Linear instability of the supersonic wake behind a flat plate aligned with a uniform stream

In this paper we present a theoretical and numerical study of the growth of linear disturbances in the high Reynolds number laminar compressible wake behind a flat plate which is aligned with a uniform stream. No ad hoc assumptions are made as to the nature of the undisturbed flow (in contrast to previous investigations) but instead the theory is developed rationally by use of proper wake profiles which satisfy the steady equations of motion. The initial growth of near-wake perturbations is governed by the compressible Rayleigh equation which is studied analytically for long and short waves. These solutions emphasize the asymptotic structures involved and provide a rational basis for a nonlinear development. The phenomenon of enhanced stability with increasing Mach number observed in compressible free shear-layers is demonstrated analytically for short- and long-wavelength disturbances. The evolution of arbitrary wavelength perturbations is addressed numerically and spatial stability solutions are presented that account for the relative importance of the different physical mechanisms present, such as three-dimensionality, increasing Mach numbers, and the nonparallel nature of the mean flow. Our findings indicate that for low enough (subsonic) Mach numbers, there exists a region of absolute instability very close to the trailing edge with the majority of the wake being convectively unstable. At higher Mach numbers (but still not large—hypersonic) the absolute instability region seems to disappear and the maximum available growth rates decrease considerably. Three-dimensional perturbations provide the highest spatial growth rates.This work was carried out while the author was a summer visitor at the Institute for Computer Applications in Science and Engineering, NASA Langley Research Center under NASA Contract No. NAS1-18605.