Görtler instability of the axisymmetric stagnation-point flow along a concave wall

Abstract

Axisymmetric stagnation-point flow, if it is along a concave wall, is susceptible to the Görtler instability, which is governed by partial differential equations with respect to both the normal-to-wall coordinate and the local Reynolds number. A series solution of the exact disturbance equations is obtained in the form expanded into inverse powers of the Reynolds number. The lowest-order equations concerning the leading terms of the series construct a non-parallel version of Görtler's eigenvalue problem and present a neutral stability curve with the critical point in a finite range of wave numbers for disturbances of the steady longitudinal-vortex type. Higher-order terms of the series solution indicate the dependence of the Görtler instability on the local Reynolds number and suggest a quantitative limit of validity of the Görtler approximation based on the lowest-order equation system alone. In the case of the concave wall that slightly rotates around the axis of symmetry, the instability induces oblique traveling waves instead of steady longitudinal vortices.