Spatial direct numerical simulation of boundary-layer transition mechanisms: Validation of PSE theory

A study of instabilities in incompressible boundary-layer flow on a flat plate is conducted by spatial direct numerical simulation (DNS) of the Navier-Stokes equations. Here, the DNS results are used to evaluate critically the results obtained using parabolized stability equations (PSE) theory and to study mechanisms associated with breakdown from laminar to turbulent flow. Three test cases are considered: two-dimensional Tollmien-Schlichting wave propagation, subharmonic instability breakdown, and oblique-wave breakdown. The instability modes predicted by PSE theory are in good quantitative agreement with the DNS results, except a small discrepancy is evident in the mean-flow distortion component of the two-dimensional test problem. This discrepancy is attributed to far-field boundary-condition differences. Both DNS and PSE theory results show several modal discrepancies when compared with the experiments of subharmonic breakdown. Computations that allow for a small adverse pressure gradient in the basic flow and a variation of the disturbance frequency result in better agreement with the experiments.