HR: 08:15h
AN: OS41A-02    [Abstracts]
TI: Large scale and small-scale components of stratified flows and their mathematical images
AU: * Chashechkin, Y D
EM: chakin@ipmnet.ru
AF: Institute for Problem in Mechanics of the RAS, 101/1 prospect Vernadskogo, Moscow, 119526, Russian Federation
AU: Bardakov, R N
EM: bard@ipmnet.ru
AF: Institute for Problem in Mechanics of the RAS, 101/1 prospect Vernadskogo, Moscow, 119526, Russian Federation
AB: Fine structure of atmosphere and hydrosphere is registered by different methods in the environment and observed in laboratory tanks where waves, vortices and flows are modelled The goal of the talk is to describe a mechanism of a fine flow structure formation in a continuously stratified fluid by the examples of internal waves produced by free or forced oscillations of compact bodies. In mathematical modelling based on the set of fundamental governing equations including continuity, Navier- Stokes, Fourier, Fick and state equations with initial and boundary conditions are solved for given particular geometry of the problem. When doing so, a structure of transient diffusion induced flows on a sphere in a continuously stratified fluid is calculated and evolable velocity and density fields are analysed. Flow produced by an oscillating or uniformly moving obstacle (sloping strip, disk, cylinder, sphere) is calculated in linear approximation taking into account viscosity and diffusivity effects. Visualized patterns of flow manifest complex flow structure. Regular components of solutions describe internal waves. Singular components describe boundary layers and their analogues in the fluid interior, which are placed on some characteristics of corresponding Euler problem. In general case there are two viscous singular solutions. One corresponds to classical Stokes periodic flow on the oscillating plane, while the other has no analogues in the uniform fluid. In frame of homogeneous fluid approximation two boundary layers turn to be identical and merged. That leads to insolvability of 3D Navier-Stokes equations both for compressible and incompressible fluids. Additionally, there is combined, or separated, salinity boundary layer, too. In non-linear analysis all regular and singular flow components interact directly upon each other. Presented solutions of linear and weakly non-linear problems of 2D and 3D periodic and attached (lee) internal wave generation match laboratory data rather well. With source oscillation amplitude increase, singular components are being visualized in by the schlieren instrument as the envelopes of the wave beams. Interaction between singular components results in formation of the interfaces in a fluid body bounding fast vortex jets running to the source. Complete classification of 3D periodic flows including the waves and several kinds of the distinguished singular components is presented. Data extrapolation on the environment conditions is discussed.
DE: 3307 Boundary layer processes
DE: 4203 Analytical modeling and laboratory experiments
DE: 4544 Internal and inertial waves
DE: 4568 Turbulence, diffusion, and mixing processes (4490)
SC: Ocean Sciences [OS]
MN: 2007 Joint Assembly