Asymptotic modelling for separating boundary layers in a channel

Abstract

The purpose of this work is to give a formal asymptotic method to analyse systematically the significant perturbations which deeply change the nature of the flow of the wall boundary layer of a channel at high Reynolds numbers. The fluid is assumed Newtonian and the flow laminar two-dimensional and steady. The theory developed here explains the separation over significant wall disturbances. In particular, we show that the perturbation that induces the triple deck structure can both displace the classical boundary layer and cause separation of the flow. Besides there exist a series of disturbances, smaller but “stronger”, that cause a separation of the boundary layer without displacing it. This series is limited by the smallest perturbation compatible with the hypothesis of the theory, thus leading to a theory in double deck.