Effect of Free Stream Turbulence and Other Vortical Disturbances on a Laminar Boundary Layer

Abstract

This paper is concerned with the effect of free-stream turbulence on the pretransitional flat-plate boundary layer. It is assumed that either the turbulence Reynolds number or the downstream distance (or both) is small enough so that the flow can be linearized. The dominant disturbances in the boundary layer, which are of the Klebanoff type, are governed by the linearized unsteady boundary-region equations, i.e., the Navier Stokes equations with the streamwise derivatives neglected in the viscous and pressure-gradient terms. The turbulence is represented as a superposition of vortical free-stream Fourier modes, and the corresponding individual Fourier component solutions to the boundary-region equations are obtained numerically. The results are then superposed to compute the root mean square of the fluctuating streamwise velocity in the boundary layer produced by the actual free-stream turbulence. The calculated boundary-layer disturbances are in good quantitative agreement with the experimentally observed Klebanoff modes when strong low-frequency anisotropic effects are included in the free-stream turbulence spectrum. We discuss some additional effects that may need to be accounted for in order to obtain a complete description of the Klebanoff modes