Natural Convection in Gravity-Modulated Porous Layers

We analyze natural convection in porous layers subjected to gravity modulation. In particular a linear stability analysis and weak non-linear analysis is presented for both synchronous and subharmonic solutions and the exact point for the transition from synchronous to subharmonic solutions is computed. It is demonstrated that increasing the excitation frequency rapidly stabilizes the convection up to the transition point from synchronous to subharmonic convection. Beyond the transition point, the effect of increasing the frequency is to slowly destabilize the convection. The weak-non-linear results show that increasing the excitation frequency rapidly decays the convection amplitude. An analogy between the inverted pendulum with an oscillating pivot point and the gravity modulated porous layer is developed and it is shown that the convection cell wavelength is related to the length of the pendulum.