Generation of large-scale structures and vortex systems in numerical experiments for rotating annular channels

Numerical methods for shallow-water equations describing flows in rotating annular channels and the results of numerical calculations are considered. The possibility of generation of global large scale flows, narrow jets and numerous small-scale vorticies in laboratory experiments is analyzed. Methods for inducing external effects in fluids involve a source-sink method and an MHD-method of interaction of electric current with magnetic field generated by a system of permanent magnets. A central-upwind method adopted to geophysical hydrodynamics is used in the numerical scheme. Initially the method was applied to shallow water equations in hydraulic problems: channels, dam break, rivers, and lakes. In geophysical hydrodynamics (in addtition to free water surface and bottom elevation) the main effects arise when external rotation is taken into account with appearence of numerous vorticies, jets and turbulence. So the basic foundations of the central-upwind method should be changed. Modifications concern the well-balanced scheme and interpolation method. In the numerical scheme the structure of artifical viscosity is considered. The main achievement of the modification is the possibility of controlling the numerical dissipation affecting the fluid motion variety. Hence, we obtain the active dynamics of vorticies transfomed into jets or large scale streams, which is more preferable for geophysical hydrodynamics. The numerical experiment provides opportunities for studying flows generated by numerous source-sinks, because the creation of an appropriate laboratory experimental setup presents some difficulties. The MHD-method can readily be realized in experiments to generate a large variety of flows and vortex currents in the channel by means of a relatively small number of magnets. Specifically, large scale circular flows, narrow jets and system of interacted vorticies were obtained in numerical experiments. For the purpose of experiments, the distribution of source-sinks and systems of permanent magnets over the bottom of annular channels is defined.