On the nonlinear stability of thermally driven shear flow heated from below

Abstract

The energy method, which gives the sufficient condition for the stability, is developed for the convection problem induced by an applied inclined temperature gradient in a shallow horizontal layer. A nonlinear stability analysis, which is valid for any Prandtl number, is carried out for the case of rigid conducting horizontal boundaries. The eigenvalue problem is solved by compound matrix method and the nonlinear stability results are compared with the results of the linear stability method.