Robustness of variance suppression in channel flows with imperfect transverse wall oscillations

摘要

Transverse wall oscillations are a sensor-free control strategy that can suppress kinetic energy and reduce skin-friction drag in wall-bounded shear flows. However, the success of wall oscillations is tied to the appropriate selection of their amplitude and frequency. We evaluate the robust performance of this flow control strategy to imperfections in the amplitude and phase of oscillations. These imperfections, which are modeled as stochastic parametric uncertainties, appear as multiplicative uncertainties in the linearized dynamics. We adopt an input-output approach to analyze the mean-square stability and frequency response of the flow subject to additive and multiplicative sources of uncertainty and provide a computationally efficient method for computing the energy spectrum of velocity fluctuations around the uncertain base state.