A study of non-parallel and nonlinear effects on the localized receptivity of boundary layers

Abstract

The acoustic receptivity due to localized surface suction in a two-dimensional boundary layer is studied using a finite-Reynolds-number theory and direct numerical simulation of the Navier-Stokes equations. Detailed comparisons between the two methods are used to determine the bounds for application of the theory. Results show a 4% difference between the methods for receptivity in the neighbourhood of branch I with low suction levels, low acoustic levels, and a moderate frequency; we attribute this difference to non-parallel effects, not included in the theory. The difference is larger for receptivity upstream of branch I, and smaller for receptivity downstream of branch I. As the peak suction level is increased to 1% of the free-stream velocity, the simulations show a nonlinear deviation from the theory. Suction levels as small as 0.1% are shown to have a significant effect on the instability growth between branch I and branch II. Increasing the acoustic amplitude to 1% of the steady free-stream velocity produces no significant nonlinear effect.