ИСТИНА

http://www.ipmnet.ru/files/conf/2017waves_school/Program_School_2017.pdf SLOW, FAST AND SUPERFAST COMPONENTS OF STRUCTURED FLOWS Yuli D. Chashechkin (IPMech RAS, e-mail: chakin@ipmnet.ru The mathematical basis of conventional fluid mechanics – the theory of motions of a continuous medium that admits the existence of infinitesimal “fluid particles” – is in deep contradiction with the reliably established discrete structure of the matter, in which several groups of scales are distinguished: macroscopic, atomic-molecular (order of cm) and nuclear ( cm). In each range of scales, the basic parameters of the medium (in particular, density of mass and energy), the exchange rates and the sizes of the regions, in which the new products of the individual elements interaction are concentrated, are presented. In this paper, we will consider some manifestations of the direct effect of atomic-molecular processes on the dynamics and structure of the flows of fluids and gases studied in the framework of macroscopic hydro- and thermodynamics. The main attention is paid to the study of the mechanisms of the formation of spatial flow structures and the evaluation of their impact on the dynamics of the studied processes. In macroscopic hydrodynamics, the effects of atomic-molecular interactions are taken into account in describing the energy of flows using thermodynamic potentials, the spatial structure of which is given by the type and localization of substances, by the values of the concomitant constants also and electromagnetic fields (direct and alternating, external and intrinsic, associated with the processes of radiation and absorption of energy-electromagnetic waves over a wide frequency range). Further, the influence of electric, magnetic, and electromagnetic fields is neglected. The study medium, which following the traditions of classical fluid mechanics is assumed the continuous, and characterized by functions of the thermodynamic state (density, pressure, temperature, concentration of substances, thermodynamic potentials - internal energy, enthalpy (heat function), the free energy, and the free enthalpy (potential of Gibbs) as well as kinetic coefficients. Under equilibrium conditions the thermodynamic parameters are determined by the gradients of respective potentials (in particular, the density is expressed by the Gibbs potential). It is assumed that definitions of quantities are also conserved in the case of non-equilibrium media. Real media in the fields of external potential fields (gravity) are characterized by inhomogeneous distributions of the basic parameters. Under the action of the fields gradients, inhomogeneous fluids are stratified, the concentrations of the constituent substances, and the temperatures are distributed non-uniformly. Accordingly, all the thermodynamic potentials, including the chemical potential, associated with the concentrations of the substances are inhomogeneously distributed. Drip fluids are bounded by a free surface, in the vicinity of which, at a depth of the order of the several molecular sizes, the inhomogeneity of atomic-molecular interactions manifests itself in the form of a surface tension that limits the volume of a dropping liquid and the available potential surface energy. The energy density sharply changes near the free surface, as well as at the boundaries of the contact of dissimilar media (immiscible liquids, fluids with a solid or gas) and are concentrated in a layer of thickness on the order of the dimensions of a molecular cluster. The time for the exchange of energy between the structural components is determined by their size and the characteristic rate of atomic-molecular or macroscopic processes. And if in the interaction of large-scale components of flows, the changes in physical quantities, in particular the energy density, occur slowly (the rate of change is determined by the ratios of characteristic length scales and velocities), then on small scales, the exchange occurs quickly, up to the intrinsic small times of atomic-molecular interactions, as the ratios of these length scale to macroscopic velocity are also small. At the same time, small-size regions with large values of density, pressure, temperature, other physical quantities and their gradients perturbations are formed in the flow, so that the medium acquires discrete features with a different degree of structuring. For a mathematical description of the dynamics and structure of different flows, a system of fundamental equations is used in which the density is determined taking into account the type of thermodynamic potentials in the energy and space-time scales of the phenomena studied. The system including the equation of state for the density and the equation for the transport of mass, momentum, total energy, concentration of dissolved substances (or suspended particles in the "diffusion approximation") with physically justified initial and boundary conditions (for many problems – no-slip and no-flux) forms the basis of Differential fluid mechanics [1]. Theoretical analysis is carried out taking into account the compatibility condition determining the rank of the nonlinear system, the order of its linearized version, and the degree of the characteristic (dispersion) equation. Classification of the components of periodic solutions obtained for weakly dissipative media by methods of the theory of singular perturbations describes traditional waves (inertial for rotating fluids, gravitational surface and internal, acoustic, hybrid and others) and accompanying dissipative components characterizing the structure of the medium. It should be emphasized that, despite the differences in their scales, all components of complete solutions (both regular and singular, analogues of boundary layers in the volume of the fluid and on contact surfaces) are formed, propagate (filling the entire volume of the medium), and damp simultaneously. Because of the specific nature of the geometric-physical properties, the singular components of the solutions are linear precursors of shock waves. Because of the non-linearity of the governing equations in real conditions, all components of complete solutions, both large and small-scale, directly interact with each other and generate new components that complicate the flow pattern. However, calculations and observations show that in characteristic regions only a few components dominate, which determine both the general geometry of the flows and the structure of the boundaries separating the individual components. Analysis of the properties of a system of fundamental equations with the corresponding initial and boundary conditions makes it possible to formulate sound requirements to the methods of laboratory and numerical modeling, the conditions for observations of natural processes, and the rules for incorporating heterogeneous data into a single database. The system of fundamental equations with the corresponding initial and boundary conditions makes it possible to carry out on a unified basis of consistent theoretical (analytical and numerical) and experimental (field and laboratory) studies, to compare the obtained data, to collect the results of dissimilar studies into a single database and to carry out a reasonable forecast of the evolution of the phenomena under study and systems as a whole. The possibilities of its practical use have expanded with the advent of high-performance computers and computer systems. Complete solutions describe both the dynamics of the flows and the variations of their spatial structure over the entire range of the phenomena studied. The merit of the approach based on the system of fundamental equations – the Differential Fluid Mechanics – is universality (applicability to the description of the flows of any media - liquid, gaseous, ionized), the validity of the problem posing, the completeness of the description of phenomena, scale and parametric invariance, constructivity (the resource for constructing approximate models, taking into account the features of the phenomenon under study), and, perhaps most importantly, the attainability of direct comparison with experiment. Known models (ideal fluid theory, viscous homogeneous, linear models) are incorporated into the Differential fluid mechanics. Only the observed quantities (invariants in ideal models without dissipation) are represented in the equations under study. And in the complete model, and in its reduced versions, the physical meaning of the symbols used to which the observed physical quantities correspond is preserved. An important consequence of the internal spatio-temporal multiscale calculations is the absence of stationary states. The structure of the studied flows gradually deforms under the influence of introduced perturbations, which, in turn, affects their dynamics. At the same time, in each of the parameter ranges, it is possible to indicate "fast changing parameters" with large variations at small space-time scales, and "slow ones," which are characterized by small changes on the whole length scales. The material basis of the differential fluid mechanics was the results of studies performed at the stands of the “Hydrophysical Complex for Modeling of Hydrodynamic Processes in the Environment and Their Impact on Underwater Technical Objects and Impurities Transport in the Ocean and the Atmosphere (UEF “GFK IPMekh RAS”)” [2]. The complex of installations, including 12 stands, is designed for coordinated laboratory and numerical simulation of the dynamics and structure of flows in industrial and natural conditions. Experiments are carried out by consistent optical, acoustic and original contact methods [2]. By the completeness of the measuring instruments, technical capabilities and metrological parameters of the instruments, the complex of the UEF “GFK IPMekh RAS” has no analogues in the country and abroad. At this stage, the primary task is metrological support for ongoing research, ensuring the accuracy of the results of experiments and observations directly in the process of their production. Visualization of slow, fast and ultrafast components of stratified flows is performed on the stands of the UEF “GFK IPMekh RAS”. Theoretical and experimental studies have shown that everything, both fast and slowest, for example, diffusion-induced flows on topography that forms around a motionless body in a fluid at rest are deeply structured. With an increase in the velocity of a fluid motion, the range of the scale of the structures expands. Flows appearing when the two-dimensional obstacles (strip, cylinder and wedge) move uniformly in the fluid in a wide range of parameters are visualized [3]. Also, thin structures of the internal wave and vortex fields that arise when bodies fall freely on the neutral buoyancy horizon are investigated. As an example of the determining influence of atomic-molecular interactions on the flow pattern, the results of recording the fastest components in the patterns of transfer of matter from a freely falling drop to the receiving liquid [4] and sound pulses generation [5] are given. The conducted experiments showed that all types of flows – both the slowest and fastest ones - are characterized by their own spatio-temporal structure, the elements of which demonstrate different rates of exchange by energy and substances. The technical and methodological capabilities of the complex GIF IPMekh RAS allow one to study an extensive class of flows in a wide range of parameters. The further development of coordinated theoretical and experimental studies based on the UEF “GFK IPMekh RAS”, existing and created analogs, will create a reliable scientific basis for solving the actual problems of fluid mechanics in terms of forecasting the evolution of the environment - the atmosphere and the ocean, improving the theory of bodies motion in liquids and gases, the creation of new chemical and biochemical technologies, which are currently developed solved empirically. Acknowledgement. The work was supported by the Russian Foundation for Basic Research (Project 15-01-09235) and the OEMPU RAS (Subprogram III-4 "Dynamics of formation and interaction of waves and vortices in continuous media", the Project "Evolution of compact vortices and waves in stratified media"). 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. Chashechkin Yu.D. Structure and dynamics of environmental flows: theoretical and laboratory modeling // Actual problems of mechanics. 50 years of the Institute of Problems of Mechanics. A.Yu. Ishlinsky Institute of the Russian Academy of Sciences. M.: Science. 2015. pp. 63-78. 3. Chashechkin Yu.D, Zagumenny Ya.V. Structure of the pressure field on the plate in the transient flow regime // Doklady of the Academy of Sciences. 2015. T. 461. № 1. P. 39-44. DOI: 10.1134 / S1028335815070022 / 4. Chashechkin Yu.D. Drops: crowns, splashes, sounds ... // Priroda. 2016. No. 11. P. 13-23. 5. Chashechkin Yu. D., Prokhorov V. E. Acoustics and hydrodynamics of a drop impact on a water surface // Acoustical Physics. 2017. V. 63. No. 1. Р. 33–44. DOI: 10.1134/S10637710160600384.