Spatial Direct Numerical Simulation of Boundary-Layer Transition Mechanisms: Validation of PSE Theory

A study of instabilities in incompressible boundary-layer ow on a at plate is conducted by spatial direct numerical simulation (DNS) of the Navier-Stokes equations. Here, the DNS results are used to critically evaluate the results obtained using parabolized stability equations (PSE) theory and to study mechanisms associated with breakdown from laminar to turbulent ow. Three test cases are considered: two-dimensional TollmienSchlichting 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 meanow distortion component of the 2-D test problem. This discrepancy is attributed to fareld boundarycondition di erences. 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 ow and a variation of the disturbance frequency result in better agreement with the experiments.