Rudnyev Y. Free surface stability of bounded volumes of electroconductive fluids in the magnetic field

The objects are MHD - systems, which consist bounded volumes of electroconductive fluids with free surface. The aim is the investigation of an equilibrium state stability for the bounded volumes of electroconductive fluids with free surface and interface, determination of the boundary of stability region in the space of dimensionless parameters for the MHD - systems under consideration. The equations of magnetohydrodynamics for incompressible viscous fluids, the Galerkin method, asymptotical method of boundary layer, analytical method of mathematical physics, stability methods for the solutions of differential equations, numerical methods of linear algebra are used for mathematical modeling of the object. The method to solve the stability problem of free surface or interface of bounded volumes of conducting fluids interacting with magnetic field is proposed. The stability problem of two-layer system of fluids filling cylindrical container of rectangular cross-section in magnetic field and the stability problem of the free surface of cylindrical volume of conducting capillary fluid are solved. The boundary of stability region in the space of dimensionless system parameters is determined. The proposed approach based on the Galerkin method allows to reduce the stability problem of magnetohydrodynamical system to the stability problem for solutions of the system of the linear ordinary differential equations. It is determined that two-layer-system of fluids is characterized by oscillatory instability and interfacial waves appear as a result of the resonance interaction of system eigenmodes with coinciding or close frequencies. Main interacting oscillation modes, forms and frequencies of generated surface waves are determined. Application sphere is in the design of the aluminium reduction cells, devices for material refining using the zone melting.