Importance of relative phase between wall pressure and transpiration for drag reduction

Wall-based active and passive control strategies for drag reduction in low Reynolds number turbulent flows cause at least two commonly observed modifications of the flow dynamics: attenuation or amplification of the near-wall cycle, and generation of spanwise rollers. The present study aims to clarify the underlying flow physics and considers a closed-loop wall transpiration, which is represented as a superposition of Fourier modes. The aforementioned modifications of the flow dynamics are shown to be associated with transpiration at distinct spatial scales. Whether control amplifies or attenuates the scales depends on the phase of the transpiration relative to the background flow, which can be parametrized by the wall pressure. Attenuation of the near-wall cycle and drag reduction occur when transpiration at large streamwise scales is in-phase with the wall pressure, while spanwise rollers and one route to drag increase are associated with out-of-phase transpiration at large spanwise scales. The coupled dynamics of the transpiration and wall pressure are discussed along with implications for control and modeling of wall-bounded flows.