Weakly nonlinear magnetic convection in a nonuniformly rotating electrically conductive medium under the action of modulation of external fields

TL;DR

This paper investigates the weakly nonlinear convective instability in a rotating, electrically conductive fluid layer under various external field modulations, deriving Ginzburg-Landau equations to analyze heat transfer dynamics.

Contribution

It introduces a perturbation theory approach to derive nonlinear Ginzburg-Landau equations for different external field modulations in a rotating conductive fluid.

Findings

Derived nonlinear Ginzburg-Landau equations for multiple modulation types

Analyzed unsteady heat transfer dynamics under different external field profiles

Provided insights into the effects of modulation on convective instability

Abstract

In this paper we studied the weakly nonlinear stage of stationary convective instability in a nonuniformly rotating layer of an electrically conductive fluid in an axial uniform magnetic field under the influence of: a) temperature modulation of the layer boundaries; b) gravitational modulation; c) modulation of the magnetic field; d) modulation of the angular velocity of rotation. As a result of applying the method of perturbation theory for the small parameter of supercriticality of the stationary Rayleigh number nonlinear non-autonomous Ginzburg-Landau equations for the above types of modulation were obtaned. By utilizing the solution of the Ginzburg-Landau equation, we determined the dynamics of unsteady heat transfer for various types of modulation of external fields and for different profiles of the angular velocity of the rotation of electrically conductive fluid.