Effect of thermal modulation on the onset of double diffusive convection in a horizontal fluid layer

The effect of time periodic boundary temperatures on the onset of double diffusive convection in a horizontal two component fluid layer is studied using a linear stability analysis. The perturbation method is used to compute the critical thermal Rayleigh number and the corresponding wave number for small amplitude temperature modulation. The correction thermal Rayleigh number is calculated as a function of frequency of the modulation, Prandtl number, solute Rayleigh number, and the diffusivity ratio. It is found that the thermal modulation may stabilize an unstable system or destabilize a stable system. In particular it is found that low frequency symmetric modulation is destabilizing whereas the asymmetric modulation and lower wall temperature modulation are stabilizing. The effect of the solute Rayleigh number, ratio of the diffusivities and the Prandtl number are also reported. It is also found that the effect of modulation disappears for large frequency.