 Okay, so this is the final session of the day. My name is Richard Sidora, and I'm going to be chairing this final session, which is on the area of non-equilibrium processes, and it will be in fluids and in plasmas. And we're very happy to have the first speaker, which is Julie Tysheshkin from Moscow, and he's going to talk about structuring in fluid flows. Thank you very much, dear chairman. Thank you very much everybody who come to listen, and thank you very much organizers who give me a chance to present this talk to you. And I am speaking about components of common fluid flows. At content of the talk is standard, some introduction, severe remarks about differences in mathematical and physical fluid mechanics, conventional models and properties, lost properties of the fundamental, set of fundamental equations, some examples, and the conclusion, what is recommended to do in future, I hope. All computers change our life in many dimensions. The first of all, it gives room to look in large scale and small scales. And everybody in all, thank you. In all dimensions of scales, one can see structures. Structure means that there are relatively smooth elements and very sharp boundaries between them. And the structures are universal from galactic scales to see surfaces which can see flying on plane. And what is interesting is that images of the structures are different in different variables. For example, in the sun, you can see generally the sun is circle, but position of bright and dark elements and boundaries between elements depend on the wavelength in which it is observed. And that is essential. There is a strong difference between modern experimental techniques which reveal fine structure of flows around the body, for example, slow-moving or fast-moving in aerodynamic, and computer modeling of the same flow with everything looks rather smooth. And another difference is a large lag between theoretical fluid mechanics and theoretical solids. 10 to 15 orders of magnitude difference and mistakes. So something wrong in common fluid mechanics because the accuracy is extremely low. A lot of people put attention to fluid mechanics and introduced brilliant discoveries, and all of them really wrote recommendation and laws, important laws. And these important laws are well known and printed in all textbooks, and they include the continuity equation of the Lambert Navier-Stokes equation for momentum transport, heat transfer, subsurface transfer, and equation of state. And what is the most important equation in this system? The most important equation is equation of state because it describes both thermodynamic properties of fluid which can be governed by very fast atomic molecular processes and initial property of fluid, the slowest property of fluid motions. And what is important is that the density really is derivative of thermodynamic potential, and certain other variables also. So the fast atomic molecular processes manifest itself first in the density field. And only after that influence reveals in other fields. So I show you realization, and in other things which I cannot understand why it was lost, it is lack of analysis of the set of the system. It is the collection of the equations. It is set, and it is the first demand which we must put in analysis of the system is condition of compatibility. And what is the rank of the system? How many independent functions describe the common total solution, complete solution? I haven't seen in textbooks analysis of the general properties of the set. And if we look on the set, we will see that there are small coefficients in the terms with high special derivatives for viscosity or heat or salinity or concentration productivity in the single-operative terms. So we have regular solutions of the set and have very rich family of single-operative solutions. And what people show this before and before talks about filament structure of the different flows and different scales and fast and very slow really means that single-operative solutions are the most important in some physics because they describe small-scale component, very fast, very variable. And mathematical analysis of this component gives a room for improvement of experimental techniques and analysis of experimental data. If we simply look on the set in general, we will see that the set contains a lot of intrinsic scales, both length scales, variables, basic variables in mechanics only three, length, time and mass. All other variables are derivatives. So we have a fundamental length, one fundamental time, two, and mass is specific analysis. And the number of length scales and temporal scales is large for the system. And it contains large values, like, for example, stratified fluids, logarithmic buoyancy scale, or it has a small connected with, very inconvenient for my fingers, connected with the dissipative parameters with viscosity, diffusivity, so on. And dividing the scales on appropriate velocity, we will see different time scales. They are very large and they are very short. And some of them, which are ratio of scales dominated by viscosity or dominated by diffusivity and velocity, they are compatible with the scale of atomic molecular clusters. So in common fluid flows, there are components which are governed by atomic molecular interactions. So to visualize and to experimental study this phenomena, we must see flow in general and resolve its component. And it now is done in wide range of parameters, as we saw in presentation today. We use conventional tank with high quality optic windows and aerospace slurring instrument, a sort of instrument which resolves very fine flow components, and use large for common fluid mechanics and slow for physical plasma cameras, so we can see microscopic structures. And any common processes in this precise visualization take new features. For example, flow past the sphere in a homogeneous fluid. The flow past the sphere in 350 is cylinder. It is visualization, electrolytic precipitation. The dye dissolved on this belt and cover the envelope of the wake. But if we have stratification and variation of density 10 to minus 3 on the distance of the sphere, you see a rectangular wake with vertical cylindrical columns and dye accumulated on interfaces of the side walls of the wake, symmetry catastrophe. And this symmetry is caused by the formation of high-gradient interfaces. And all features are collected really on these high-gradient interfaces. And the largest gradients of thermodynamic potentials occur on these high-gradient interfaces. So small variations in position, small intersection of high-gradient interfaces, leads to the general variations of the flow. Exactly the same. You can see we have a convection above point. See of heat, source of heat. You see conductive cells and interfaces separating different layers. And intensive convection around the cooling device produce very complex flow field and formation of ice really on the freezer doesn't change the general property of convection and the existence of these very fine structures. And these fine structures have a large effect on some properties. For example, on redistribution of matter. Before the experiment you see the markers which was placed here, not placed really dissolved from the coating of the cylindrical freezer. In vertical and after the experiment, double diffusion of convection and layering, you see that all markers are collected on interfaces, general restructuring of the flow. So coming back to the equation, what we see, we must estimate the symmetry of the flow, estimate what parameters can be observed in the experiment and what parameters of the equation cannot be observed in the experiment. And if we look on this set, we will see that density and other thermodynamic parameters, temperature, pressure can be observed. But about dynamical parameters, can velocity be observed in the experiment? No, it is kinematic parameters. It's related only with coordinate frame. We have no features in the flow which can be attributed as the flow velocity. We can estimate the transport of marker, we can estimate the transport of substances, we can estimate flux, but we cannot estimate fluid particle. So velocity is an observable parameter. And only momentum is observable parameter. And of course ratio momentum to density gives the velocity, but density is fast variable. It's a very unstable parameter. And the next question, what is the rank of the system? Why the system is good? The system is sequence of low conservation, conservation of mass, conservation of momentum which homogeneity of energy, conservation of energy which homogeneity of time, and conservation of matter, knowing momentum and fluid. And if we calculate the symmetries of the flow of the system, we will see that symmetries exactly correspond to these physical laws. Only shifts in time, space, and pressure invariance with rotation for homogeneity fluids and Galileo transformation. No other local groups symmetries. But if we look for conventional Navier-Stokes equation for homogeneity fluids, we will see that some groups saved, but principle of Galilean relativity is expanded to accelerantly moving systems. And pressure is supplemented by artificial sub-algebra of pressure shifts. And there is another generator of extension which explains the efficiency of boundary layer approximation. But this generator has nothing common with the property of the original set of equations. It's only the sequence of the crossing, the relation between pressure and density. It is artificial. Another approximation has its own intrinsic negative properties. And for example, a lot of theories of turbulence have no physical law symmetries. They save nothing physical property. So people have no right to denote the same symbols, the parameters of this equation as in the fundamental set. They absolutely have no common, absolutely different. Coming back to the equations, basic equation, first step in analysis is to realize, linearize. And if we linearize, we will see that these equations belong to the singular-perturbed kind of equations. So to construct complete solution, we must wrote both expansion in regular and singular form. This was done. Dispersion relation function was for wave theories. Function are searched in exponential from infinite to medium. It's typical. And dispersion relation, for example, for certified fluid with dispersion and with diffusivity, has very specific form. It has a typical wave form connecting wave and dissipation. It's typical dispersion relation connecting frequency and wave numbers. And it contains another terms, which first order of the wave number, which means that the solution is very sensitive to the boundary condition. And this is Stokes boundary layer. So Stokes periodic boundary layer existed at any point of fluid flows, not only in the boundary. At any point. And if we start to simplify these equations, for example, we introduce the permanent density, constant density, you will see that the Stokes flow became twice doubled. There are two identical Stokes flows at any point. So the system became generated. It is conventional Navier-Stokes equation. It is singular perturbed degeneration set. And compressibility doesn't change the situation, because the degeneration is the sequence of connection between material density and material pressure, not only the compressibility. So the scheme of the fluid mechanics, conventional fluid mechanics equation, looks like if we take it to account all physical properties, complete equation of state, we can end variation of density, we can solve, and these problems are well posed and solvable. But very complex, because they contain a lot of singular perturbed solutions or small scale solutions. If we say the variable density, we can receive solutions up to the Navier-Stokes equations. If we put approximation of homogeneity, we immediately, in a third step, we receive the condition of degeneration and unsolved problem. Examples. First, a number example was constructed in the periodic internal wave theory. It is analytical solution. It is numerical realization of the set and analytical solution. And this quantity manifest in very simple interesting, source of wave is oscillating piston. Sequence of waves is vertical wave cone. But this vertical wave cone really is covered by thin interfaces. And these interfaces are pronounced when the viscosity is small and very smooth at what is important. It is not permanently existing interfaces. Their intensity depends on the wave phase. So, in some phase, these interfaces is pronounced in other phase, this interface. But in this area where the singular perturbed solutions intersect, their interaction became very important. So, it is view, it is interfaces, bound in the wave shock. It is experiment, a salient experiment with oscillating strip. You see internal waves. And you see these interfaces, which are really cause diffusion and use flows, because the certified liquid is non-homogenious, not uniform. And, sorry, I did something wrong. Can anybody help me to come back to the normal size of this computer? Yes, Masha, yes. But the size is... Thank you very much, excuse me, please. And the frequency is less than buoyancy frequency. Simultaneously, we see different modes, not only the linear waves. And it is important that all waves, all wave fields exist and fill the whole space. Only the intensity is different. And accuracy of our instruments is our method of observations. Slewer interferometry is more sensitive, but resolution is worse than the resolution of Slewer method. And we do not see these interfaces, which are diffusion and use flows on the sequence. We see here, and do not see here. So our instrument, its dispersion relation is rather good. And what has happened when we increase the amplitude of oscillation? If we increase the amplitude of oscillation, of course waves became more energetic, became the interfaces covering the waves. And the thickness decreased with the velocity of the wave motion, the interface motion. And gradually, due to Brody's mechanism interaction between stronger, stronger, and like interfaces forms, and vertices very well outlined form in these areas. Not near the body, not only the body, but far from the body in the free space where in the conventional description, only this most variables exist. And it is oscillation of neutral buoyancy body near the horizon, neutral horizon. You see that all is disturbed around and far from the body surface. Method is good to pre-calculate. For example, this is variable buoyancy frequency distribution and permanent frequency waves cannot propagate in this area. Calculation was done. And 14 years later, the difference between calculated waves amplitude and measured by Pauliades vini up to several percents. Then in all slides was shown the filament structure in the high energy physics in models of nuclear fusion. Filament structure existing in all vertical and all wave flows. I show you only one kind of flows and propagation of marker from the small drop of dye put on the free surface and drop of dry dye transformed into spiral tongue and spiral tongue is separated on different interfaces and this time the boundary between interfaces between sharper and sharper opposite to the action of diffusion. If we put the solid marker inside the water flows, solid marker not only transported but also rotate and disturb fluids around itself and behavior of dye wake became looks like turbulent behavior but if you look at the same experiment and the dye introduced from the dye drop fall on the free surface without disturbances you will see smooth pattern here and very complex pattern here. And coming to the most for me impressive experiment and statements. I remember the repeat experiment of Rogers concerning the creation of vortices by drop falling into the fluid and Thompson observed a cascade of secondary vortices and Darcy Thompson and other English scientists 100 years ago published beautiful book on growth and forms in which he discuss different types of growth and different forms around the falling drops and the question why this secondary and other vortices consist from filaments? How these filaments are formed? Why they does not disappear? This is drop contacting with the fluid surface dropper smooth fluid surface is cold and you see the trace of net put on the bottom to check the quality of images so no disturbances of the surface and all disturbances look like coming out of the area of impacting of the drop so you have a number of spikes but what we can see if we look from side we can see that spikes and particles fluid particles propagate not only out of the domain of interaction some of these drops go back and hit on the surface of the initial so these droplets results of very strong accumulation of energy in this area and velocity of these droplets is larger than velocity of this drop how it can be? how the energy can be increased? so we need an additional source of energy to produce these fast and local interfaces another example if the drop is constructed from dye it does not cover the surface of the cavern and doesn't cover the surface of the crown uniformly as a sheet it covers its separated linear filaments but it is universal behavior does it matter? fluid must be mixable it doesn't matter what kind of mixable fluid it is milk it is a brilliant green dye which used in some medicine and it is common pen dye result is the same the third mechanism leads to the redistribution of continuous dye accumulated in compact drop into similar in the independent interfaces it is non-uniform distribution of internal energy in the fluid internal energy depend only on temperature and pressure for example only in uniform fluid depending on the balance situation but when you have a liquid drop you have a surface with strongly anisotropic and maybe even ionized components and another with thickness 10 to minus 8 cm another layer 10 to minus 6 cm it is layer of accumulation of surface tension where atomic interaction is anisotropic and exchange of energy this and this when these two volumes start to contact of course different firstly when you have the energy the amount of energy total in this layer is small it is percent less than 10% with respect to the general mechanical energy of the moving drop but the density of energy on several loads of magnitude is larger so this high dense energy produced the most the most important effect redistribution of matter the momentum distributed uniformly you have round crown but masses redistributed absolutely in uniform so and another very important moment interaction moment impact on the quality of fluid flows is chemical potential concentration in small variation is supported by the large gradients and in large gradients there are large gradients of chemical potentials and interaction of different with large gradients of chemical potentials leads to the to the exchanging of energy and the manifestation of internal intrinsic potential energy which was accumulated in the fluid is then converted into motion and temperature and pressure and this process is regular up to the last slide it says some mechanical analog of pellets when you have it is common dye and it is dye coated by the oil when the dye with oil interact with free water surface immediately crown starts to grow and number of volume of dye inside the spikes depend on the ratio of the sizes the larger ratio the more intensive color but formation of these structures very complex but regular periodic depend on the ratio of the volumes and only prescribed by the existence of several interfaces several mechanisms of distribution and redistribution and realization of internal potential surface potential energy internal potential energy so coming to the conclusion equation of state is basic thermodynamic equation of state is basic equation to describe fluid flows dynamics and structure compatibility condition prescribes the order of the system and the number of dependent function producing common total solution energy is change of energy the most fast processes in fluid flows and number of temporal parameters of components slow in exchange of momentum fast in exchange of energy and very fast when we have accumulation and releasing of available potential energy so thermodynamic potential is very important parameter which can be studied more carefully and described more properly and coming back to the experiment fluid mechanics experiment must be renovated must be renovated basing on fundamental set of fundamental equations so the same phenomena wave motion, vortex motion jets, waves have absolutely different parameters when we study all flow components when we can resolve internal structure of the flows