Dar. Davis et Ft. Smith, ON SUBSONIC, SUPERSONIC AND HYPERSONIC INFLECTIONAL-WAVE VORTEX INTERACTION/, Journal of engineering mathematics, 30(6), 1996, pp. 611-645
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.