Optimal linear growth in the asymptotic suction boundary layer

Abstract

A variational technique in the temporal framework is used to study initial configurations of disturbance velocity which maximize perturbation kinetic energy in the asymptotic suction boundary layer (ASBL). These optimal perturbations (OP) excite significant and remarkably persistent transient growth, on the order of that which occurs in the Blasius boundary layer (BBL). In contrast, classical modal analysis of the ASBL predicts a critical Reynolds number two orders of magnitude larger than that for the BBL. As in other two-dimensional boundary layer flows, disturbances undergoing maximum amplification are infinitely elongated in the direction of the flow and take the form of streamwise-oriented vortices which induce strong variations in the streamwise perturbation velocity (streaks). The Reynolds number dependence of the maximum growth, and the best choice of scaling for the spanwise wavenumber of the perturbation causing it, are elucidated. There is good agreement between the streak resulting from OP and disturbances measured in experiments in which the asymptotic suction boundary layer is subject to free stream turbulence (FST). This agreement is shown to improve as the level of FST increases.