Towards minimal perturbations in transitional plane Couette flow

Abstract

For parallel shear flows, transition to turbulence occurs only for perturbations of sufficiently large amplitude. It is therefore relevant to study the shape, amplitude, and dynamics of the least energetic initial disturbances leading to transition. We suggest a numerical approach to find such minimal perturbations, applied here to the case of plane Couette flow. The optimization method seeks such perturbations at initial time as a linear combination of a finite number of linear optimal modes. The energy threshold of the minimal perturbation for a Reynolds number Re=400 is only 2% less than for a pair of symmetric oblique waves. The associated transition scenario shows a long transient approach to a steady state solution with special symmetries. Modal analysis shows how the oblique-wave mechanism can be optimized by the addition of other oblique modes breaking the flow symmetry and whose nonlinear interaction generates spectral components of the edge state. The Re dependence of energy thresholds is revisited, with evidence for a O(Re(-2)) -scaling for both oblique waves and streamwise vortices scenarios.