Nonlinear Thermal Instability in a Rotating Viscous Fluid Layer Under Temperature/Gravity Modulation

Abstract

In the present paper, the effect of time-periodic temperature/gravity modulation on the thermal instability in a rotating viscous fluid layer has been investigated by performing a weakly nonlinear stability analysis. The disturbances are expanded in terms of power series of amplitude of modulation, which has been assumed to be small. The amplitude equation, viz., the Ginzburg–Landau equation, for the stationary mode of convection is obtained and using the same, the effect of temperature/gravity modulation on heat transport has been investigated. The stability of the system is studied and the stream lines are plotted at different slow times as a function of the amplitude of modulation, Rossby number, and Prandtl number. It is found that the temperature/gravity modulation can be used as an external means to augment/diminish heat transport in a rotating system. Further, it is shown that rotation can be effectively used in regulating heat transport.