SIMULATION OF TURBULENT MHD FLOW IN A RECTANGULAR CAVITY IN A ROTATING MAGNETIC FIELD
The article deals with numerical solutions of MHD equations describing turbulent flow of a conducting fluid in a rectangular cavity in the rotating magnetic field at large values of the magnetic Taylor number, and Reynolds number. It is known that there is a mechanism of turbulent mixing in natural systems, leading to an increase in the viscosity of the continuous medium. In this regard, we suggest methods of regularization of the Navier-Stokes equations, similar to the natural mechanisms of mixing. The models based on the properties of currents of the turbulent environment proposed. A modification of the continuity equation taking into account the final magnitude of pressure fluctuations was considered. It is shown that due to pressure fluctuation the incompressibility condition can be violated even for flows with low Mach numbers. Modification of continuity in the system of Navier-Stokes equations by the introduction of turbulent viscosity allows the regularization of the Navier-Stokes equations to solve the problems with rapidly changing dynamic parameters, for example, in the case of a conducting fluid flow in a magnetic field rotating with a high frequency. It was shown that the modification of the continuity equation taking into account turbulent fluctuations leads to a system of nonlinear equations of parabolic type. A numerical model of turbulent MHD flow in a rectangular cavity with rapid change in flow parameters was proposed. In numerical calculations revealed that under the influence of a rotating magnetic field in a conducting fluid there are forces occur, causing unsteady vortex flow, which is consistent with experimental data. We have discovered a type of large scale instability of the turbulent flow, connecting with the secondary flow in a form of vortices