Quantitative Comparison of Results from DNS and Nonlinear Parabolized Stability Equations for the Subharmonic Transition Process

Kurzfassung

The laminar-turbulent transition in two-dimensional boundary layers typically begins with the amplification of Tollmien-Schlichting waves, evolving into three-dimensional structures that ultimately lead to turbulence. Among the various nonlinear interaction scenarios, this study focuses on the subharmonic resonance process—known as H-type transition—by providing a quantitative comparison between Direct Numerical Simulation (DNS) and Nonlinear Parabolized Stability Equations (NPSE) in modeling this pathway. Under conditions replicating established wind-tunnel experiments, controlled disturbances at specific frequencies and wavelengths are introduced, inducing subharmonic resonance and generating staggered vortical structures in the boundary layer. Tracking the spatial evolution and amplitude growth of multiple modes reveals close agreement between DNS and NPSE results. Although NPSE ceases to converge as nonlinearity intensifies near the transition point, it remains effective in modeling the nonlinear processes in the subharmonic breakdown up to its convergence limit.