Numerical simulation of K-, N- and O-regime boundary-layer transition at early nonlinear stage

Abstract

Boundary layer transition is usually associated with the amplification and breakdown of three-dimensional waves (3D waves). However, the details of the development of 3D waves in different transition regimes are not well resolved. The present study attempts to examine the transition process at early nonlinear stages of K-, N-, and O-regimes by the solution of nonlinear parabolized stability equations (NPSE). The spatial and temporal variations of streamwise velocity are compared at the one-spike stage. Timelines and material surfaces are presented using Lagrangian tracking method. The development of 3D waves are observed to contribute to the upward lift and downward sweep of flow behaviors, causing inflectional regions in the boundary layer. The evolution of material surfaces reveals that the nonlinear 3D wave manifests as a warped wave front in the near-wall region and as a soliton-like structure at the upper region of the boundary layer. The 3D wave structure is hypothesized as a soliton-like coherent structure. Markedly similar flow behaviors are observed between the regimes, which indicates a similar underlying physical mechanism.