On the instability of flow in a streamwise corner

Abstract

The linear stability of an incompressible laminar flow in the blending boundary layer between the boundary layer in a 90° streamwise corner and a Blasius boundary layer well away from the corner is examined using a locally parallel flow approximation. It is shown that the magnitude of the cross flow in the boundary layer is too small to be a significant factor in the observed early transition in the blending layer. However, the influence of the outer boundary conditions associated with oblique modes of disturbances which are anti-symmetric about the bisector plane are shown to have a profound effect on the stability of the flow. As a result, the square root of the critical streamwise Reynolds number R er , associated with a spanwise location is significantly reduced as the corner is approached, being R er = 54 approximately for spanwise distance of z * = 6 x * R -1 from the corner compared with R er = 322 approximately for z * = 20 x * R -1 , where x * measures downstream distance from the leading edges and R 2 is the streamwise Reynolds number. At R = 600, the growth rate of the most amplified mode of disturbance at the former location is over six times greater than that at the latter; the corresponding wave angle at the two locations is respectively 44° and 5°, approximately.