ИСТИНА

http://indico.ictp.it/event/7985/other-view?view=ictptimetable Slow, fast and ultra-fast components of formation and evolution of spatially ordered structures in fluid flows Yuli D. Chashechkin Picturesque structures in the patterns of substance distribution and other physical quantities characterizing continuous media, including fluids, gases and plasma, are observed through the entire range of scales available for observation starting from microscopic to galactic ones. The structures evolve continuously, new flow components appearing and some of the old ones disappearing. Some structural elements exist for a quite long period of time that allow scurrying out flow classification into components, such as waves, vortices, jets, wakes, etc., while other structural elements, which are short-lived, haven’t been studied adequately. The stellar sky, stratified atmospheres of stars and planets, the Earth's hydrosphere serve as examples of structured media. The universal approach developed for describing the dynamics of non-equilibrium systems is carried out in the "continuous medium" representation. The media are characterized by continuous and discontinuous inhomogeneous fields of physical quantities, such as thermodynamic (potentials and their derivatives, which are density, pressure, entropy, temperature, concentration), kinetic (transport coefficients) and dynamic (momentum, total and internal energy) parameters. As a basis for theoretical analysis and experimental techniques construction the fundamental system is considered, which includes the equations of state (thermodynamic potentials, empirical relations between thermodynamic quantities,which are density, pressure, temperature, concentration of substances, in the range of flow parameters studied) and analogues of conservation laws, which are the differential equations for transport of mass (continuity), momentum, energy (temperature) and concentration. The equations, which include the observable physical quantities (since measurement techniques for unobservable variables, such as fluid velocity, do not allow objective error estimation) are supplemented by physically valid boundary conditions on solid boundaries or contact surfaces. The equations are analyzed accounting for the compatibility condition, which determines rank of a nonlinear system of equations, order of its linearized form, and power of the corresponding characteristic (dispersion) equation. Due to a high rank of systems of governing equations for fluid mechanics problems, the fluid flows are characterized by a large number of coexisting heterogeneous structural components, which in combination leads to non-stationary effects. A qualitative analysis is carried out for a combination of intrinsic temporal and spatial scales characterizing observable structural elements. Relations of the scales form dimensionless parameters, such as the traditional Reynolds, Froude, and Peclet numbers in problems on flows past obstacles and the Rayleigh, Prandtl, and Nusselt numbers in convection problems, and, as well, some new ones which are not included into the traditional description. Descriptions of the processes in weakly dissipative media are carried out using methods of the singular perturbations theory that makes it possible studying both the large long-lived components with dimensions given by geometry of the problem and dissipative ones with fine scales characterizing medium structure.The fine scales are defined by relations of kinetic coefficients to flow velocity and frequency or velocity multiplied by duration of action of disturbing factor. Since the velocity or frequency can attain large values and the time of action can be quite short, the fine scales can be comparable to individual or cluster atomic sizes. Effects of such localized intense perturbations, which shock and detonation waves belong to, on the energy and substance transport require an additional profound study. On the large scales, typical times of processes variability are determined by the mechanical and diffusion parameters of a medium. In the structural elements with small scales of an order of the size of atomic-molecular clusters (~ cm) or the thickness of atomic layers (~ cm), the exchange rate is determined by fast atomic-molecular interactions. This ensures a rapid transformation of the available potential energy, which can beeither chemical one in layers with a concentration gradient orsurface potential oneon contact boundaries, into thermal and mechanical energy of motion. Within the framework of the approach unified for the entire scale range, processes of formation and evolution of various flows are studied theoretically, numerically and experimentally. The problems under consideration include diffusion-induced flows on topography with various shapes; generation, propagation, reflection and nonlinear interaction of internal wave beams; flows around obstacles in transient vortex regimes; free multicomponent convection over heat sources with various dimensions, such asa point, a cylinder, a plane, etc. Processes of structures formation in an initially homogeneous suspension are investigated experimentally at transient eigen oscillation modes in a rectangular vessel, compound vortices, around a drop falling into a fluid, as well. In all the cases under consideration, a filamentization of compact volumes of soluble admixtures, i.e. splitting into fibers, occurs under action of fine flow components. Analytical, numerical and experimental results of the independently performed studies are in a good quantitative and qualitative agreementbetween each other. Extrapolation of the data obtained to processes in the environment and experimental facilities is discussed with the purpose of studying controlled thermonuclear fusion. References 1. Chashechkin Yu. D. Differential fluid mechanics – harmonization of analytical, numerical and laboratory models of flows. // Mathematical Modeling and Optimization of Complex Structures. Springer Series “Computational Methods in Applied Sciences” V. 40. 2016. P. 61-91. DOI: 10.1007/978-3-319-23564-6-5 2. Dimitrieva N.F., Chashechkin Yu.D. The Structure of Induced Diffusion Flows on a Wedge with Curved Edges // Physical oceanography. 2016. No. 3. P. 70-78. 3. Kistovich A. V., Chashechkin Yu. D. Fine Structure of a Conical Beam of Periodical Internal Waves in a Stratified Fluid // Izvestiya, Atmospheric and Oceanic Physics, 2014, Vol. 50, No. 1, pp. 103–110. DOI: 10.1134/S0001433814010083 4. Ilynykh A.Yu., Chashechkin Yu. D. Hydrodynamics of a submerging drop: lined structures on the crown surface // Fluid dynamics. 2017. V. 52. No. 2. P. 309-320. DOI: 10.1134/S0015462817020144 5. Chashechkin Yu. D., Prokhorov V. E. Acoustics and Hydrodynamics of a Drop Impact on a Water Surface // Acoustical Physics, 2017, Vol. 63, No. 1, pp. 33–44. DOI: 10.1134/S1063771016060038 6. Chashechkin Yu. D. Prokhorov V.E. The structure of the primary audio signal in a collision of a free-falling drop with water surface // J. Experimental and Theoretical Physics 2016, Vol. 122, No. 4, pp. 748–758. DOI: 10.1134/S1063776116020175 7. Zagumennyi Ya. V., Chashechkin Yu. D. Pattern of unsteady vortex flow around plate under a zero angle of attack (two-dimensional problem) // Fluid Dynamics, 2016, Vol. 51, No. 3, pp. 53–70. DOI: 10.7868/S056852811603018X