Linear Stability of Three-Dimensional Boundary Layers: Effects of Curvature and Non-Parallelism

Absh-act In this paper we study the effect of in-plane (wavefront) curvature on the stability of threedimensional boundary layers. It is found that this effect is stabilizing or destabilizing depending upon the sign of the crossflow velocity profile. We also investigate the effects of surface curvature and nonparallelism on crossflow instability. Computations performed for an infinite-swept cylinder show that while convex curvature stabilizes the three-dimensional boundary layer, nonparallelism is, in general, destabilizing and the net effect of the two depends upon meanflow and disturbance parameters. It is also found that concave surface curvature further destabilizes the crossflow instability. 1. Introduct ion The three-dimensional (3D) boundary layer exists when the inviscid streamlines are curved in a plane parallel to the surface. Because of viscous effects, the pressure gradient that exists in the direction normal to the streamline causes a velocity component inside the boundary layer which is perpendicular to the inviscid-velocity vector. This component is'called crossflow. The crossflow profile has a maximum velocity somewhere in the middle of the boundary layer and goes to zero on the body surface and at the boundary layer edge and contains an inflection point. The description of the inviscid instability caused by the crossflow in an incompressible flow was first given in a classic paper by Gregory, Stuart and Walker (1955) (hereinafter referred to as GSW). When the crossflow component is combined with the velocity component in the inviscid streamline direction, they form a mean velocity profile which has an inflection point at which the velocity is zero. This permits stationary disturbances which appear as vortices that all rotate in the same direction and take on the form of

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