On the Görtler Vortex Instability Mechanism at Hypersonic Speeds
The linear instability of the hypersonic boundary layer on a curved wall is considered. As a starting point real-gas effects are ignored and the viscosity of the fluid is taken to be related to the temperature either by Chapman’s Law or by Sutherland’s Law. It is shown that the flow is susceptible to Görtler vortices. If Chapman’s Law is used the vortices are trapped in the logarithmically thin adjustment layer in which the temperature of the basic flow changes rapidly to its free stream value and the non-uniqueness of the neutral stability curve associated with incompressible Görtler vortices is shown to disappear at high Mach numbers if the appropriate “fast” streamwise dependence of the instability is built into the disturbance flow structure. If, on the other hand, Sutherland’s Law is used, the vortices are found to spread into an O(1) region and the concept of a unique neutral stability curve is not tenable because of the non-parallel effects. For both laws the leading order terms in the expansions of the Görtler number are independent of the wave number and are due to the curvature of the basic state.
KeywordsBoundary Layer Mach Number Lead Order Term Neutral Curve High Mach Number
Unable to display preview. Download preview PDF.
- 1.El-Hady, N. and Verma, A.K. (1981), Growth of Görtler vortices in compressible boundary layers along curved surfaces, AIAA paper No. 81–1278.Google Scholar
- 3.Görtler, H. (1941), Instabilität laminaren Grenschichten an konkaven Wanden gegeniiber gewissen dreidimensionalen Storungen, ZAMM, 21, 1, 250.Google Scholar
- 8.Hall, P. (1988), The growth of nonlinear Görtler vortices in growing boundary layers, J. Fluid Mech., 193, 243.Google Scholar
- 9.Hall, P. and Malik, M.R. (1987), Görtler vortices in compressible boundary layers, ICASE Report 87–46 and to appear in J. Eng. Maths.Google Scholar
- 12.Stewartson, K. (1964), The theory of laminar boundary layers in compressible flows, Clarendon Press.Google Scholar