Effect of Three-dimensional Surface Elements on Boundary Layer Flow

Abstract

The perturbation velocity field induced by a three-dimensional surface distorsion in a boundary layer flow is considered. For small amplitudes, the kinetic energy is shown to be composed of two factors; one associated with the surface structure and the other with the velocity profile. Level curves of the profile factor, in the (α,β) wave-number plane, are ridge-like and approach the β-axis as the Reynolds number increases. Thus, in the inviscid limit, the kinetic energy is confined to structures infinitely extended in the streamwise direction. For a certain class of surface structures, also the level curves for the kinetic energy have been determined. It is shown how a spanwise modulation and an aspect ratio of the surface distorsion change the position of the level curves and the amplitudes.