Abstract
The linear instability of the hypersonic boundary layer on a curved wall is considered. As a starting point the viscosity of the fluid is taken to be a linear function of temperature and real-gas effects are ignored. It is shown that the flow is susceptible to Görtler vortices and that they are trapped in the logarithmically thin adjustment layer in which the temperature of the basic flow changes rapidly to its free stream value. The vortices decay exponentially in both directions away from this layer and are most unstable when their wavelength is comparable with the depth of the adjustment layer. The nonuniqueness 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. It is shown that in the hypersonic limit wall-cooling affects the leading-order term in the expansion of the Görtler number which is independent of the wavenumber and which is due to the curvature of the basic state but it has a negligible effect on the other terms which are dependent on the wavenumber.
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Communicated by M.Y. Hussaini
This research was supported in part by the National Aeronautics and Space Administration under NASA Contract No. NAS1-18605 while the first author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23665. This work was also partially supported by NASA under Grant NASA 18107 and by USAF under Grant AFOSR89-0042.
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Hall, P., Fu, Y. On the görtler vortex instability mechanism at hypersonic speeds. Theoret. Comput. Fluid Dynamics 1, 125–134 (1989). https://doi.org/10.1007/BF00417916
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DOI: https://doi.org/10.1007/BF00417916