Laminar-Turbulent Transition of Blasius Boundary-Layer Flows Using the Nonlinear One-Way Navier-Stokes (NOWNS) Approach

The nonlinear One-Way Navier-Stokes (NOWNS) approach has recently been applied to perform stability analysis of two- and three-dimensional Blasius boundary layer flows. In NOWNS, a projection operator (based on the linearized Navier-Stokes equations) is applied to the nonlinear equations to remove upstream propagating modes, which results in a set of equations that can be solved efficiently in the frequency domain as a spatial initial-value problem. To date, the NOWNS approach has only been demonstrated for cases where the existing nonlinear parabolized stability equations (NPSE) are already effective. Therefore, we seek to demonstrate the advantages of the NOWNS approach by examining cases where the NPSE are less effective. In particular, we will consider boundary-layer flows with strong nonlinearities (where NPSE fails to converge), and cases with non-modal and multi-modal effects. We will validate against direct numerical simulation (DNS) results in the literature, and against an in-house harmonic balance method (HBM) code.