HR: 14:25h
AN: OS53B-04    [Abstracts]
TI: Mathematical Classification and Laboratory Observations of Stratified Flow Components
AU: * Chashechkin, Y D
EM: chakin@ipmnet.ru
AF: Institute for problems in Mechanics of the RAS, 101/1 prospect Vernadskogo, Moscow, 119526, Russian Federation
AB: New mathematical classification of a stratified fluid flow components based on analytical theory of partial differential equations with small coefficients and theory of continuous (Lie) groups is given. The conventional set of governing equations including equations of continuity, Navier-Stokes, Fourier, Fick and the state equation, was selected for further analysis as a result of comparison of general properties and infinitesimal symmetries of different sets of governing equations, which are mostly used in theoretical oceanography. Boundary and initial conditions are no-slip and no-flux on contact surfaces, decay of all disturbances at infinity and trivial for negative time. Firstly the diffusion induced flows on finite topography were studied analytically and numerically as an undisturbed state of stratified liquids. Then infinitesimal periodic flows were treated for different frequency ranges. In addition to waves of different types (inertial, internal, acoustical or hybrid) described by regular disturbed functions of complete solutions, a rich set of singular disturbed solutions is identified. The singular disturbed functions describe boundary layers on contact surfaces and their analogues in the fluid interior forming thin elongated structures. Viscosity effects cause two different boundary layers. They are linear predecessors of vortices and vortex systems. In frame of a homogeneous fluid approximation two different viscous boundary layers lost their features, turn to be identical and unified. So an insolubility of 3D Navier-Stokes equations both for compressible and incompressible fluids is explained by degeneration of the solvable equation set and incompleteness of problem posing. Exact solutions of linearized periodic internal waves generation problems induced by forced and free oscillating obstacles (strips, discs and spheres) are constructed and visualized numerically. Developed theory is compared with results of more than 4000 schlieren and probes experimental studies of flows generated in continuously stratified tanks by forced and free oscillating obstacles. Experiments with bodies of different shapes (strips, discs, spheres, cylinders) were performed in a wide range of buoyancy frequency, size, amplitude and direction of oscillations. On results of experiments we have identified a number of well-reproduced flow singular components besides the internal waves. They include boundary layers on the obstacle surface and high gradient interfaces inside continuously stratified fluid far from the source. Presented solutions of linear and weakly non-linear problems of 2D and 3D periodic internal wave generation match laboratory data rather well. Conditions of fine streaky structures existence are found and processes of their transformation into vortices directly inside the fluid are visualised. Following from the studies demands of completeness of a fluid dynamics experiment and direct control of accuracy are discussed. Extrapolation of received data on environmental systems is speculated.
DE: 4524 Fine structure and microstructure
DE: 4544 Internal and inertial waves
DE: 4599 General or miscellaneous
SC: Ocean Sciences [OS]
MN: 2007 Fall Meeting