THE ONSET OF INSTABILITY IN UNSTEADY BOUNDARY-LAYER SEPARATION

The process of unsteady two-dimensional boundary-layer separation at h igh Reynolds number is considered. Solutions of the unsteady non-inter active boundary-layer equations are known to develop a generic separat ion singularity in regions where the pressure gradient is prescribed a nd adverse. As the boundary layer starts to separate from the surface, however, the external pressure distribution is altered through viscou s-inviscid interaction just prior to the formation of the separation s ingularity; hitherto this has been referred to as the first interactiv e stage. A numerical solution of this stage is obtained here in Lagran gian coordinates. The solution is shown to exhibit a high-frequency in viscid instability resulting in an immediate finite-time breakdown of this stage. The presence of the instability is confirmed through a lin ear stability analysis. The implications for the theoretical descripti on of unsteady boundary-layer separation are discussed, and it is sugg ested that the onset of interaction may occur much sooner than previou sly thought.