Linear and nonlinear stability of plane stagnation flow

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Abstract
Plane stagnation flow is known to be linearly stable to three-dimensional perturbations. The purpose of this theoretical study is to show that the same flow can be destabilized if fluctuation levels are sufficiently high. In the present formulation, finite-amplitude disturbances are expanded in terms of the eigenfunctions pertaining to the linear stability of potential stagnation flow and a Galerkin method is used to derive the nonlinear amplitude equations coupling the different modes. Two- and three-mode interaction models based on the least-damped eigenfunctions of linear theory indicate that three-dimensional fluctuations can be triggered to grow exponentially above a certain critical intensity. The existence of such a threshold is in qualitative agreement with experimental studies of the secondary vortices arising in flows past blunt bodies.