The effect of heating on the stability of flow over concave walls

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Abstract
The effect of heating or cooling on the linear Görtler instability of the boundary layer flow over a concave wall is described using an asymptotic analysis for short-wavelength disturbances. The analysis takes account of all nonparallel flow effects in a uniform and systematic manner without making the quasiparallel flow approximation. The fluid viscosity is assumed constant while the perturbation in density is allowed to vary linearly with the perturbation in temperature. Both steady Taylor–Görtler disturbances and those that propagate downstream are considered. An analytic expression for the neutral curve is obtained. It is found that the critical disturbances are concentrated in thin viscous layers near the middle of the boundary layer; the precise location depending upon the basic velocity and temperature profiles. Heating the boundary layer destabilizes the short-wavelength disturbances and cooling does the reverse. While steady Taylor–Görtler disturbances are more unstable than those propagating downstream under the assumptions of the present analysis, the difference between the neutral stability boundaries for the two types of disturbances is decreased by heating at low Prandtl numbers and by cooling at moderate to high Prandtl numbers.