On estimating the complex growth rates in ferromagnetic convection with magnetic-field-dependent viscosity in a rotating sparsely distributed porous medium

Abstract

It is proved analytically that the complex growth rate of an arbitrary oscillatory motion of growing amplitude in ferromagnetic convection with magnetic-field-dependent viscosity in a rotating sparsely distributed porous medium for the case of free boundaries is located inside a semicircle in the right half of the plane whose centre is at the origin of the coordinate system and whose radius depends on the Rayleigh number, Prandtl number, Taylor number, and magnetic number. Bounds for the case of rigid boundaries are also derived.