THE EFFECT OF SMOOTH DECELERATION OF THE EXTERNAL STREAM ON AN ALIGNED FLAT-PLATE BOUNDARY-LAYER

A numerical and analytical investigation of the non-interactive unstea dy (Prandtl) boundary layer is undertaken for an unsteady external mai nstream flow past an aligned finite flat plate, where initially the ma instream flow is steady and uniform. In contrast to previous investiga tions for flow past smooth bodies, the importance of the trailing edge is clearly identified, in particular with regard to the appearance of reversed flow, both on the plate and in the wake. A small-time analyt ical solution is presented first to consider the effect of the plate s moothly decelerating. This is then combined with a numerical solution for a parametric family of mainstreams which vary sinusoidally with ti me and hence subject the flow to varying degrees of deceleration and a cceleration. Above a critical parametric value, and at a finite time, reversed flow appears near the trailing edge, before moving upstream a long the plate. Various numerical solutions are presented, under incre asing grid resolution, together with an analysis of the trailing-edge flow near the critical time when reversed flow first enters. The study here tends to highlight the appearance of strong short-wave instabili ties.