Non-linear Optimal Perturbations in the Asymptotic Suction Boundary-layer

An asymptotic suction boundary layer (ASBL) flow is obtained when a given homogeneous suction is applied to a boundary- layer flow, highly stabilizing the flow with respect to Tollmienn-Schlichting waves. This work aims at verifying the stabilizing action of this homogeneous suction on linear and non-linear transition growth. Thus, the analytical ASBL solution is perturbed by optimal disturbances yielding the largest energy growth over a short time interval. Such perturbations are computed by a linear and non-linear global optimization approach based on a Lagrange multiplier technique. The results show that non-linear optimal perturbations are characterized by a localized basic building block, formed by staggered inclined vortices. In order to obtain a threshold amplitude for transition the optimization is coupled with a bisection of the perturbation initial energy, in order to compute the minimal seed, defined as the perturbation of minimal energy which lays on the frontier between the laminar and the turbulent states. This energy threshold is found to be 1 to 4 order of magnitude lower than the ones found by Levin et al. (2005) for other transition scenarios.