Abstract
The purpose of the present study is to resolve a long-standing paradox intrinsic to the triple-deck theory that predicts stability of a supersonic boundary layer against two-dimensional disturbances for all Mach numbers M1 > 1 of the oncoming stream. Thorough investigation of disturbances in the transonic range of velocities results in a new interaction law and points to the formation of an additional stable mode missing from incompressible and subsonic flows. At some value of the transonic similarity parameter K1 the new mode “collides” in an auxiliary complex plane composed of the disturbance frequencies and wave numbers with the conventional Tollmien– Schlichting unstable mode typical of two-dimensional waves in incompressible and subsonic regimes. As a result, the mode exchange takes place and the new mode continues after collision as an unstable one. A rigorous proof of the existence of the neutral frequencies and wave numbers for arbitrary values of K1 substantiates this conclusion. In the limit, asK1 ! 1, the interactive boundary layer turns to the classical boundary layer by Prandtl extending over the reference length of developing viscous flow.
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