Two- and Three-dimensional Instabilities of Confined Flows: Numerical Study by a Global Galerkin Method

A version of the global Galerkin method applied to a wide range of hydrodynamic stability problems is described. The numerical algorithm is based on a non-orthogonal set of globally defined basis functions, which satisfy all linear boundary conditions and the continuity equation. This leads to a significant reduction of the number of scalar degrees of freedom of the numerical model. The relatively low number of degrees of freedom makes it possible to solve the eigenvalue problem associated with the linear stability of flow, and to approximate asymptotically the slightly supercritical flows that arise after the onset of instability. The main objective is the analysis of stability of steady state flows which are calculated numerically. Details and advantages of the proposed approach are illustrated on several examples.