Minimal transition thresholds in plane Couette flow

Abstract

International audienceSubcritical transition to turbulence requires finite-amplitude perturbations. Using anonlinear optimisation technique in a periodic computational domain, we identify theperturbations of plane Couette flow transitioning with least initial kinetic energy forRe ≤ 3000.We suggest a new scaling law Ec = O(Re−2.7) for the energy threshold vs.the Reynolds number, in quantitative agreement with experimental estimates for pipeflow. The route to turbulence associated with such spatially localised perturbationsis analysed in detail for Re = 1500. Several known mechanisms are found to occurone after the other: Orr mechanism, oblique wave interaction, lift-up, streak bending,streak breakdown, and spanwise spreading. The phenomenon of streak breakdown isanalysed in terms of leading finite-time Lyapunov exponents of the associated edgetrajectory