Study of the general laws of spatio-temporal behavior of nonlinear fields in dissipative nonequilibrium media is of great interest for various applications (technical, chemical and geophysical hydrodynamics, biomechanics, the physics of gaseous and semiconductor plasma, liquid crystal electrodynamics, laser physics, and others). The recent studies are based on the earlier works of the IAP RAS school in "oscillations and waves" (А. B. Ezersky, S. V. Kyashko, M. I. Rabinovich, V. P. Reutov). The principal results were obtained in the following directions.

Spiral structures at parametric generation of waves in a vibrating layer of silicone oil

Dynamics of defects and domain walls in homogeneous and inhomogeneous media. The dynamics of irregularities in spatially periodic structures — defects, domain walls, fronts, etc. that may serve as "elementary blocks" for constructing models of "moderate" (transitional) spatio-temporal chaos has been investigated. The qualitative and quantitative characteristics of dislocations in the domain walls between roll domains were determined in the experimental study of wave structures at parametric excitation of capillary waves and a possibility of exciting multiturn (containing several arms) standing spiral waves was demonstrated. The experiments on the excitation of parametric waves in a liquid layer with single, smooth and periodic inhomogeneities demonstrated generation of different patterns (rolls or spirals), depending on the shape of inhomogeneity of layer depth, as well as generation of a superposition of spiral structures in the liquid layer with inhomogeneous initial temperature distribution. Phenomenological models describing the observed phenomena were proposed. Tetragonal modulation cells with defects observed in experiment were obtained by means of numerical solution of equations for two orthogonal pairs of parametrically coupled waves and the phenomenon of the onset of narrow spectra of spatial harmonics in an isotropic medium was explained.

Particle transport in structured nonlinear fields. Transport of passive scalars in a structured field of parametric waves was studied experimentally. A method of obtaining hard materials with periodic transparency inhomogeneities was proposed. The main idea of the method is to use a viscous photopolymer with admixture in the form of metallized microparticles as an operating liquid.

Solidified photopolymer layer with domain wall between two cellular structures

Pattern selection and spatio-temporal chaos in anisotropic media. The effects of pattern selection and arising of spatio-temporal disorder in hydrodynamic flow systems that are interesting for applications were studied in laboratory experiments and using dynamical models constructed on the basis of classical (following from "the first principles") equations. Convective structures with coherent cells of different size in a blown layer of ethyl alcohol were obtained experimentally and theoretically within the framework of low-mode models and direct numerical simulation. The transition from quasiregular cellular convection to convective rolls with defects with an increase of the speed of blowing was explained. The revealed pattern transformations represent qualitative features of convection in the ocean and in the atmosphere in the presence of wind. A numerically oriented analytical model of the interaction of viscoelastic coatings with a potential flow was constructed. The principal properties of essentially nonlinear divergent patterns observed on the coatings in laboratory experiments and on the skin of a swimming dolphin were explained within the framework of this model. It was found that local nonlinearity of coating elasticity plays the fundamental role in the processes of selection of the period of structures. The step-wise character of the transition of two-dimensional to three-dimensional patterns with increasing flow velocity was explained. The mechanisms of the competition between baroclinic and barotropic modes giving rise to the common nonlinear critical layer in a zonal shear flow on a beta-plane that are interesting for understanding the nature of weather anomalies on the Earth were elucidated (V. P. Reutov, G. V. Rybushkina, S. V. Shagalov).

Convective rolls of different size with defects on the surface of a blown layer of ethyl alcohol