A direct boundary-layer stability analysis of steady-state cavity convection flow

Natural convection flow in cavities with insulated top and bottom and heated and cooled walls is known to exhibit travelling wave instabilities in the thermal boundary layers that form on the walls. In water (Pr = 7.5) at Rayleigh number Ra = 6 × 10⁸, these waves have been observed at start-up. However no such waves have been observed for the fully developed flow, although it may be assumed that the stability character of the boundary layers is at least approximately the same. The start-up waves are generated by perturbations to the system. In the present paper, an artificial perturbation is applied to the system to determine the stability character of the boundary layers in fully developed flow. It is shown that the thermal boundary layers in the fully developed flow have approximately the same stability character as the start-up flow.