Computation of 3D-wave packet characteristics in an unstable boundarysubsonic layer

Abstract

Realistic perturbations of technical flows are usually of limited spatio-temporal extent (e.g. gusts in the freestream, roughness elements, active control devices etc.). Early results for three-dimensional wave packets in incompressible flow were obtained in (1). Here, the time asymptotic response of the subsonic adiabatic flat plate boundary layer flow upon a pulsewise and localized perturbation is studied theoretically at supercritical Reynolds number using the saddlepoint technique as in (2). The analysis is based on linear theory and is local, i.e. parallel flow is assumed. An unstable disturbance wave packet moves as a whole and spreads out at the same time. Thus, the moving packet defines a set of velocities (U, V) in the (x,y)-plane (x-streamwise, y-spanwiseI by which it's disturbance content is transported. Only an observer, assuming a velocity in this range will see a non- decaying energy density A. It's temporal evolution A (t) measured.