Nonlinear optimals in the asymptotic suction boundary layer: Transition thresholds and symmetry breaking

Abstract

The effect of a constant homogeneous wall suction on the nonlinear transient growth of localized finite amplitude perturbations in a boundary-layer flow is investigated. Using a variational technique, nonlinear optimal disturbances are computed for the asymptotic suction boundary layer (ASBL) flow, defined as those finite amplitude disturbances yielding the largest energy growth at a given target time T. It is found that homogeneous wall suction remarkably reduces the optimal energy gain in the nonlinear case. Furthermore, mirror-symmetry breaking of the shape of the optimal perturbation appears when decreasing the Reynolds number from 10 000 to 5000, whereas spanwise mirror-symmetry was a robust feature of the nonlinear optimal perturbations found in the Blasius boundary-layer flow. Direct numerical simulations show that the different evolutions of the symmetric and of the non-symmetric initial perturbations are linked to different mechanisms of transport and tilting of the vortices by the mean flow. By bisecting the initial energy of the nonlinear optimal perturbations, minimal energy thresholds for subcritical transition to turbulence have been obtained. These energy thresholds are found to be 1–4 orders of magnitude smaller than those provided in the literature for other transition scenarios. For low to moderate Reynolds numbers, the energy thresholds are found to scale with Re−2, suggesting a new scaling law for transition in the ASBL.