THE DEVELOPMENT AND LINEAR STABILITY OF ROTATING BOUNDARY LAYERS

Abstract

In this study, the effect of Coriolis force on the development and linear stability of the boundary layer on a rotating flat plate is examined. The parabolized governing equations are solved using a Legendre spectral element method with a marching scheme. The shape of the velocity profile is a function of the nondimensional rotation rate Rox/Rex, where Rox is the rotation number and Rex is the Reynolds number. For a given value of Rox/Rex, the base flow is self-similar, but the shape of the velocity profile changes when Rox/Rex is varied. These results are confirmed by demonstrating that the governing partial differential equations can be reduced to one ordinary differential equation by similitude analysis. The linear stability of the boundary layer to spanwise perturbations is also considered. The non-Blasius shape of the base flow velocity profile does not have any appreciable effect on the growth rate of the vortices compared to that obtained with a Blasius profile for all Rox/Rex ≤ l×l0-4 considered. Thus, the rotational Görtler number Re1/4Rox1/2(δ/δB)3/2 (where δ and δB are the actual and Blasius boundary layer thicknesses respectively) is the appropriate parameter to describe the growth of the vortices.