Coupled dynamics of wall pressure and transpiration, with implications for the modeling of tailored surfaces and turbulent drag reduction

Wall-based active and passive flow control for drag reduction in low Reynolds number (Re) turbulent flows can lead to three typical phenomena: i) attenuation or ii) amplification of the near-wall cycle, and iii) generation of spanwise rollers. The present study conducts direct numerical simulations (DNS) of a low Re turbulent channel flow and demonstrates that each flow response can be generated with a wall transpiration at two sets of spatial scales, termed "streak" and "roller" scales. The effect of the transpiration is controlled by its relative phase to the background flow, which can be parametrized by the wall pressure. Streak scales i) attenuate the near-wall cycle if transpiration and wall-pressure are approximately in-phase or ii) amplify it otherwise, and iii) roller scales energize spanwise rollers when transpiration and wall pressure are out-of-phase. The dynamics of the wall pressure and transpiration are coupled and robust relative phase relations, which are required to trigger the flow responses, can result if the source term of the linear fast or nonlinear slow pressure correlates with the wall transpiration over a scale-dependent height or if the temporal frequency content of the wall transpiration is approximately sparse. The importance of each condition depends on the relative magnitude of the pressure components, which is significantly altered by the transpiration. The analogy in flow response suggests that transpiration with the two scale families and their phase relations to the wall pressure represent fundamental building blocks for flows over tailored surfaces including riblets, porous, and permeable walls.