Weak nonlinear rotating Bénard convection with modulation using Ginzburg- Landau model

Abstract

This article theoretically investigates the effect of modulated rotation speed on rotating Rayleigh-
Bénard convection. The Rayleigh-Bénard momentum equation with Coriolis term has been used
to describe the fluid flow in the medium. The system is consider to rotate about vertical axis with
non-uniform rotational speed consisting of steady and time dependent parts. In particular, we
assume that the rotation speed i.e time dependent part is varying sinusoidally with time. A
nonlinear stability analysis has been performed to find the effect of modulation on heat transport.
The heat transfer quotient, Nusselt number obtained in terms of amplitude and frequency of
modulation, and depicted graphically with respect to slow time, showing the effect of various
parameters of the system on heat transport. It is found that the effect of rotation speed modulation
is to stabilize or destabilize the system depending on the amplitude and frequency of modulation.
The corresponding streamlines and isotherms are presented at different states of slow time .