Optimal amplification of large-scale structures in plane turbulent couette flow

Abstract

International audienceIn the present study, we investigate the optimal perturbations in plane turbulent Couette flow with turbulent mean flow and the associated eddy viscosity at Reh = 750. The three canonical types of optimal perturbations are computed: the initial perturbations for transient energy growth, the response to harmonic forcing and the variance to stochastic excitation. In all the cases, the maximum responses are obtained for streamwise uniform perturbations (λx = ∞). The optimal spanwise spacings of the transient growth and the stochastic forcing are λz = 4.2h and λz = 5.2h, respectively. These values are in very good agreement with the spanwise spacing of the large-scale streaks reported in previous studies. Moreover, the velocity field of the responses to the optimal perturbations are strikingly similar to that of large-scale structure obtained with direct numerical simulation. Finally, the optimal response to the harmonic forcing, more related to flow controls, reveals the maximum by steady forcing with larger spanwise wavelength (7.4h)