Laboratory for Modern Hydrodynamics

Scientific results:

1. Analytical and numerical modeling of the chain of interacting modes in two turbulence models has been carried out: generation of the second harmonic in pairs and resonant interaction of triplets. The spectra and cumulants for forward and reverse cascades in both models are analytically derived and numerically confirmed in the limiting case of balanced (two-stage) chains. The amplitudes and dependences on the mode number for a chain of irreducible correlators (cumulants) invariant with respect to gauge symmetry in these two turbulence models are determined. The self-similarity of the distribution function is found in the limiting case of balanced (two-stage) chains.
2. It is shown that the mutual information between the waves is stationary and small in equilibrium, and in weak turbulence it grows linearly with time. The growth occurs due to the concentration of probability on resonant surfaces. Conclusion: for arbitrarily weak interaction and proximity of the statistics of one mode to the Gaussian, the stationary distribution in the full phase space of all waves is very far from the Gaussian one, which is expressed in an abnormally large relative entropy.
3. In the experiment it was found that at a sufficiently low speed of rotation of the liquid in a turbulent flow, a large geostrophic vortex is formed-an anticyclone, stable in time, which is fueled by small turbulent pulsations. As the rotation speed increases, the anticyclone collapses, and instead the volume is filled with long-lived cyclones, the number of which increases from 3 to 20. The characteristic features of the absorption of inertial waves by geostrophic vortices and the properties of such vortices themselves have been analytically established. The analytical results and experimental data are compared. It is noted that the mathematical description of the absorption of inertial waves by geostrophic vortices is almost identical to the description of the absorption and reflection of internal waves in a stratified liquid by a horizontal flow having a vertical shift. This proximity of the mathematical description allows to compare the data of our experiment and the dynamics of currents in the oceans.
4. The obvious physical applications of the two-dimensional formulation of the incompressible fluid flow problem are the turbulent states of soap films and thin layers of various liquids. The most important situation where a two-dimensional picture serves as a good approximation is large-scale atmospheric turbulence. The sizes of cyclones and anticyclones are usually much larger than the thickness of the atmosphere. The structure of these vortices has been described analytically. A deep and subtle point of the constructed theory is the awareness of the role of dissipative mechanisms: viscosity, although small and not included in the final expressions for the velocity and vorticity profile, is fundamentally necessary for the formation of coherent structures.
5. Long-term observations of dynamic phenomena on the free surface of the He-I layer with a depth of about several centimeters in a wide temperature range above Tλ made it possible for the first time in one experiment to study the excitation, evolution and attenuation of vortex flows on the surface of the "deep" and "shallow water" layer.
6. A complete system of nonlinear dynamic equations for nematic and smectic A liquid crystals under the action of an alternating electric field is presented.

Education and personnel occupational retraining:

Three dissertations have been successfully defended for the degree of Doctor of Philosophy.

Two master's thesis have been also defended, and the authors have been admitted to postgraduate studies.

Cooperation:

• Institute of Solid State Physics named after Yu.A. Osipyan RAS
• Institute of Design Automation of the RAS