Nonlinear Description of Transversal Motion in A Laminar Boundary Layer with Streaks

Abstract

The nonlinear streamwise growth of a spanwise periodic array of steady streaks in a flat plate boundary layer is numerically computed using the well known Reduced NavierStokes formulation. It is found that the flow configuration changes substantially when the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-spanwise plane), which is normally not considered, becomes non-negligible in the nonlinear regime, and it strongly distorts the streamwise velocity profiles, which end up being quite different from those predicted by the linear theory. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks, and compare them with available experimental results. Streaks naturally develop in a flat plate boundary layer in the presence of small free stream perturbations. They are three dimensional boundary layer flow structures that take the form of spanwise thin and streamwise elongated regions of high speed and low speed flow that alternate in the spanwise direction. The resulting streamwise velocity profile exhibits a strong modulation in the spanwise direction, with a characteristic scale of the order of the width of the boundary layer, and a slow downwards motion in the high speed region and upwards in the low speed region (see Fig. 1).