Turbulence suppression in channel flows by small amplitude transverse wall oscillations

We model and analyze the influence of small amplitude transverse wall oscillations on the evolution of velocity perturbations in channel flows. We quantify the effect of stochastic outside disturbances on velocity perturbation energy and develop a framework for the optimal selection of transverse oscillation parameters for turbulence suppression. A perturbation analysis is used to demonstrate that depending on the wall oscillation frequency the energy of velocity perturbations can be increased or decreased compared to the uncontrolled flow. Our results elucidate the capability of properly designed oscillations to reduce receptivity of the linearized Navier-Stokes equations to stochastic disturbances, which entails decreased levels of variance in wall-bounded shear flows.