Low-complexity modeling of mode interactions in boundary layer flows

摘要

Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In this paper, we augment the linear parabolized stability equations with Floquet analysis to capture mode interactions and their effect on the evolution of fluctuating quantities in the transitional boundary layer. To this end, we leverage Floquet theory by incorporating the fluctuations that arise from primary instability mechanisms into the base flow and accounting for different harmonics in the flow state. We examine the formation of streamwise elongated streaks in the presence of weakly nonlinear effects. In this process, we capture the growth of various harmonics observed in the direct numerical simulation of laminar streaks. Our proposed model provides a convenient linear progression of fluctuation dynamics in the streamwise direction and is thus well-suited for stability analysis and real-time control of spatially-evolving flows.