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

Methods for solving shallow-water equations that describe flows in rotating annular channels are considered and the results of numerical calculations are analyzed for the possible generation of global large-scale flows, narrow jets, and numerous small-scale vortices in laboratory experiments. External effects in fluids are induced using a mass source–sink and the MHD-method of interaction of radial electric current with the magnetic field generated by the field of permanent magnets. A central–upwind scheme modified to suit the specific aspects of geophysical hydrodynamics. Initially, this method was used to solve shallow-water equations only in hydraulic problems, such as for flows in dam breaks, channels, rivers, and lakes. Geophysical hydrodynamics (in addition to free surface and topography) requires a rotation of the system as a whole, which is accompanied by the appearance of a complex system of vortices, jets, and turbulence (these should be taken into account in the formulation of the problem). Accordingly, the basic features of the central–upwind method should be changed. The modifications should ensure that the scheme is well-balanced and choose interpolation methods for desired variables. The main result of this modification is the control over numerical viscosity affecting the fluid motion variety. The active dynamics of a large number of vortices transformed into jets or generating large-scale streams is the general result of modifications suitable for geophysical hydrodynamics. Because there are technical difficulties in the creation of an appropriate laboratory setup for modeling of geophysical flows with the help of numerous source–sinks, it will be appropriate to use numerical experiments for studying the motions generated by this method. Unlike this method, the MHD-method can be rather easily used in laboratory conditions to generate a large variety of flows and vortex currents in the channel by a relatively small number of permanent magnets. Specifically, this method made it possible to obtain large-scale circular flows over the entire channel area, jets, and systems of interacting vortices. For the purpose of experiments, the distributions of source–sinks and systems of permanent magnets over the bottom of annular channels are determined.