Abstract
The optimal response of the turbulent Couette mean flow to initial conditions, harmonic and stochastic forcing is computed at Re = 750. The equations for the coherent perturbations are linearised near the turbulent mean flow and the effect of small scales is modelled with the standard eddy viscosity. The mean flow is linearly stable but it is shown to amplify coherent streamwise streaks from streamwise vortices. The largest amplifications are realized by streamwise uniform structures associated to spanwise wavelengths of 4.3h for largest amplifications of the energy of initial conditions, 5.1h for the maximum amplification of the variance of stochastic forcing. These spanwise scales compare well with the ones of the coherent large-scale streaks observed in experimental realisations and direct numerical simulations of the turbulent Couette flow. The optimal response to the harmonic forcing can be very large and is obtained with steady forcing of structures with larger spanwise wavelength (7.4h)..
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