Nonlinear optimal perturbations and formation mechanism of localized wave packet in channel flow

Abstract

The subcritical transition in a two-dimensional channel flow is characterized by the emergence of localized wave packet (LWP). In this paper, the nonlinear nonmodal optimization method is used, and when the target time is long enough the minimal seed, the minimal-energy perturbation triggering the transition is found to be the localized wave packet tilted upstream with energy scaling as Re−3.8 for Re>2500. The formation of LWP from a minimal seed includes three stages. First, the disturbance kinetic energy of the minimal seed increases to a local maximum through a transient growth governed by the Orr mechanism, and second, large scale vortex structures are generated due to the nonlinear forcing mainly contributed by the wave components and causes a streamwise symmetry breaking, i.e., a long but weak upstream tail and a strong downstream front are formed. As a result, the perturbation structure approaches the unstable lower branch solution and is attracted and captured at the last stage by the stable upper branch solution of LWP in the phase space.