Magnetic Convection in a Nonuniformly Rotating Electroconducting Medium under the Action of External Magnetic Field Modulation

Abstract

We have analyzed the magnetic convection regime (Rayleigh–Benard problem) in a nonuniformly rotating electroconducting liquid in an external periodic magnetic field. In the linear theory of oscillatory convection, the critical value of Rayleigh number Rac is obtained as a function on the nonuniform rotation profile (Rossby number Ro). It is shown that the Kepler profile of rotation with Rossby number Ro = –3/4 produces a destabilizing effect. Using the method of perturbation theory in small supercriticality parameter of the Rayleigh number, we have derived the Ginzburg–Landau nonlinear complex equation. The numerical solution of this equation has enabled us to determine heat transfer (from the Nusselt number Nu) in the layer of the liquid for different values of amplitudes δ and modulation frequencies ωB. Using the Galerkin method, we have obtained a linear dynamic system of nonautonomous Lorenz-type equations. Numerical analysis of these equations has revealed the possibility of controlling the chaotic behavior of convective flows in a nonuniformly rotating (Ro = –3/4) liquid by varying the modulation parameters of the external magnetic field.