The onset of Rayleigh–Bénard convection in non-planar oscillatory flows

Abstract

The onset of thermal convection in the presence of an oscillatory, non-planar shear flow is investigated on a linear basis. For the case of planar oscillations, the basic shear has no effect upon the value of the critical Rayleigh number but does act as a pattern selection mechanism. For the non-planar case, when there are two horizontal components of the basic velocity, the same result is true if the components are either in phase or directly out of phase. For the general case, however, stabilization occurs because convection rolls experience the stabilizing effects of shear regardless of their orientation. The results are obtained both by expansion in terms of the amplitude of the oscillating flow and in terms of its frequency, assuming the frequency to be small. The degree of stabilization increases with the Prandtl number. Pattern selection still occurs with non-planar oscillations.