Transient growth of time-localized resolvent modes in a turbulent channel

To better understand transient growth in wall-bounded turbulence, this work studies the effect of the time-localized principal resolvent forcing mode on a fully-nonlinear turbulent channel flow. The principal resolvent forcing mode creates the largest energy amplification in the linearized Navier-Stokes system; this work aims to characterize how this mode affects the fully nonlinear flow and how predictable the resulting perturbation is using the optimal linear response trajectory. To obtain the time-localized resolvent forcing modes and its corresponding transient response, we formulate resolvent analysis in a wavelet basis in time for a turbulent channel flow at Re_τ = 180, and constrain the forcing to a compactly-supported wavelet by windowing the resolvent operator. We then test the effectiveness of the resolvent forcing modes in a fully-nonlinear turbulent channel flow by running an ensemble of direct numerical simulations in which we inject the computed resolvent forcing mode, then extract relevant statistics. The results show that the principal resolvent forcing mode follows the linear response for short times and close to the wall, and is more effective in changing the energy of the system compared to random forcing.