A NUMERICAL INVESTIGATION OF HYDRODYNAMIC INSTABILITY OF A SHEAR FLOW IN A THERMALLY UNSTABLE FLUID LAYER

Abstract

The stability characteristics of a shear flow in an unstable stratified fluid layer is investigated based upon a finite difference approximation of the linearized Boussinesq equation system. The feasibility of numerical calculation is tested with the aid of the convection theory established by Rayleigh which yields the exact solution. Since the result obtained is satisfactory, the procedure is applied to the thermal convection in a Couette flow. It is found from the calculation that constant shear has the effect which suppresses development of the thermal convection. This effect of shear is striking for a convection cell of short wave length and decreases as a wave length of the convection cell increases. The convection cell which is long in the direction perpendicular to the basic flow suffers severely the prohibitive effect of the shear, while this effect decreases as the convection cell becomes longer in the direction parallel to the basic flow.