Instability in temperature modulated rotating Rayleigh–Bénard convection

The problem of instability in an infinite horizontal thin layer of a Boussinesq fluid, uniformly rotated and heated from below with time periodic oscillations of the wall temperatures is investigated theoretically and numerically. In doing so, modest rotation rate is considered such that the Froude number does not exceed 0.05 which allows neglect of centrifugal effects. The Floquet analysis is used to obtain the critical Rayleigh number as a function of the parameters controlling the system. The instability is found to manifest itself in the form of a flow which oscillates either harmonically or subharmonically depending upon the control parameters. Instability regions in an appropriate parametric space of the dimensionless wave number of disturbance imposed over the flow and the dimensionless amplitude of modulation, at the onset of time periodic fluid flows are obtained numerically. The modulation amplitude, the modulation frequency and the rotation rate, are observed to affect the stability of the flow considerably. (paper)