Influence of Vibration on the Onset of Convection in Second Grade Fluid

The problem of convective stability of a second grade incompressible fluid in a horizontal layer heated from below is considered. The fluid is subjected to vertical or horizontal vibrations. A state of relative equilibrium is possible in this situation. The case of high-frequency vibrations is considered first. Specifically, the averaging method is used to formulate a spectral problem for finding the critical Rayleigh number; this problem is similar to the one arising in the classical problem of convective stability of a Newtonian fluid. It is shown that the critical Rayleigh number increases insignificantly when relaxation terms are taken into account. Similar results are obtained by analyzing the stability of relative equilibrium in the case of finite-frequency vertical vibrations.