Boundary layer stability analysis using the nonlinear One-Way Navier-Stokes approach

TL;DR

This paper extends the One-Way Navier-Stokes (OWNS) method to nonlinear analysis, enabling efficient and robust simulation of boundary layer instabilities and transition phenomena with improved accuracy over existing methods.

Contribution

The authors develop nonlinear OWNS (NOWNS), allowing for nonlinear wave interactions in boundary layer stability analysis, with validation against DNS and PSE results.

Findings

NOWNS accurately captures nonlinear disturbance evolution.

It is more robust to numerical noise than nonlinear PSE.

NOWNS converges for stronger nonlinearities.

Abstract

We extend the One-Way Navier Stokes (OWNS) approach to support nonlinear interactions between waves of different frequencies, which will enable nonlinear analysis of instability and transition. In OWNS, the linearized Navier-Stokes equations are parabolized and solved in the frequency domain as a spatial initial-value (marching) problem. OWNS yields a reduced computational cost compared to global solvers, while also conferring numerous advantages over the parabolized stability equations (PSE), despite its higher computational cost relative to PSE, that we seek to extend to nonlinear analysis. We validate the nonlinear OWNS (NOWNS) method by examining nonlinear evolution of two- and three-dimensional disturbances in a low-speed Blasius boundary layer compared to nonlinear PSE (NPSE) and direct numerical simulation (DNS) results from the literature. We demonstrate that NOWNS can be used to simulate flows involve blowing/suction strips, is more robust to numerical noise, and converges for stronger nonlinearities, as compared to NPSE.