Propagation of perturbations in the boundary layer on the walls of a flat channel

Abstract

The interaction of the boundary layer and the Inviscid part of the flow is considered for the laminar, steady-state motion of a perfect gas in a symmetrical plane channel at large characteristic Reynolds numbers. The interaction zone lies at a large distance from the channel entrance and has a longitudinal dimension that exceeds the channel width in order of magnitude. It is shown that at supersonic flow velocities in the main part of the channel the perturbations introduced into the boundary layer are damped exponentially upstream from the perturbation source. In the case of a subsonic flow, as in an incompressible fluid, there is no propagation of the perturbations upstream. The propagation of perturbations in the boundary layer upstream from the perturbation source is encountered in many problems of fluid dynamics at large Reynolds numbers. A rational mathematical description of this effect has been obtained within the framework of the asymptotic theory of interaction between the boundary layer and the inviscid part of the flow (see reviews [1, 2]). Here we shall consider one of the possible interaction regimes for steady motion of a perfect gas in a symmetric plane channel (the various types of interaction for internal incompressible flows are reviewed in [2]). Attention is concentrated on the particular features of the supersonic and subsonic flow regimes in fairly long channels.