A non-parallel theory for Görtler instability of Falkner–Skan boundary layers

Abstract

Centrifugal instability of two-dimensional similar boundary layers along a concave wall is governed by partial differential equations with respect to the normal-to-wall coordinate in a nondimensional form and the Reynolds number based on local velocity of external stream and a boundary-layer thickness. In a particular case of the stagnation-point flow with the Falkner–Skan parameter m = 1, however, the exact equations admit a series solution expanded in inverse powers of the Reynolds number and its coefficients can be obtained by solving a sequence of ordinary differential systems. Of particular importance is that the leading term is determined from an eigenvalue problem more involved than Görtler's parallel-flow approximation. Numerical evaluation of the series solution thus obtained shades light on fundamental effects of the boundary-layer nonparallelism and finite Reynolds numbers on theoretical prediction of Görtler instability.