The Nonlinear One-Way Navier-Stokes (NOWNS) Approach for Boundary-Layer Transition

This work seeks rapid prediction of laminar-to-turbulent transition based on first principles, rather than commonly employed empirical correlations. The nonlinear one-way Navier-Stokes (NOWNS) equations were recently applied to the early stages of boundary layer transition where it was demonstrated that NOWNS can accurately replicate direct numerical simulation (DNS) results with similar accuracy to the nonlinear parabolized stability equations (NPSE). While having greater computational cost than NPSE, NOWNS is a more robust, convergent parabolization of the governing equations and is expected to succeed for stronger nonlinearity where NPSE fails. We demonstrate that NOWNS succeeds for stronger nonlinearity by applying it to an oblique-wave breakdown case where NPSE fails. In addition, we demonstrate that NOWNS supports non-modal disturbances in the form of random noise applied to the inlet boundary condition of the oblique-wave breakdown case, and a blowing/suction strip for a K-type (fundamental) transition case.