Streamwise oscillation of spanwise velocity at the wall of a channel for turbulent drag reduction

Abstract

Steady forcing at the wall of a channel flow is studied via direct numerical simulation to assess its ability of yielding reductions in turbulent friction drag. The wall forcing consists of a stationary distribution of spanwise velocity that alternates in the streamwise direction. The idea behind the forcing builds on the existing technique of the spanwise wall oscillation and exploits the convective nature of the flow to achieve an unsteady interaction with turbulence. The analysis takes advantage of the equivalent laminar flow, which is solved analytically to show that the energetic cost of the forcing is unaffected by turbulence. In a turbulent flow, the alternate forcing is found to behave similarly to the oscillating wall; in particular an optimal wavelength is found which yields a maximal reduction in turbulent drag. The energetic performance is significantly improved, with more than 50% of maximum friction saving at large intensities of the forcing, and a net energetic saving of 23% for smaller intensities. Such a steady, wall-based forcing may pave the way to passively interacting with the turbulent flow to achieve drag reduction through a suitable distribution of roughness, designed to excite a selected streamwise wavelength.