Stability of the compressible laminar boundary layer

Abstract

In previous theoretical treatments of the stability of the compressible laminar boundary layer, the effect of the temperature fluctuations on the viscous (rapidly varying) disturbances is accounted for incompletely. A thorough re-examination of this problem shows that temperature fluctuations have a profound influence on both the inviscid (slowly varying) and viscous disturbances above a Mach number of about 2·0. The present analysis includes the effect of temperature fluctuations on the viscosity and thermal conductivity and also introduces the viscous dissipation term that was dropped in the earlier theoretical treatments.Some important results of the present study are: (1) the rate of conversion of energy from the mean flow to the disturbance flow through the action of viscosity in the vicinity of the wall increases with Mach number; (2) instead of being nearly constant across the boundary layer, the amplitude of inviscid pressure fluctuations for Mach numbers greater than 3 decreases markedly with distance outward from the plate surface. This behaviour means that the jump in magnitude of the Reynolds stress in the neighbourhood of the critical layer is greatly reduced; (3) at Mach numbers less than about 2, dissipation effects are minor, but they become extremely important at higher Mach number, since for neutral disturbances they must compensate for the generally destabilizing effects of items (1) and (2); (4) the minimum critical Reynolds number for an insulated flat plate boundary layer decreases with increasing Mach number in the range 0 ≤ Me ≤ 3.A full list of symbols is given at the end of this paper.. Since the wave-number varies like 1/M2e when Me [Gt ] 1, the minimum critical Reynolds number is likely to increase sharply at hypersonic speeds.Numerical examples illustrating the effects of compressibility, including neutral stability characteristics, are obtained and are compared with the experimental results of Laufer & Vrebalovich (1960) at Mach 2·2, and of Demetriades (1960) at Mach 5·8.