One-Way Navier-Stokes (OWNS) Approach for Nonlinear Analysis of Instability and Transition in Boundary-Layer Flows

This work extends the One-Way Navier Stokes (OWNS) approach so that it supports nonlinear interactions between waves of different frequencies, which will enable nonlinear analysis of instability and transition in boundary-layer flows. The OWNS approach has previously been used for linear analysis of boundary-layer flows. In linear OWNS, the linearized Navier-Stokes equations are modified such that all upstream propagating modes are removed. The resulting equations can be solved efficiently in the frequency domain as a spatial initial-value problem, where an initial perturbation is specified at the domain inlet and evolved in the downstream direction using spatial integration. In nonlinear OWNS, the fully nonlinear Navier-Stokes equations are marched in the downstream direction. At each step of the march, a projection operator (based on the linearized Navier-Stokes equations), is applied to the fully nonlinear equations to remove modes with upstream group velocity. We examine the spatial stability of two-dimensional boundary layers, corresponding to Blasius flows. The method is validated against results from the literature, including results based on direct numerical simulation (DNS) and the nonlinear parabolized stability equations (PSE).