravity, and and rotation, align so you think of yourself as being at the North Pole. 09:15:25 And he was looking at a two dimensional version of this problem. 09:15:31 So you can write the basic equations in terms of a string function, a temperature fluctuation. And the quantity called V which represents the velocity in the y direction that into the page. 09:15:49 So I'm going to refer to the as, as the solo velocity and sigh and vn Sita of functions just of XZNT so everything is two dimensional independent of the wind direction. 09:15:59 And the parameters of this problem of the usual pronto number value number. Taylor number, which is in for a second number. 09:16:08 Now, one thing that Veronese did not notice in his work is that with stress free boundary conditions, which he used. 09:16:17 You can show very easily that d by dt of the domain average zone velocity, that's this visa are defined here, that that is actually zero. And that means that this system conserves the bar, and without loss of generality, you can take the bar to be zero. 09:16:37 And then you can also define just the vertical average zonal velocity v sub x here. 09:16:45 In this way, so he's just a vertical average of the zone of velocity, integrate over z, and then you'll find that on TV by dx is driven by these rental stressors. 09:16:56 Now the reason this is interesting is that if I have a locally confined convection, then these random stresses will drive gradients DVD x through this mechanism, and I'll show you that on the next slide. 09:17:14 And the reason we're interested in these gradients is because in the inertial reference frame. 09:17:21 The local rotation rate is to omega that's the that's the 09:17:27 rotation rate, about the vertical plus a bV problem is this local zonal velocity gradient. 09:17:37 What I'm going to show you on the next slide is that this v prime is negative in the region of convection, meaning that you have anti cyclonic locally anti cyclonic flow. 09:17:50 And, but the rotation is enhanced outside of that region. So here are some plots obtained by Cedric Bowman few years ago, showing both the localized structures that are present in the system. 09:18:04 So here is an example of the stream function on the top panel and below is the corresponding view of x right that's the vertically average velocity. 09:18:13 And you see it has a negative slope, there's a little bit of an imprint of the convection but basically you have a large scale negatively primed, meaning that locally is convection reduces the rotation right. 09:18:26 And because we is actually conserved across the system that means you have to have a positive gradient elsewhere. 09:18:33 And you can see, depending on the length of the localized structure that you know this same situation persists, but its strongest say in this region here. 09:18:44 Look at the vertical scale. 09:18:47 You have a relatively large region of a large difference, V, from the left to the right of the competitive structure. 09:18:55 And the same thing occurs here with the, with a different number of of these convention halls. 09:19:03 So I just want to contrast that with what happens if I change the boundary conditions. 09:19:12 So here I'm looking at the case of Knowsley boundary conditions that top and bottom. And in that case, the same quantity divided up bar is non zero. 09:19:22 So you no longer have that concern quantity that domain average zone flow. 09:19:29 And you can do in fact numerically you can do Homer topic continuation from the free slip case that I talked about earlier, to this no slip case i'm talking about now through this parameter beta. 09:19:41 So the previous case was be dial, zero now I'm going to go to beat it was one which is the know slip case where there is no conservation law. 09:19:49 And what you find is structures like this, he said the same pictures, essentially, same parameters. 09:19:56 And you'll see that the V mode has been mixed up by the convection, but there's no large scale structure, there's no logical gradient MV. 09:20:16 OK, so the conserve property of the, of the zone on momentum was on the flow is what's responsible, breath for the presence of this large scale structure in the system. 09:20:20 And that's what expels locally the rotation from the region of convection reduces the convection. 09:20:27 Excuse me reduces the rotation in the region of convection by adding this anti psychotic component and enhancing the rotation outside of the local I structure so this does not occur with these mostly boundary conditions which destroys the conservation 09:20:45 law. 09:20:46 So that really is the message of this little example. 09:20:51 I have a little summary. I just want to go through. 09:20:55 So conventions in rotating convection know generate this anti psychotic cheer to reduce the local rotation rate as I explained, and you get cyclonic shear generated outside, enhancing the rotation right there. 09:21:10 It's a nonlinear effect, it's driven by rentals, As I showed you. 09:21:15 It of course regardless of whether the onset of connection is self critical or supercritical. 09:21:21 It's a direct consequence of the presence of this fixed flux, and hence of the boundary conditions the stressor boundary conditions are top and bottom. 09:21:30 It occurs in the primitive equations right so I'm not modeling anything here I'm really dealing with the exact equations and comment that the same fixed flux requirement arises, of course in many other problems, including Magneto convection binary for 09:21:48 a convection. 09:21:50 And in particularly if I had no one boundary conditions rather than periodic boundary conditions horizontally in x. 09:21:57 Then I would expect structures that look something like this. 09:22:01 So this is for binary convection so that's convection, where you have separation due to a cross diffusion of fact all the story effect. 09:22:12 And here again I have one of these localized structures. 09:22:15 And you can see that the role and trains, the salinity from the bottom mixes it into the localized structure and then dejected on the other side. And so you get to kind of step like structure with low salinity on the left is still in the on the right 09:22:32 that's supported by the North flux boundary conditions and designed with a mixing region in between. 09:22:38 So there are many examples of this kind of behavior. 09:22:42 But I think I've shown enough to indicate that if conserve flux really plays an important role in generating level like structures, so thank you. 09:22:53 Thanks again, it was really interesting, and anyone, a test question, Greg. 09:23:00 I had girl that was very interesting. Just a quick question can you comment on the fact that even without the conservation law. Serve quantity. I mean, you still have localization happening it seemed in the example you showed. 09:23:15 I absolutely had localization but what I did not have was the presence of the large scale node. 09:23:22 So here, in the absence of the concert quantity, you know, everything is just mixed up on the scale of the convention in other words on the small scale so like, whereas in the case where I had the concert on. 09:23:35 That's a bit distressed for the boundaries at top and bottom. I have a large scale structure in the Wiimote, not in the demo not industry function, but in the Wiimote. 09:23:44 Okay. 09:23:46 Okay, thank you, because the small scales are imprinted on this you can kind of barely see that, perhaps. But, but the point is there are now two scales. 09:23:55 Got it. 09:23:57 Thank you. 09:23:58 Okay, we have two more questions, as long as they're very quick. David Oh Patrick, 09:23:59 Right. 09:24:06 David. 09:24:09 Hi. 09:24:10 Are you able to make any contact with the, with the 3d problem of rotating connection at the bottom, you know where you have water seeds which I guess my thing they feather their nest as well in some snaps right so i mean i i believe that, you know, 09:24:28 I mean the short answer is no because I haven't done, you know, haven't done that but I believe that these kinds of localized structures and Benjamin fovea talked about this in his presentation a couple weeks ago, that they do kind of locally, arranged 09:24:42 for the conditions through nonlinear effects that, you know, facilitate, you know, self sustaining processes, know that maintain that structure. 09:24:53 So this could be an example of that kind of behavior. 09:24:58 You know this is not a trivial problem of course this is relatively, you know, low Reynolds number, I mean these flows are all laminar. 09:25:06 In fact, they're all stationary there in time. 09:25:09 But I think this the principle that this, you know, that the conservation is that is an important ingredient in layering i think you know remained. 09:25:22 Okay, thank you. Okay, Pat, tiny, quick question. Well, it's a tiny quick comment if I understood your system correctly I would remark. 09:25:33 It seems very similar to a degenerate limit of things we do in fusion, particularly where your V is like the the flow in the third direction and the other dynamics would be something like you know some generalized Hasegawa mean, whoever type thing. 09:25:52 And basically this is this system would describe the generation of a structured to flow in the third dimension, if you imagine allowing allowing it to extend and it's a it's a well established industry in fusion and important thing in the fusion program, 09:26:11 which goes by the name of intrinsic rotation. 09:26:15 So I mean that would be an interesting parallel to pursue. Well, I'd be very happy, you know, to discuss that further with you, and if you can send me references on that we might Dragoon you for one of the other groups where it's more legitimate to mention 09:26:31 plasma, you know, so Okay. 09:26:38 Can you share your screen Edgar and then your next. 09:27:02 Okay Can everybody see my presentation screen. Yeah. 09:27:06 Okay, very good. So, I've become interested recently and partially missable interfaces, especially in the context of pores media flows. 09:27:16 This is a collaboration with my former student Qingdao Chen and a couple of his colleagues. 09:27:22 And thanks very much to Rahul for introducing the con he approach for modeling, because that's also what we based on. So, our motivation for this word comes from the field of co2 sequestration and aquifers. 09:27:42 So if you look at this picture here on the top right. 09:27:46 The idea is the following. We collect the co2 that we generate on the Earth's surface, we compress it into a supercritical state and then inject that into a sale line, aka firm way below the surface, and could you go full screen. 09:28:10 Let me see. 09:28:13 should be able to do that. 09:28:15 Yes. So we inject the co2 here into the skyline aquifer. and the supercritical co2 is less dense than the water, so it will rise to the top of this reservoir here until it gets trapped beneath the cap rock so where it cannot rise any further it'll stop 09:28:37 there and it'll accumulate there. 09:28:41 And the problem now is that this co2 is partially missable with a water. 09:28:48 So it's not fully missable, but it's partially missable so we can form up to 5% concentration of co2 and water. 09:29:00 And that's one thing. The other thing is that when we have this mixture of co2 and water that is actually denser than the water itself. And so as a result, where if we now look at the lower right picture. 09:29:17 So we have this supercritical co2 at the top we have the salt water below. And now we have some partial dissolution of the co2 into the water. And because this mixture of co2 and water is is denser than the water below we form a conductive instability. 09:29:39 So that convective instability then carries this co2 downwards. It brings fresh brine upwards towards the interface, which then allows for additional co2 to become dissolved in the brain. 09:29:55 And so eventually all the co2 will dissolve into the brine. And it will be carried away by the flow in the aquifer and so in that way. 09:30:06 The co2 sequestration process essentially fails. And so we need to understand this. 09:30:14 Convection driven by this partial dissolution, so that we get an idea of the timescales over which these processes happen, and so on. 09:30:25 And so we base our modeling of these kinds of processes on the Darcy con, he had model. 09:30:33 So we have our usual incompressible continuity equation, then we have here Darcy LA for the momentum equation, where we have here. 09:30:44 Effective surface tension term, can everybody see my point, my, my mouse here. 09:30:50 Yeah. Okay, so, So we have here in effect of surface tension term. 09:30:57 And then we have here. 09:30:59 Our. 09:31:07 Yeah, convection diffusion equation for the supercritical co2 were here, notice in the diffuse of term we don't have the concentration See, but instead we have the chemical potential, and the chemical potential now involves both the hem halls free energy, 09:31:21 and the gradient energy coefficient. And so, the dynamics of the system now depends entirely on this handholds free energy, and how that depends on the concentration. 09:31:36 And so below here and the figure I have sketched a few possibilities for what this free energy can look like as a function of the concentration. So if we have our standard missable situation that would correspond to this blue parabola, where we see that 09:31:56 the energy is lowest at concentration point five. And it's the highest at concentration zero and one. And so that means if we have an interface where on one side we have concentrations zero on the other side we have concentration one, the system tries 09:32:14 to proceed towards the lowest energy state, which means concentration point five everywhere. 09:32:21 And so that's our traditional missable case, then the green curve shows our traditional invisible case where we have the highest energy at sea holds point five. 09:32:34 And the lowest energy at concentration zero concentration run. So here now, if we were to start from a perfectly mixed system was safe of equal point five. 09:32:47 It developed into a separate system where we have C equals zero and C equals one, Because again, that's the state of lowest energy. And now for partially missable system that's the red curve here, we see that a minimum is reached at a concentration of 09:33:04 point 05, meaning that that's the state towards which the system develops. So this partial dissolution of point 05. 09:33:16 And then on the right, we see the density profile as a function of the concentration. And we see that the density has a maximum at around this concentration of point 05, and that is what causes this dissolution driven convection, because the layer of 09:33:38 brine with co2 dissolved in it that forms at the interface is denser than the brine without the co2 below and so it sinks down. 09:33:50 So that's the idea of the model. 09:33:54 Now let me just show you a couple of representative DNS simulation results. So here we see in the top panels, the fully missable case and the bottom panels the partial missile but actually missable case. 09:34:08 And then Time goes from left to right. So, we see here the initial condition. We have this supercritical co2 above and pure brine below. And now things develop with time towards the right. 09:34:25 So we see in the fully missile system that the co2 dissolves into the brine, we obtain our, you know, usual expected very broad concentration profile, we trigger this dissolution driven convection here. 09:34:46 And the final state will be that we have a constant concentration everywhere. 09:34:53 On the other hand in the partially visible case. 09:34:58 We can have a maximum of concentration of point 05 of the co2 in the brain. 09:35:00 there. 09:35:06 And so we maintain a sharp interface where we have the dissolution driven convection below, and the pure co2 above, and even for long times we can say this, we can see that the interface remains very sharp. 09:35:26 And as I'm talking state that we reach now is one in which the concentration is point 05 below the interface. And it's one above the interface. 09:35:37 And so the system in the long time limit behaves quite differently from the fully missable lemon. 09:35:46 And so that's the situation that we want to study or that we have been studying to develop scaling laws for these conductor flow patterns, and so on. So I've tried to keep it short and I'm already at the end here. 09:36:04 Thank you very much again that was really interesting kind of surprising results, some extent. 09:36:13 Any questions. 09:36:17 I can't see anybody's hands. 09:36:27 Okay, um, maybe in the interest of time, if you think of questions we can bring them up again in the discussion, I'd like to move to our next invited speaker which Chico 09:36:40 pronounced it correctly. 09:36:42 Okay. 09:36:45 I'm not sure if you can see my screen. 09:36:49 Yes. Okay, so the Saudi a short talk about postdoc word that dead. 09:36:56 It's all published in this paper that's four years old now. So the question is, we're going to put this density interface in stratify share flow so you see the initial condition of the DNS so the red interface is pretty sharp one over there, and the blue 09:37:11 curve is share the info profile induced by the wall so there is no rotation no double diffusion. So the question we're asking really is. So with this war driven share and the turbulence that we put in our initial condition. 09:37:27 Will this interface survive. 09:37:31 And what I'm going to show you two things. 09:37:34 Yes, the answer is yes, it's going to survive if the panel number of pack the number is high enough. So, and the other things I want to show is this tool that we use to analyze the problem so we want to use this trace interface card and so we get rid 09:37:48 of the reverse for mixing processes. Okay so 09:37:58 I got three cases from here so each column is one case, and each row is different times. So, we started with us sort of small rich numbers so that the stratification is pretty weak and moderate seven. 09:38:01 this okay here we go. 09:38:15 So that's basically heating water. What do you see here is because certification is not strong enough right so the shares able to overturn that interface. 09:38:24 So everything becomes trivial, so it's troubling to start with, and turbulence. In the end, so that's basically the one you see on the left. 09:38:31 If you go to the right column right here so basically I increase rich summer by effective for keeping the same parental number. What do you see here is you see some humble wave like structure right so you can do the stability analysis and indeed you do 09:38:47 expect that kind of waves to exist for this profile. And eventually, as time goes on, the interface gets thicker thicker and thicker and eventually the turbulence is dies, right so you should say that the interface becomes broader, and the motion is the 09:39:03 disappearing. 09:39:04 So the most interesting case is right in the middle of soft mixture of the two cases on the sides. So, hi rich number right there. Pine Tree two and a higher parental number, so we really want to go to the panel number of salty water which is 700 but 09:39:19 it's too expensive for the simulations. So what do you see here is, you still see some humble like structures right you see this counter-rotating word is it says kind of stretching that interface. 09:39:30 But after pretty long time. Right. The interface is still there. Even though the flow is still turbulent and there's definitely turbulence going on, above and below the interface. 09:39:42 So we're excited to see this because we see a case where interface characters survive, subtract two triggers, and we want to do some analysis on this one so we tried initially is just to take a cleaner average of density and whatever. 09:40:00 The result is not very clear because you have all those reversible processes are just displacing the so picking off you're actually not mixing so in order to look at the actual irreversible processes. 09:40:11 We use this framework, proposed in the 90s so we're looking at this tracer based coordinate meaning. 09:40:18 We're following one ISO Piccolo surface at a time right so I can go up this that star according the system so each location this star recording is one ice will pick no surfaces, so I can do some conditional average of the flexes that's going through each 09:40:34 other so pick nose, and I can quantify the effective diversity right so there's a nice interpretation of the character. He here which is just a molecular do festivity motivators factor that's due to the surface area of the ice will pick no surfaces. 09:40:51 And the other thing we can do using this coordinate system is that we can write up a budget equation for the buoyancy gradient so on, which I've shown here. 09:41:01 hopefully you can see my mouse. 09:41:03 So this is the buoyancy gradient in that star quarter, and this is a time of change so you have the usual source and direction diffuse in terms on the right hand side, we can focus on this one right here. 09:41:16 So it's basically the curvature of the effective. 09:41:30 The facility multiplied by the gradient itself right so if this circle term is big right you expect that the gradient to grow in time. So interface is actually strengthening itself. 09:41:37 So that's what I'm plotting on the vertical axis here on the horizontal axis we are plotting the packet numbers, it's a target and patent number, and physical picture here really is. 09:41:45 Goddess Eddie's acting on either side of the interface right we can think of some sort of scouring motion, that's trying to take material away from interface and keep the interface sharp, so we calculate the rms velocity of the turbulence and sort of 09:42:00 a tailor micro scale the triggers and come up with this type of number. 09:42:04 So we divided by the molecular diffusion marketing facility so what you see here is for those cases that's our letter lender rising. 09:42:15 Okay. The one on the right, right column on. 09:42:18 So basically, the darker symbol means later time so he started with a pretty big curvature term, which you need for the source and indicates with time, right so all those cases that are memorizing all follow that trend in time, but once you're packing 09:42:38 That's the one you saw in the middle column, you started with a moderate curvature and this curve drudgery goes up in time. 09:42:46 So we think there might be a packing numbers threshold for the turbulence, to actually be able to sponsor that that interface. So, that's something we typically ignored in numerical simulations because it's really expensive to run hyper no number of cases, 09:43:03 and maybe things so much clearer. If you use this trace interface coordinate. 09:43:12 And that's pretty much what I have for now. 09:43:17 Thank you very much. any questions for ci. 09:43:28 I have one. 09:43:42 Do you have you considered studying the double defensive interfaces in similar ways because we do see very curved turbulent interfaces. In that case, And what do you think would change when you do that, about the fusion. 09:43:46 There's so much conviction going on. 09:44:00 And I don't know if, how this framework I extended to scalars, tell me how you to think about, okay, they're thinking about it. Yeah. Okay, good. 09:44:03 Yeah. 09:44:05 Any other questions. 09:44:08 Okay, um, our next speaker is Justin Brown who is going to talk about shared stumbled abusive interfaces. 09:44:17 Yep. 09:44:20 me share 09:44:26 my screen. 09:44:27 Yeah. 09:44:28 All right. Hi, my name is Justin Brown, I'm a research assistant professor at the Graduate School for those who I haven't met, I've been working with the team or Ratko for the past several years on numerical studies have doubled abusive convection and 09:44:53 client region. 09:44:55 So our setup that we use typically so we've got a pseudo spectral code which is for a modes and all three directions. So, if we can imagine so what we do with this code is we seed it with sort of an initial Arctic thermal client staircase so we're hot 09:45:10 and salted the bottom cold and fresh the top, but with an already pre existing staircase structure and then we take the whole domain of the simulation and we apply a sheer to it. 09:45:19 So we end up with this kind of like shared domain. This does introduce an issue as you go to later times because the grid gets more deformed and the derivative calculations become more inaccurate so we do have to introduce a remapping step where we effectively 09:45:34 shift the simulation to become more vertical sort of infrequently. 09:45:39 And this is relatively easy to do. 09:45:41 So then we characterize these simulations in terms of to non dimensional numbers primarily First we have a density ratio which I'm sure you're all familiar with. 09:45:49 of the background gradients so we have the background temperature gradient here and the background solidity gradient. 09:45:56 And then we also characterize it in terms of a sort of mean Richardson number of the flow where we talk about the mean going to frequency squared divided by the mean shear squared. 09:46:06 So now we want to do is I'm well I want to focus in on this interface and take a look at the general sort of behavior in the presence of sheer. So here we're looking at for one simulation of the density ratio of five and 40 which is the number of 10 which 09:46:20 are relatively characteristic of the Arctic DOMA climb. 09:46:25 And we're looking at horizontally average vertical profiles of several different quantities, so up on top here we have temperature, the end solidity. 09:46:32 So the interface is here as equals zero. 09:46:36 And you can see in the convective part of the staircase is your convective above and below the interface you see the temperature enslaving stay relatively well mixed from the initial conditions, but you do develop this kind of finite with interface in 09:46:49 both temperature and salinity here which we kind of attempt to, to show via this these black dotted lines. 09:46:58 The temperature interface is a little bit thicker than misleading interface which is what you would expect in the system since temperature defuses more and more quickly than salinity. 09:47:06 But the one of the interesting things that we've noticed is that as you apply sheer the temperature interface does become slightly narrower so you're looking at potentially increased thermal flexes. 09:47:16 One thing we're really curious about those the behavior of this interface with respect to the philosophies on the bottom here about them right I'm showing the horizontal velocity profile. 09:47:26 This dashed line is the initial sort of uniform shear and you can see as time goes on in the convective parts. There's mixing of velocity so you end up with a philosophy interface as well. 09:47:38 And this, this has much stronger shear than sort of the natural background problem. So we look at the Richardson number the local Richardson number of the interface, we find that it's about three at the interface itself, which is much so much higher sheer, 09:47:54 then you would sort of naively expects based on the background reference number of 10. 09:48:01 So one thing we wanted to ask was sort of what would we expect to happen at this higher shear interface and still not unstable to Calvin Hamilton's abilities. 09:48:13 So then we were wondering Could it be thermal halen sheer instabilities or possibly development Palumbo waves and in fact, because we have such a thick velocity interface here as compared to the density interface we do expect to see home bow waves here 09:48:23 so here's a 3d visualization of two of these simulations the case in the left has no shear in case in the right has Richards number of 10. And you can see that in the case without true The interface is very flat, or as the with the application of sure 09:48:37 you see the development of these humble waves which leads us was just talked about to the formation of the interface and so we expect to see higher fluxes through the interface. 09:48:50 The connection itself also promotes higher flexes in the or the sheer itself pretty much higher flexes and the conviction region itself. So we do actually see higher flexes overall. 09:48:56 So if we look at the flux is a function of time in these simulations. Since the non dimensional time here and dimensional time their muscle number on the less the thermal listen number on my left and then the heat flux on the writing dimensional units, 09:49:13 see that for any given set of parameters which are color coded here of the case with sheer is solid line case without shares a dashed line that there's at least a factor of two, increase in the flux is from the non share case to the shared case, since 09:49:29 which is number 10 is relatively reasonable for the Arctic this actually seems to be a very substantial effect for modeling the sheer through the staircases and so we think this would be very important going forward for full Arctic models, thinking. 09:49:46 Any questions for Justin 09:49:50 could read. 09:49:52 So the slide where you're showing the temperature celebrity profiles, was the dashed line, like the initial condition and the way that it ends up. Yes, correct. 09:50:04 Okay. 09:50:05 Sorry. 09:50:07 Sorry. That's it. Thanks. 09:50:12 I have a quick question. Um, my understanding is that traditionally humble waves are from a fully stratified system on the stratified interface where you basically have a conductive layers and reaching a stable interface so you still have humble waves 09:50:30 I mean, really, is that really what they are. I I'm, I'm not sure, to be honest, it's it's the closest thing we've found to something that makes sense. 09:50:39 So I don't know. 09:50:41 Okay, but. 09:50:50 are the. So you started with an interface already are these parameters this parameter regime where the interface would have formed naturally. No. 09:50:55 Any other questions. I think we're fine What 09:50:58 Okay. Yeah, they don't they don't form naturally in these in these systems the the density ratio provides too much stratification so like double defensive instabilities don't typically form in this regime. 09:51:09 Got it. Thanks. 09:51:11 Alright, thank you, Justin, David, we have a diva choose is going to give us a little presentation on turbulent interfaces as well. 09:51:30 Right. Can you see that. 09:51:35 Yes. 09:51:38 So it really will be a little presentation I'm following your guidelines Pascal. being minimal 09:51:48 so minimal don't know equations, but there was some pictures. 09:51:51 So this is a little bit of work that Nick and nine equipment and I have been doing for the longest time. 09:52:00 And the problem is astrophysics Lee motivated says, Can you get, can you get layering and magnetic magnetic system. 09:52:10 And so the equations would go on forever so I'm just going to say a little bit about what the system is that it's a horizontal horizontal field that stratified in depth, and it's the motivation really would be in radiative interiors and stars. 09:52:30 Because we know layering leads to enhance transport, one of the great problems in astrophysics is transporting radiative interiors, there's an awful lot of things which go on in there, and this is another possibility that hasn't been addressed. 09:52:45 So magnetic buoyancy instabilities. Again, it's a lot to go into it turns out that this, you can have instabilities whether the field increases with height or decreases with height for completely different reasons. 09:52:58 Okay. 09:53:00 And it also turns out. Again, lots of details not put in that you can turn one but you can turn the magnetic buoyancy problem under some assumptions into thermal halen conviction. 09:53:12 Okay. And the way you do it again in kind of waving hands, sort of, manner, is that the salt goes to magnetic pressure and the twist what makes it interesting is that the temperature in the thermal a line problem does not go into temperature in the magnetic 09:53:31 problem it goes into a combination of the temperature and the magnetic pressure. 09:53:35 Okay. And so if you, if you're used to double diffusion and you know about the really salt really thermal rarely so it rarely number stability diagrams then they look different. 09:53:48 In particular, you can have instability and what you might think of as the stable stable regime. 09:53:53 Okay so here we're going to look at the diffuse it regime. 09:53:57 So there's three parameters. 09:53:59 We've already seen these today inverse density ratio diffuse ever to ratio here is the ratio of magnetic to them or diffusion so that's small astrophysics, and the parental number is also small, of course, has to physically. 09:54:14 So I'm just going to show you some pictures, really, to two cases, just to show you how messy the interfaces are said that said I can't advance my slides or I can. 09:54:29 Okay, so right so you don't really need to bother about the top one it was part of the figure and it's kind of cute, but that's the initial instability it leads to a mess and then a layering state at the bottom here emerges. 09:54:42 And since we're talking about interfaces, I would say, this is how messy, an interface can be had these parameter values. Okay, 09:54:54 so the the layering is is enhanced, you see it better in the magnetic pressure because the magnetic diffusion is much less. 09:55:04 But these are incredibly turbulent. And they don't survive, you wouldn't expect them to survive. 09:55:12 So this is a delay to time when four was become three and this is a yet a later time when three has become too. So if we're discussing interfaces In this problem, we need to somehow discuss this. 09:55:25 And how they already voted so they were eroded on 09:55:30 thousands of turnover times. Okay. 09:55:34 And it depends where we are with with inverse density ratio so if we looked at another inverse density ratio, we get a much, we get a nice picture this is quite nice. 09:55:46 It's not really. Okay, I mean this is this is how the forum. This is how the latest form you can see them that formed in places and, but there's a gap, and then they all merge and so you get this nice much nicer layering less turbulent structure here 09:56:00 again these will you have the computational resources and the willpower to keep going. They would presumably also decay. So it's a very, it's a very turbulent problem that you must if you're going to consider interfaces in double diffuse connection. 09:56:17 That's the sort of thing you need deal with. 09:56:20 That's it. Thanks. 09:56:23 Thank you, David. Any questions Adrian. 09:56:28 Thanks. This is really cool. I didn't know about any of this. So, so I'm wondering, I've got a few questions but maybe in the spirit of clarifying questions I'm kind of wondering what you're plotting here. 09:56:41 fields are, and also what the initial magnetic field profile was. Yeah, yeah, that was that was the weakness of me. What I'm plotting ok so the left which you can is not very clear is the is the vortices Battisti okay so what how you should consider this 09:56:55 is that you're looking along the field, the field is into the screen and emotions are 2d. So the relative quantity, the relevant quantities are the entropy variation, and the magnetic pressure variation so the magnetic pressure is is negative salt, and 09:57:16 the entropy variation is a combination of heat, and salt. 09:57:22 Okay in the thermo land problem. 09:57:25 So that's, 09:57:28 That's what you're looking at the initial magnetic field is is horizontal, and linear linearly stratified instead. 09:57:41 And you said that the motions are two D. 09:57:47 Is that, is it a 3d simulation and they just happened to be mostly 2d or your. It's a 2d simulation like you're enforcing to include the simulation because the and the. 09:58:01 So we're working from the analog with them a land convention in the analog codes in 2d. However, what whereas in 2d one might argue that today is nothing like 3d. 09:58:18 not that far of 3d, because there's a there's a guiding field the field remember is that into the page. So, whether it's 3d. 09:58:22 It would not be very 3d. 09:58:25 So I think these are there's more chance that these look like the 3d magnetic version, then, then, then in terms of a line that they would look like the 3d them a line. 09:58:38 Chris Do you have a question. 09:58:38 Yeah, just a quick clarification. Can I Can you go back to something you described as a sort of more of a very turbulent interfaith. I'll try. 09:58:52 Okay, sorry. Yeah. Yeah. Okay. Um, you kind of pointed it to regions on the plot, saying the bottom right. 09:59:02 And then the bottom right panel. 09:59:05 Yep, that so that the interface in the middle is really sharp right. 09:59:11 I would just caution sort of interpreting the white patches around it as being interfaces because what what does the column white actually denote color white is the is the color map, and the color map like changes quite strongly around the white right 09:59:32 so then I'd say the gradient, say on the 09:59:36 quieter point. 09:59:38 Okay, I mean, I mean. 09:59:42 So once I could show but I was trying to stick to three slides. 09:59:47 I could show you the staircase structure of course, which, you know, so there is, there are definite interfaces I mean there is a there is a if you average it and horizontally average it then there is a, you can you can see a clear staircase in those 10:00:01 okay. Yeah, because in the middle I see a clear, like, jump, essentially. 10:00:07 Yeah, away from those, it's a bit less clear. 10:00:10 Yeah, but you can, there is a basically a staircase and then, and then this one is an extremely close yeah yeah of course, but there is a clear case even in this one. 10:00:23 I probably should have done that but anyway. Yeah, thanks. 10:00:27 Okay, um, can you share your screen and then I'll quickly share mine. 10:00:34 So I wanted to finish this by reminding people of a few other types of interfaces that come up Can you see my screen. 10:00:46 Yes. Okay. 10:00:49 So, basically in Timor's talk he introduced these staircases in the tropical ocean, which are convective layers sandwich Ching fingering interfaces, and I thought, these are particularly interesting. 10:01:08 And I'd like to bring them up for discussion later So, and there are some beautiful experiments by reading Krishna more TNGFM about 20 years ago, looking at specifically this interface between the convective region and the fingering interface and, and 10:01:24 I mean the connection between the two. So here in this picture you have a shadow graph. 10:01:29 And these motions appear and down here are the turbulent convection. And it's blurry thing here is the finger interface and that's a zoom with a better shadow graph of that transition so you see the fingers here in the fingering interface and the connection 10:01:44 here below. 10:01:46 And this is basically what is supposed to happen in these very very sharp steps here. 10:01:51 So that's one type of very interesting double defensive interface I wanted to bring back to people's mind. 10:01:58 Another one is this one, so this is related to what Justin talked about the interfaces in high France on number diffuse if double defensive convection so this is related to Mary Louise is talk so we have these again Thermohaline staircases in the Arctic 10:02:16 Ocean now which of these inputs temperatures cylinder profiles. 10:02:20 And, in the absence of sheer which Justin talked about you have these very stable diffuse of interface and that's what Justin said when they said they were very flat and above and below these very stable defensive interface you have again convective layers 10:02:35 and these scour the interfaces and the transport is primarily due to the scouring motion. 10:02:42 And they are a lot of, there's been a lot of research done to try and characterize the structure of these interfaces notably the Linden and Shurtleff interface model about about this topic. 10:02:56 And then if you move too low Principle number defensive double diffuse of interfaces. 10:03:03 In the defensive regime so we have what David just proposed with try these very turbulent interfaces. 10:03:10 There we go. 10:03:11 And so this is another example of a very turbulent interface and diffuse etc. So, in here you need to think of a system which has hot temperature, high salinity at the bottom except it's not salinity in astrophysics it's some kind of chemical element, 10:03:29 and at the top you have lower temperature, lower composition. 10:03:33 And depending on the density ratio, this can either have a very turbulent interface just like David just showed. 10:03:41 So in that case, the interface is well defined and that's the profile. So this is what David's profiles would have looked like. If we had done a density profile. 10:03:52 And this is the fluid motion. This is the total. 10:03:57 I believe WRMS so the rms velocity in the vertical directions you see there's a reduction in the region of the interface, but it's pretty high above and below where you are in the fully connected layers. 10:04:07 What's quite interesting is if you move to very high density ratio interfaces, which can only happen really in these low Principle number systems. 10:04:19 The interface thickens. And it becomes quite stable, but it's not a defensive interface as we would see in the ocean, it's an interface that supports the military double diffuse of instability and so it's full of these internal gravity waves in the interface. 10:04:37 So we have this funny system where you have a, an interface riddled with gravity waves sandwiched between two convective layers. And you can see it in here, you have the connection here with a region of high turbulent kinetic energy. 10:04:52 And then in the interface here, you have low but non zero turbulent kinetic energy. 10:04:59 So this is another example of an interesting interface. And here are the facts through the interface is clearly regulated by whatever can be accommodated find these gravity waves. 10:05:09 So with that in mind, I wanted to give you a brief recap of what I think are all the types of interfaces that were discussed in this meeting so far. 10:05:21 So, we've had density interfaces in singly stratified fluid so we had talks by column Alexi ci. And then, Greg mentioned how you might be able to form them and Neil had a model for them. 10:05:33 We had double defensive interfaces in the different possible regimes have Wi Fi connection. So we had talks by tomorrow Mary Louise, David myself and Justin Brown. 10:05:44 We had talks about interfaces and multi-phase flows. So the talks by round pen date and accurate mind Borg. 10:05:51 We have interfaces which are PV interfaces, in a rotating stratified spheres, for example. 10:06:02 So these are the talks of jump on giant planets and atmospheric dynamics by and Rachel read feral Marcus and Haynes. 10:06:10 And then we had all the plasma interfaces these equals be interfaces so we have talks by one again. 10:06:19 Schmidt our Siobhan and pat will be talking next week about these. 10:06:25 And we also had some talks, where we didn't necessarily have an interface, but we definitely had structure formation in rotating convection leading to a separation of quote unquote phases of convection with then some kind of an interface in between them. 10:06:40 So these are a list of interfaces we saw. 10:06:45 And so the topics for discussion, I'd like to raise so I'm just going to bring up the topics. 10:06:50 And we're going to take a five minute break and I'd like you to think about whether these are good topics of discussion if you have additional topics to talk about, please put them in the chat. 10:07:01 And then I'll take a poll after the break to see which of these topics we want to start discussing. OK, so I'll leave this up. 10:07:11 So we can reconvene in about five minutes. And in the meantime, please write in the chat, what you think should be other discussion topics and what you think or which one should we focus on. 10:07:26 Alright, so we'll see everybody in about five minutes. 10:07:53 Are you still seeing my screen. I can't see my own screen. I don't know what happened. Yeah, it's up there. 10:08:01 Okay, good. 10:08:55 loudly. 10:08:57 They don't explode. 10:12:39 Okay, I think maybe we can start again. 10:12:44 I don't know if everybody is back. 10:12:51 So, at this point, I don't think we necessarily have time to address all the topics of discussion in the remaining however long people in the chat for I think we're not going to go past 11 that's for sure I mean 11 pacific time. 10:13:08 So, is there a way to make a poll. 10:13:14 KITP people. 10:13:15 Is there a way to pull, because my zoom doesn't allow it from here I think. 10:13:25 Yeah, I don't see a poll, either. 10:13:28 Okay, some some zooms allow it. And so maybe I would like. 10:13:36 Can we do it by show of hands, maybe. 10:13:41 So I put these five discussion topics on the screen. I don't know if you can see them. 10:13:46 So maybe I'll just ask people, and now count the results who would like to discuss these various topics and we'll just take it. We'll start with the first one and then we'll see what happens next. 10:14:00 So who is interested in the discussion on interfaces. 10:14:06 As interfaces versus transport barrier and that does have obviously overlap with the topic of transport barriers in the other working group. 10:14:15 So please show of hands if this is something that you'd like to discuss now. 10:14:23 And do it visually if you don't know how to work your little hand, otherwise. 10:14:32 So I have 567. 10:14:34 Yeah, I can see roll. 10:14:40 Okay, so we have about nine people, including myself 10. 10:14:48 Okay. 10:14:49 please put your hands down and. 10:14:52 Let's look at, is there. 10:14:56 Maybe, maybe this is something that we could just discuss very quickly now, I give you a list of interfaces in the previous page Did I miss anything obvious is there. 10:15:11 So this was the list here. 10:15:13 Can some somebody think about topics that I completely forgot about. 10:15:15 Oh Pascal my question about pitcher of conviction was, was it fits under this topic too is this does this count as an interface and your list in, maybe the first one of your list of interfaces. 10:15:26 I mean I would say in as much as the dynamics of penetrated convection probably have a lot to say about a scattering of diffuse of interfaces that does play a role so 10:15:44 yeah i mean i think there was a question there. 10:15:47 You know whether predefined with a predefined layers. 10:15:51 You know, the interface in pre predefined layers is an interesting topic or not against. 10:15:56 I mean there's certainly been a lot of research on that topic so I think we should put it in there as possible. Yeah. Is anybody else. 10:16:04 I was wondering if I should include reactive interfaces in that list but then that becomes a little bit overwhelming and nobody here has brought it up as a research topic of interest. 10:16:15 We something that's sort of tying a bunch of these problems together, including the list that you went through is like turbulent non trivial and interfaces which are not quite like they're not necessarily an interface, in and of themselves but like they 10:16:29 are one that you hear about in the literature. 10:16:42 So, like the environment for example interacting with the floor around it, something more like that. Yeah. 10:16:45 I'm not sure this comes under double diffuse of interfaces, but there's a lot of different ways you can get interfaces, whether it's just say hot and salty over cold and fresh. 10:16:55 But you could also say have ice at the side and have injure leaving and intrusions forming, which looks, it seems dynamically different to me, so I'm not sure if it should be a different category or not. 10:17:09 I mean the inter leaving and intrusions I usually think of them as wq soon. 10:17:17 I don't know if anybody disagrees with. 10:17:20 I guess I'm curious whether it's, let's say a horizontal convection in some senses supposed to vertical. 10:17:26 The if you have heart and soul to call impression of fingering, which seems dynamically different to me from an interview and 10:17:34 I'm not sure if it's worth subdividing or lumping them together and linking into that. I mean, I suppose, part of that question, maybe it's doing boundary layers. 10:17:46 You know, if you have a very strong interface outer boundary layer. Does that count, or is this, you know, too broad strokes talk about something slightly different. 10:17:58 Are you talking about viscous boundary layer or, like for instance, you could have a double the thing about ice is you have a double diffuse of interface at the boundary layer. 10:18:06 So it's sort of half of a interface up like that does that go into multi-phase flow interfaces where you have a face transition. Right, yeah. 10:18:16 90 here. 10:18:20 And I don't know if we have any, you know in the past you know I put plasma equals the interfaces is very generic thing. Are there subdivisions in there and that we need to be aware of that would be interesting. 10:18:33 I mean there's, first of all, that couple of comments. 10:18:38 There are many different types of barriers. In other words, that the barriers in different is put it this way, in this community of fluids and MHD largely is written. 10:18:53 In contrast, we in plasmas are what we would call you know two are multi fluids so there are distinctions of behaviors in density momentum momentum and heat barriers so that's one point can they're quite different, because the transport is different. 10:19:10 I would somewhat disagree with your implied zoology here in that you talk about the barrier as the interface. I would say the interface is the, if you think of a barrier is going you know say from profile with one slope to a profile with another steeper 10:19:32 slope. The interface is the corner right it's the it's the region of high curvature of the profile where you have a transition in the gradient of the thermodynamic quantity. 10:19:44 That's the interface. And that's of great interest right and going hand in hand with that is the question of what's going on at the bottom of the ER well in the, in the H mode, so that you know just, I would not call the the barrier itself the region 10:20:04 of high slow. Good confinement the interface per se. 10:20:11 I see So in terms of trying to rephrase it in this picture here for instance where you have conductive layers and then what I used to call an interface which would be the fingering interface, you would more see the interfaces this particular region. 10:20:29 Yeah, in your in region and the layers. Yeah, I mean if I had a picture of one of these things are my own thing or my own our own things in front of me I could point at it, and, but that's in terms of something we haven't talked about much in this happy 10:20:47 meeting which I'll talk about a little in one of the working groups is the question of how these propagate. 10:20:55 And I mean when you formulate that problem, which is hard the thing you keep track of is the how the point of maximum curvature moves. 10:21:05 That's the interface as it were. 10:21:07 I mean certainly there will be another discussion later on how the interface will structure. 10:21:13 You can take motion of the interface and the evolution itself of the layer in your back. Now that that that's in a different form that appears in the con Hillier now VA Stokes to, so. 10:21:28 Okay, so if you think of more interfaces that have not been discussed yet and that you would like to hear about, please let me know by email. 10:21:36 So let's talk about, is anybody interested in talking about common themes observed in observed interfaces or in in in interface models that hint to similar physics and please raise your hands if you have some things to discuss on that. 10:22:09 So I see, I don't know if Patrick racism. 10:22:21 Maybe not. Okay, so I'm seeing four or five people six, I did, I did. Okay. And then another one that I think came up as a number of times is given an interface now, not even talking about the interface in motion but talking about whether there exists 10:22:37 a steady state of the interface or not, where and how do you maintain the sharp transitions against diffusion of mixing, is that a topic of interest. 10:22:53 I think that's popular. 10:22:56 Okay, Very good. So food team steady state maintenance. 10:23:04 Okay. And then final. Okay, this one I'm just going to remove it because we added it. Okay, so let's start with that final topic then steady state versus time dependent interfaces and I think that's probably all we'll have time to discuss today. 10:23:18 And then in the next meeting will come back to these other questions. Okay. 10:23:24 So does anybody want to leave this with some suggestions for topics. 10:23:38 Well, at least in con helium nucleus jokes. 10:23:43 You know, you can keep track of some things. 10:23:47 For example, we've looked at a droplet to one fluid in another in a turbulent flow. 10:23:54 And in 2d it's quite easy you can see how the perimeter the forms. 10:23:59 And you can actually analyze the time series of that and get the statistical properties of that interface. 10:24:09 Now, I don't know whether similar studies have been done or can be done in the other fields in which I'm not an expert like double diffusion. 10:24:21 But if they are. I'd like to know 10:24:31 anybody would like to reply to this lead Leo you have your name, countries. 10:24:38 I mean, once you're sorry. 10:24:42 Yeah, I was left up from earlier, sorry, to answer your question, I will, I think there's a lot of studies in double digits of interfaces where we analyze the system. 10:24:55 Once it has reached either a statistically stationary state or a state, which appears to be evolving on a much slower timescale associated with the entire staircase evolution. 10:25:07 And then we look at C density profiles struggling and kinetic energy profiles and all of this to determine a quote unquote structure of the interface and the big questions there is indeed whether they are statistically stationary, whether there's a balance 10:25:25 of fluxes that maintains the interface or not. 10:25:29 And I think the, what she's what she's analysis was was quite useful in that sense to revisit that if we could 10:25:44 running. 10:25:53 of a problem in which in some limit. 10:25:57 You have a nonlinear fixed point solution. 10:26:02 So, you may have, I see this, sometimes it's a statistical mechanical methodology where you go to infinity and some number of variables say, and in that limit. 10:26:19 there is a analytic fixed point structure. 10:26:25 Whereas anytime you do a observation, or a simulation. 10:26:31 You have all sorts of fluctuations going on. 10:26:35 So, it's I think it's interesting to collect together. The examples of interface formation that map directly to analytic fixed point solutions in some limit save an ensemble go to infinity limit when in the real world, there was some financial ensemble 10:26:55 of course in some fluctuations think 10:27:07 anybody would like to respond, Patrick. 10:27:12 You was to your original question there I mean I would say you solo thar Schmitz is talk where the barrier or interface let's not quibble was the limit cycle structure, right so there is again very clearly a non stationary state. 10:27:32 It was coherent, there were fluctuations about this non stationary state but it was very, very clearly non stationary. And the question of what maintains it in our game The issue is the external heat source right the token Mac is well for plasma is well 10:27:51 thought of as a heat engine, which converts the power input to all sorts of nifty things flows and structured profiles and things like that, right so that's clearly where, where the energy is coming from. 10:28:12 Sure I guess the key is whether there exists a self. 10:28:16 If we assume the interface has to be maintained as a thin structure. What makes it thin, right, what against say diffusion other might be other system where that's that's a given given the physics that he wants to remain thing. 10:28:31 I mean, if I think that's an interesting question because you're asking what is the width of the barrier in my language. 10:28:43 And, I mean that's that's a question of it's a again going back to keep it to something you've seen the Lh transition where you have a barrier at the edge how deeply does the barrier penetrate. 10:28:57 And that is really putting aside, additional physics which there's a zoo, as you can well imagine that's determined by the pre transition profiles. And the answer to that is in some sense determined by a kind of Maxwell construction right determines how 10:29:30 Be the two phases being the the turbulent and the you know the quenched phase then if you can calculate in principle at least how far it advances from a kind of a game of that you would very similar to a Maxwell construction and that's determined by the 10:29:50 pre transition profiles. That's the cleanest way to define it beyond that of course there's a lot of additional physics that enters. 10:30:01 We have an dm. 10:30:12 I was trying to formulate a question and I think we're getting we're getting there with what you just discussed with Pat. 10:30:13 I don't know who wants to speak first. 10:30:19 It's appears that we have at least a possibility to, to, to discriminate between interfaces depending whether or not they actively participate in their sustainment or not, or they're just a byproduct of what happens in other in the, in the neighboring 10:30:40 regions, and in plasmas, there is. 10:30:45 Well, it's, it's just a hunch, but 10:30:49 the interface is likely to also generate its own phones, emits emit its own phones or avalanches which may dynamically participate into sustaining, or erasing the the interface, and that does not seem to be the case and the double the shoes if, for instance, 10:31:10 So, whether or not the they appear as dynamical agents to their self organization is probably going to lead to a very different way to describe how they appear and how they sustain. 10:31:25 And I guess it's probably goes back to Brad's comments about tracking either the gradient, the slope or tracking the curvature. 10:31:36 Because for avalanches we we track the curvature, I guess that's a very interesting point of view, I would have sent something to say about the web interface, but let's talk let's hear from Lothar first. 10:31:51 Oh, just one more comment on the, on the transport barriers and also the cross be staircases that we saw in the Lh transition of course the the the phenomenon condense that the boundary right and the interesting phenomenology is that the width of the 10:32:07 barrier is actually pretty much independent of the heat flux. So there's some intrinsic scale in the system that we don't fully understand yet that may have to do is the, the driving mechanisms, or the scale of the saturated turbulence that develops then 10:32:24 in the conjunction of Reynaud stress and all the other constants that we and dimensional as numbers that matter that sets the, the base of the barrier. 10:32:38 Now n equals be staircase. 10:32:40 There's no such constraint proceed, have a boundary, so that the, the self organized spatial structure can form, sort of, without the without the boundary condition itself. 10:32:55 And the question is, of course, are there other boundary conditions for example in my net magnetized classmates you have of course magnetic shear. 10:33:01 And you have what we call rational surfaces. 10:33:05 We are basically the islands can condense for example, magnetic islands. And that often seems to be the the impetus that makes transport barriers form in every form the boundary in the volume, and of course the the staircases may not have that constraint, 10:33:24 but I think to find out how the boundary conditions and the scaling of the problem. 10:33:30 effect spatial localization is a very important point. Certainly as far as plasmids are concerned. 10:33:39 Before we quick reply pass okay. 10:33:45 I think we are, we're slowly reinventing Bly or ballsy or whatever you want to call it thinking in this discussion we're back to to link scales, right the quick summary of this of the this kind of array of things is multiple couple of length scales are 10:34:21 And that basically, I think, captures a lot of these models, these stories in a kind of metal structure. 10:34:33 Yeah. And actually that's a good transition, I was gonna ask the community I was struck by turbulence and double diffusion what they thought of Dylan's comment on interfaces that exists, just because they happen to be there versus interfaces that genuinely 10:34:47 participate in their self regulation. 10:34:52 Other examples in that you can think of. 10:34:58 Alexi Chris, and then Chris and Brian you've had your hand up for a while. 10:35:03 Sorry. 10:35:04 Um, so it's it's interesting to bring this up because there's, there's been some recent work looking at in the context of sheer instability so your Calvin hormones versus your home bow. 10:35:14 There has been a hobo is the one that keeps things sharp right keeps your initial stratification kind of intact throughout. And there is some suggestion that humble induced turbulent self organizes that it's kind of maintaining itself in a marginal state. 10:35:28 There is a bit of an analogy there, if I'm understanding gams comments earlier correctly there I think there is some analogy there in terms of that interface sort of playing a role in keeping itself alive in the actual dynamics. 10:35:46 Chris, do you want to comment. 10:35:49 Yeah, I just kind of wanted to comment this is kind of the discussion about sort of dry weather weather and interfaces kind of self sustaining on its own, or whether it's being sort of sustained by some external. 10:36:08 Some something external say, like, in just a singly stratified case, your. 10:36:17 in the double diffuse of case, the diffusion of the two elements, sort of, essentially sustains that but then I think it's important to distinguish between the like various cases and tying back to that something Bruce mentioned earlier about how when 10:36:45 you have the lateral gradients and the double diffuse of case it really, it's kind of fundamentally different and how that system is driven and how the interfaces can be sustained that mess, wouldn't necessarily survive on their owners purely, sort of 10:37:24 a 1d profile, but it's the latter adventure that really matters for sort of sustaining those interfaces so it's I don't know I think there's something interesting to think about in terms of whether an interface is sort of sustained through some large 10:37:25 external effects, or whether an interface intrinsically like maintains itself. 10:37:40 David is that on the same topic. Yeah, kind of, I mean it's just a comment really that if we look at observations like these that Mary Louise shows and things It seems that double diffuse of interfaces can be maintained. 10:37:55 You know, for long periods of time over long distances in the ocean. 10:37:59 And when we do the simplest numerical simulation, that's never the case right. 10:38:05 So there's something, there's something missing in standard boost in SMA line simulations or there's something extra that's really going on to keep the real interfaces sharp whereas in the US, you know, in the, in the simulations. 10:38:25 I believe that in the end they would always run down to one step. 10:38:35 Mentally sure that's true for the high potential number limit as appropriate for the ocean. Okay, let me rephrase that. Okay, if you do, if you do numbers which look like the ocean, I suppose so you know parental number seven and if you say that the ratio, 10:38:45 you know, point one or something, then, then I think they suppose I know the simulations I've seen they always run down to, you know, the steps just keep going and keep voting. 10:38:59 They keep voting. But in reality they seem not to, which is kind of an interesting it seems seems some active something active to keep them going in reality that is missing out of those simple systems. 10:39:12 Brian you had a 10:39:18 chance to really come in on this particular topic so different. 10:39:25 So where are we at the interesting, I wanted to comment on the web interface is what's interesting is in the for the defensive interface in the Arctic. 10:39:37 They are self maintaining in as much as it's the diffusion of the temperature fields that then drives the convection in the adjacent layers and then scours the interface to maintain thin. 10:39:48 So I think that's a good example of a of an interface where the interface will structure means meetings itself. 10:39:57 game did you want to comment again on that topic. 10:40:03 Yes, sorry. 10:40:07 I had a comment, maybe two to connect to what David just said, and connecting also to my earlier one. 10:40:15 If we were to put some suggested city in the problem maybe that could unite things in the sense that barriers that would keep existing by themselves. 10:40:26 Regardless of an amount of statistics city in the problem, versus barriers or interfaces that would vanish, or be hindered or would be wiped away with some amount of statistics city that could make a good distinction maybe between the type of interface 10:40:46 where we're talking about an element of robustness that's an interesting point as well. 10:40:53 And Brian, I think you've been waiting so long. 10:40:58 Yeah, this is that probably a change in topic is, is there a distinction or should we discuss a distinction between mechanisms and an analytical theories. 10:41:15 To give an example, in the case of the beta plane jet, like the jets to the caches planets, 10:41:25 a simulation will be done and shows the formation of the jets and of course the observations show the Jets as well. 10:41:32 And so, a mechanism is conjured, the inverse cascade. 10:41:40 In a scale intrinsic to the problem is conjure day. 10:41:49 And, and an agreement is pointed to between the concept of the energy going to larger scales, some form, and a link scale. 10:42:01 And this is the called the theory upscale it's called the rest of cascade theory. 10:42:09 And the other hand, there are some examples of explanations in which there actually is an analytical structure in which a solution is found to be compared with the observations, rather than a scale and a supposed mechanism. 10:42:25 So is it is it useful to make a distinction between a theory which actually has an analytic structure and a theory which is composed of supposed mechanism, but has no analytic structure. 10:42:47 Does anyone want to comment on that question. 10:42:56 Adrian. 10:42:58 I, I'm sorry I think I misunderstood part of it I can you clarify what you mean by an example where there isn't this analytic structure and trying to follow your point. 10:43:19 A theory has to have an analytic structure and make specific predictions. 10:43:24 The in the arrested cascade theory of jet foot formation in beta plant terminals has no analytics structure and makes no predictions, it has a link scale. 10:43:25 It's to make a distinction, oftentimes people speak of theories what they read is a mechanism. 10:43:37 And it has a concept the mechanism of so have an inverse cascade. 10:43:44 But it makes no specific predictions. So, I'm saying. Shouldn't there be a distinction between a theory, which doesn't have an analytic structure and doesn't make predictions and a theory which really consists of a supposed mechanism, and maybe a link 10:44:04 scale or some part maybe a, you know, some something which is a property of the equations of motion, it would be true for any correct theory, it's just a light scale it appears in the problem of course it's going to be satisfied. 10:44:19 I mean, possibly one is a necessary step to the second Ryan you need a mechanism before you propose a theory and and i agree that in, in a lot of at least in the, in the subjects described that is one problem in double diffusion it's another right where 10:44:37 there's a lot of hand wavy arguments for the nature of the structure and the structure of the interface, but they're very, very few theories that actually capture into facial structure and when compared with the data actually provides the right structure. 10:44:53 there's a lot to be done there. I completely agree. 10:45:01 Perhaps 10:45:01 you're wanting to go back activity, just interject something related to what we were discussing with dm before. 10:45:09 I think it's useful to note on this subject of robustness in the face of external, shall we say irregularities which can be noise chaos etc etc. There are two short talks in the plasma applications Working Group next week, I, I guess the cataract student 10:45:32 Robin Moran's and my students Samantha Chen on exactly on what happens in barriers and layering when you have irregularities in the magnetic field, so it hits on exactly this point. 10:45:49 So, I wanted to mention those because this group might automatically write off plasma applications but it's a it's a good illustration of precisely what was being discussed there. 10:46:07 Any other comments on statistically stationary versus slowly involving interfaces maintenance processes. 10:46:21 I mean, I generally would like to encourage people to do precisely what Brian was suggesting is create formal models for interface structure and that's something I personally have been struggling for years because we have all this data on say the very 10:46:43 turbulent interfaces that David has been talking about some partially turbulent interfaces and although we have a lot of empirical results on say transport through the interface, there's very little that or we don't really know how to model them, so any 10:46:54 suggestions for how to do this would be very welcome I think. 10:47:00 Is there enough energy left in the room for approaching a second discussion topic or shall we just briefly discuss what we want to do next time. 10:47:12 Maybe the second. 10:47:17 So that's me. 10:47:18 Okay. 10:47:20 All right. 10:47:21 Is this format. Okay, I don't think next time we'll have so many short talks I really wanted to have a broad view of interfaces. 10:47:30 Are there any volunteers for discussing aspects of interface structure or interface evolution next time. 10:47:38 We're thinking 10 minute talks. 10:47:43 packed. 10:47:55 And we're going to talk about, you know, some aspects of the con Hillier Naveed a Stokes problem and how the interfaces evolve and how that constrains the dynamics, then I could keep it fairly short, that would be. 10:48:05 And then we also have David drip show who's going to talk about control dynamics for PV interfaces. 10:48:15 So, any other maybe we could do a third one, again, thinking under 10 minutes. 10:48:25 Pat. 10:48:31 Allah. 10:48:31 Yes, I think we had discussed that in gathered town right after this meeting, I'll be just briefly, introducing an outline of a stochastic approach in. 10:48:49 You're only a discussion. 10:48:52 And based on that, gather time discussion we can consider whether it would be of interest to the group more generally to present that at some point. Okay, that's a good. 10:49:02 That's a good idea. 10:49:06 Um, okay, well we'll, the next meeting will be on Friday next week, so we meet on Fridays every week from now on. 10:49:15 And if anybody has discussion topics for weeks beyond that, please let me know so next week we'll talk about interface motion. Okay. 10:49:28 interface motion, and, and, and how it's controlled by the interface will structure in some in some sense. 10:49:34 Okay, so thank you very much for participating discussion I encourage you to join the gather town.