 of the Turbulent Mixing and Beyond Conference in 2017. And in this section, we will have talks which are discussed in the Turbulent processes using experimental data and analysis, as well as the mathematical works. And it would be, maybe, I will see, like, you know, if I will be given my own presentation. And then after this, we will make the program closure. And then the members of the organizing and evaluation committees will be staying for evaluate to compare the results for the best, post of the world and the unsidest of the world. However, we are still in a good shape, I think. We should proceed now with the work of Professor Redonda. Professor Redonda and his collaborators on admire mezcal mixing and fractal analysis. OK, thank you. I think that you can hear me. Well, I will come in on several aspects. And first of all, I would try to convince you that there is more to see in the complex interfaces, and not only in admire mezcal. For example, this is, let me see how. OK, this is, I have to go forward like this. Well, some of the motivation spans to astrophysical and environmental flows. But this is one of the important examples of a enormous galaxy, sort of Rayleigh Taylor, or rich by a mezcal, like a super galactic structure. And at the same time, you have very small scale processes in shops. And we want to understand from the large scale to the small scale. And I will be concentrating on scaling, basically. This is an old story, because you know Takanawa's wave. OK, and you notice that this sort of observed filamentary structure is probably more revealing to what it seems. Because not always we see all that is there, not even in the experiment. So you sometimes have to go to higher order processes or to non-linear processes to detect really what is there. Because in simulations, David Young compared different types of simulations. And of course, you see that the topology is totally different from simulation to simulation. And you don't have to perform a multi-fractal analysis to see by eye that, well, the resolution really is very different. The same type of simulations from above. And this is well-known. It was published by Shershanna. And you see that, well, they have some sort of structure. But when you zoom in the interface, and I would say a bit further, when you zoom at either side of the interface, you find a different story. This is still to be examined. OK, well, this is something which I will leave you to read. While I comment a little bit on the two basic aspects of when do you decide it's Rayleigh Taylor, when do you decide it's Rick Meyer-Meshkov, well, if you have the acceleration, and you have it in time, and it is smooth, and it increases that Rayleigh Taylor, in a limiting case, like in the shock experiments, we did that, and this was Paul Lindens' experiment and many other setups paid by the atomic weapons establishment in Cambridge. And eventually, we would get these growing fronts. What happens if you just give it a shock? And our interesting idea that Jacobs has exploded in the Lawrence Livermore lab is to do like the typical, and I want you to try it with a tequila glass. This is what Mexicans were doing for many, many years. You just bang it into the table, and you shoot up the, OK, you can do a more or less sophisticated Rayleigh analysis. But if the density with height in the basic Rayleigh Taylor analysis, it began being heavier on top and lighter, stored DL, and I would not feel at all between 1998 to 2018. Has tried, you know very well, the different configurations. You can have something like this. And with this configuration, it's possible to measure something which is very difficult. It's a mixing efficiency. But you do it per unit area, and there's different combinations between how the potential energy goes to kinetic energy and again to potential energy. And this is a complex process. But I will concentrate on what happens, for example, when this hits the floor. Then you shoot and have a different type of flow because the main difference is that here the acceleration is just a heavy side function. And there's no or you can have something like this. And then you accelerate and then you decelerate. This was one of the problems in the initial test because everything that goes up, it must come down. But I will continue with some more detailed visual analysis. And I will set up for the second fractal. It's important to notice that there can be different fractal dimensions for everything. Even in the same experiment, you'll see that the fractal dimension of the vorticity is not the same as that for the helicity or the hyperviscosity and so on. But going to the real detail and reach my front, OK, the velocity jump, like in a shock. And I will not go over the experiment, but layers, theses and what Lazarou has and all the group have been doing with a plane and modified interfacial waves is really very important. The interesting thing is, and this is all history, but the interesting thing is, well, what do we learn extra from things like that? And you've already seen this very, very often. The type of all experiments were like this. This was the first configuration, but now it's improved a lot. But I must tell that many of Jacob's experiments, they include, well, even if there's mixing some di-frontal number or either there is artificial smoothing, not only because of the surface tension. In cases, there are clearly different fluids, but also because the other processes are taking place. Many of the experiments initially were done on heli-show cells, and then you could have a, I could call it a tertiary Kelvin-Hellholz instability coming from the shear from the two sides. And these were some of the interesting new experiments in which you say, well, where the hell is a secondary line coming from, and Andrews showed that for very large-scale shear Rayleigh Taylor. But again, as Shersana said last in her talk, it's not the same to investigate the structure of a Rayleigh Taylor or a Kelvin-Hellholz instability than an accelerated or a non-uniform. And non-uniform can be in time or in space. So this comparison of different interfaces is what I would like to point out a little bit in a parameter space. And when you have differences between the number of boxes on the sides of the box, you're really looking at some of the isolines you were seeing before. But if there is mixing, if there is not just scalar detection, but velocity detection, the problem is that now you can get three-dimensional velocity profiles with resolution. And it's very difficult to do that in the experiments. But what is true is that an infinitely sharp interface is impossible. And within the range of intensities, each of the fractal dimensions of the different intensities, here you just count the number of boxes which is covered by the complex interface. And it has to be between if you have a long, long plot. This is the scale of the box. Well, it would be the inverse. So this is the scale, the higher the numbers. If the slope is 2, then the whole surface is covered. But again, this can be a 3D or a N or a multidimensional space. And the experimental information. But notice this is for one value. You can have, even in the same process, you have different processes that modify the topology of your flow. And if here you have a dominant voltage or a secondary or tertiary instability. And for example, this is what you normally see very clearly. But you don't just see this. You really have secondary and three dimensional complex instabilities as soon as you increase the rate of number. Of course. This type of parametrization sometimes it doesn't show in the first order statistics. And notice if N is 1, again, it's the mean. If N is 2, the second order, it's the diffusion. If N is 3, it's the skewness. If N is 4, it's the cool process. And here is where you begin to look at intermittency. And from structure functions, you know that a PDF does not tell you much. And you can say the mean, the variance, square root of the variance is a standard deviation. The skewness, you're going to have it like this or like this. And all half the same mean, I like. And it was the first time I realized that certification has a huge effect on the kurtosis, which is really talked about like the intermittency. Because if you have something like this, you have a huge intermittency, which it really means the very strange far away from the mean. On the other hand, if you have a flat, kurtosis in Greek means actually flat, then you have something like that. And basically, this leads you to the intermittency. Everybody thinks there's only one type of intermittency. It doesn't matter if it's in time or in space. And of course, Taylor's hypothesis should not be valid. But the important thing is that, well, we just compare this distance. So what you actually measure as the six order structure function, so the relationship between topology and intermittency is very close. And of course, the topology in filling up the space is given by the fractal dimension. So the main point is that I will comment something which is not different at size of, OK, that still has to be proven seriously. But how you define it? Well, as a single intermittency, it's just twice the third order structure function minus the sixth order structure function. But OK, if you really measure that, you get a wide range of intermittenal models, 0.1 and 1. Intermittency is not a unique parameter. So probably, yes, this is, well, the actual intermittency also is related to the Kolmogorov basic hypothesis. But K61, it really eventually says that it's like, eventually, mu prime Q over L, and that leads to the straight line. But because this is related to the correlation, this should be squared. So what is important is all of the type of structures, because in stratified flows, you don't only have the, well, annual number. I prefer to call it the richest number, but some relationship, let's call it density interface, or density difference, or annual, OK, but the average, or it's normally twice. But for example, you can have a rainbow number effect. You can have, I prefer to use a richer zone. It's a number, but it's similar. You have a rosary number effect, rotation, and other type of compressibility and all sorts of body forces. And in principle, I will just show you this complex parameter space, where if you point out different fractal dimensions in different interfaces, you get a chaos. It's not the same at all. And I will show some more, these were basic experiments for a range of annual numbers, which of course, if you use mercury, then it's smooth. Everything is smooth. The density difference is so high. But the density difference really influences more surface tension than other things. This type of complex structures, which you will see, were calculated in Moscow. And you begin to have these secondary and tertiary spikes. But still, the actual inner resolution is much more complex. And for example, if you can detect the basic topology of the growth of these rigmaribusco scales, well, to fit a line, if you would fit a leopold of exponent, which is not a bad idea, is that it goes exponentially. And the exponential has all of the possible power loss. So when you have, and this is a secondary structure, or a large or an initial eddy, that really has a surprising long memory. And it also has a surprising long memory on the structure of the fractal dimension. And how different parts of the interface have different fractal dimensions. And not only that, different qualifiers. Because Fritz wrote his whole book on homogenous flows. So you need another freezer for that. So you need another freezer for the students. It's an interesting reference, but it's not the Bible. So it's not the, and of course, the color effects at both sides of the interface will be different. Not only because the solute or the diffusivity can be different, but because the topology is different. And there's a whole thing, OK, you can compare it with, and remember, Malik's in the presentation. Now we will do a large-scale, intermittent fractal force experiments. But for example, these are some results of what I was telling. The fractal dimensions go all over the place. And they have to be treated, OK, from the simple to the complicated. Here, for example, we compare the multifractal flows of single plumes or multiple plumes. Anya Matulka participated in these experiments. So you know that the work. And even this type of analysis, and now I will generalize, can be applied to helicity in the atmosphere or even have vorticity and helicity cascades. And look at the scaling, like you did for acceleration. For example, this is a vorticity evolution. And here you also have to compare the multifractal self-similarity of velocity, vorticity, higher order intermittency, et cetera. And I will finish more or less showing some more wind information, which is really Yahweh and Edel and some other colleagues. And Claude Cambone is here, every yogurt, like me. But this was in Villanova in La Gelture. You're only invited, eventually, to come before the Marseille conference. We have to arrange who wants to lecture, basically, for the students, Ercov-Tac, Euromake, Simne course. But I think Marseille will be to Jean-François, knows very well Marseille. But perhaps you don't remember Robert Keane from the state. And well, this is just what I wanted to say. And well, I will not extend. Yeah.