ON SUBSONIC, SUPERSONIC AND HYPERSONIC INFLECTIONAL-WAVE VORTEX INTERACTION/

An unstable inflection point developing in an oncoming two-dimensional boundary layer can give rise to nonlinear three-dimensional inflectio nal-wave/vortex interaction as described in recent papers by Hall and Smith [1], Brown et al. [2], and Smith et al. [3]. In the current stud y on the compressible range the flow is examined theoretically just do wnstream of the linear neutral position, in order to understand how th e interaction may be initiated. The research addresses both moderately and strongly compressible-regimes In the latter regime the vorticity mode, the most dangerous one, is taken as the wave part, causing the h ypersonic interaction to become concentrated in a thin temperature-adj ustment layer lying at the outer edge of the boundary layer, just belo w the free stream. In both regimes, the result is a nonlinear integro- differential equation for the wave-pressure which implies four differe nt types of downstream behaviour for the interaction-a far-downstream saturation, a finite-distance singularity, exponentially decaying wave s (leaving pure vortex motion) or periodicity. In a principal finding of the study, the coefficients of the equation are worked out explicit ly for hypersonic flow, and in particular for the case of unit Prandtl number and a Chapman fluid, where it is shown that for sufficiently h igh wall temperatures the wave angle of propagation must lie between 4 5 degrees and 90 degrees relative to the free-stream direction and als o no periodic solutions may occur then. The theory applies also to wak e flows and others. Connections with experimental findings are noted.