ON THE INITIAL-STAGES OF VORTEX WAVE INTERACTIONS IN HIGHLY CURVED BOUNDARY-LAYER FLOWS

The nonlinear interaction equations describing vortex-Rayleigh wave in teractions in highly curved boundary layers are derived. These equatio ns describe a strongly nonlinear interaction between an inviscid wave system and a streamwise vortex. The coupling between the two structure s is quite different from that found by Hall and Smith [13] in the abs ence of wall curvature. Here the vortex is forced over a finite region of the flow rather than in the critical layer associated with the wav e system. When the interaction takes place the wave system remains loc ally neutral as it moves downstream and its self interaction drives a vortex field of the same magnitude as that driven by the wall curvatur e. This modification of the mean state then alters the wave properties and forces the wave amplitude to adjust itself in order that the wave frequency is constant. Solutions of the interaction equations are fou nd for the initial stages of the interaction in the case when the wave amplitude is initially small. Our analysis suggests that finite ampli tude disturbances can only exist when the vortex field is nonzero at t he initial position where the interaction is stimulated.