Plenary Lecture

Adequate Modeling of Fluid Flows

Professor Yuli D. Chashechkin
Laboratory of Fluid Mechanics
Institute for Problems in Mechanics of the
Russian Academy of Science
101/1 prospect Vernadskogo, Moscow, 119526 RUSSIAN FEDERATION

Abstract: For definition of adequate analytical and laboratory modeling of fluid flows conditions the conventional fundamental governing equations set is analyzed thoroughly. The basic equation in this approach is a state equation defining a number of thermodynamic variables which are necessary to characterize properties of particular medium and flow conditions. The total fundamental set of governing equations consisting of state, continuity and transport of momentum, temperature and constituent component equations is treated as singular disturbed system. Dissipative properties of the fluid are characterized by kinematic viscosity, temperature and diffusivity coefficients of constituent. General solutions of the linearized governing equations sets consist of regular and singular disturbed on dissipative factors functions. All flow components are characterized by their scales. Regular disturbed solutions (redics) of the set describe waves and vortices. Rate of their dissipation is proportional to viscosity and other kinetic coefficients. In limiting case redics are matched continuously with solutions of appropriate Euler equations set. Rich family of singular disturbed functions (sidics) describes fine flow components. Sidics transverse length scales are defined by dissipative factors and intrinsic frequencies of the problem that are by frequency of buoyancy (or rotation) in stratified (or vortex) flows. Besides boundaries the fine flow components manifest themselves inside the fluids as interfaces. The sidics are responsible for energy dissipation, production and transport of vorticity and anisotropic transport of contaminants. In general non-linear description all flow components interact between themselves directly in spite of the scales differences. Illustrative experimental investigations of 2D and 3D periodic internal wave beams, lee waves and wakes past uniformly moving obstacles in a continuously stratified fluid were performed in laboratory tanks using markers, schlieren instruments and conductivity sensors. Restructuring of interfaces and their transformation into vortices and vortex systems were registered far from the solid boundaries directly inside the continuously stratified fluid. New structural elements that are "tubular structures" were visualized in the periodic internal wave beams. Extended singular components accumulate contaminants and provide their fast transport. Strong anisotropy of a dye transport in a stationary compound vortex motion produced by uniformly rotating disc in cylindrical container was observed. Spiral arm was spinning from a dye drop put into center of surface trough produced by compound vortex. Set of all flow scales ratios form conditions of adequate laboratory modeling. Extrapolation of model data on environmental and technical conditions is discussed.

Brief Biography of the Speaker:
Yuli D. Chashechkin is head of the Laboratory of Fluid Mechanics of the A.Yu.Ishlinski Institute for Problems in Mechanics of the Russian Academy of Sciences and professor of Physical Faculty of M.V.Lomonosov Moscow State University. His main research interests concern foundations of fluid mechanics, theory of stratified and rotating flows, optical visualization of fluid flows. In these fields, he authored or co-authored over 200 scientific papers published in reviewed journals or presented at international conferences. Well known his schlieren images of internal waves, convective flows, vortices and wakes. As invited research professor he visited and worked in a number of Western and Eastern Universities including Arizona State University (USA), Ecole Normale Superior (Paris, France), The Tokyo University (Japan), University Toulon-Sud (France), University Polytechnic Catalonia (Barcelona, Spain) and others. He took part in a number of national and international marine cruises for studying marine turbulence, fine structure and internal waves. He is European regional editor of Journal of Visualization, organizers of biannual conferences on Fluxes and Structures in Fluids and co-editor of their Selected Papers Volumes.




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