Shear Type Instabilities in the Benard Problem

Abstract

The aim of the present paper is to argue that if a generic mechanism for the transition to turbulence in parallel flows exists, the same mechanism should also be generic in low Prandtl number thermal convection. In order to stress similarities between both types of flows we shall assume they share the same geometry: A doubly periodic domain in the horizontal directions, bounded on top and bottom by two horizontal surfaces. It will be shown below that a mean horizontal flow — i.e.: a wind — is possible even in the absence of both a head pressure and external shear stresses. Buoyancy force itself may be enough to produce a mean flow. Therefore, a unified treatment is possible. We shall talk in the following about doubly periodic channel flows, and this will explicitly include thermal convection.