The Nonlinear One-Way Navier-Stokes (NOWNS) Approach for High-Speed Boundary-Layer Flows*

The Nonlinear One-Way Navier-Stokes (NOWNS) approach has recently been applied to low-speed Blasius boundary-layer flows, where it has been demonstrated to support non-modal and multi-modal effects, as well as strong nonlinearties, which can cause the Nonlinear Parabolized Stability Equations (NPSE) to fail. 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. For hypersonic boundary-layer flows, linear OWNS has been demonstrated to accurately capture complex multi-modal effects where linear PSE fails. Non-modal and multi-modal effects are critical to high-speed boundary-layer transition, and a nonlinear tool that accurately models these effects is of critical importance to the development of optimized aerospace vehicles. Therefore, we seek to demonstrate that NOWNS can capture these effects when performing nonlinear instability and transition analysis of high-speed boundary-layer flows by validating against direct numerical simulation (DNS) results in the literature.