Triple-Deck Instability of Supersonic Boundary Layers

摘要

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 M∞ > 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 K∞ 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 K∞ substantiates this conclusion. In the limit, as K∞ → ∞, the interactive boundary layer turns to the classical boundary layer by Prandtl extending over the reference length of developing viscous flow.