Landau Equation and Mean Flow Distortion in Nonlinear Stability Theory of Parallel Free Flows

Weakly nonlinear stability theory of parallel flows is known to encounter a difficulty when it is applied to free shear layers, that is, the mean flow distortion induced by the disturbance does not satisfy the boundary conditions. A new formulation of the nonlinear stability theory of general parallel free flows is proposed by considering an initial value problem of a disturbance and taking a fast-time-dependence of the induced flows into account. In this formulation, a non-secular condition for the third-order-term gives the Landau equation and the difficulty concerning the mean flow distortion does not arise.