Stability of temperature modulated convection in a vertical fluid layer

Abstract

• Time-periodic modulation of boundary temperatures on natural convection is considered. • Floquet analysis of the basic flow is done leading to a generalized eigenvalue problem. • The numerical results are computed using MATLAB programming. • The instability appears in form of harmonic or subharmonic oscillations . • Transition between these oscillations occurs through a bicritical state. We investigate the effect of time periodic oscillations of the boundary temperatures on the onset of natural convection in a fluid layer bounded by two vertical planes. The fluids with Prandtl number up to 12.5 are considered. For these fluids, the mode of instability with constant temperature gradient is the steady convection mode. The parametric instability of the modulated fluid layer is found to appear either in the form of harmonic oscillations or in the form of subharmonic oscillations, depending upon the modulation parameters and the Prandtl number. The transition of the instability between harmonic and subharmonic oscillations occurs via an intermediate bicritical state in which the fluid layer oscillates with coexistence of distinct harmonic and subharmonic wave numbers. A proper tuning of the modulation parameters offers a good control over the mode of instability in the fluid layer.