Excitation of instability waves in wall boundary layers with adverse pressure gradients by various types of Dirac sources

Abstract

The receptivity of plane, incompressible wall boundary layers close to separation is investigated for the time-harmonic excitation by Dirac sources at the wall and within the shear layer. The basic flow is treated as parallel and modelled by a hyperbolic-tangent velocity profile with an adjustable inflexion point. The receptivity is measured by a ‘production integral’ which describes the initial energy transfer from the basic flow to the unstable part of the excited disturbances. The growing instability of the velocity profiles with growing wall-distance of the inflexion point is not completely reflected by a likewise enhanced receptivity. The influence of the Reynolds number depends strongly on the position of the inflexion point. The excitation by a Dirac source in the shear layer results in a considerably higher receptivity than the excitation by a Dirac source at the wall, if the sources is placed near the critical layer.