Turbulent flow over a wall with a streamwise traveling Rayleigh wave motion*

The drag-reduction effect of a traveling wavy surface has been a central topic since Kramer's research on dolphin skin suggested it as a possible solution to improve vehicle efficiency. However, many simulations and experimental works have focused on the wind-water wave interface, when the surface wave pattern on the solid surface usually follows the Rayleigh wave pattern. The Rayleigh wave, contrary to the prograde airy wave, has the particle traveling in the retrograde direction, i.e., traveling in the opposite direction of the wave transmitting direction at the surface. We performed a direct numerical simulation of turbulent Couette flows over waving Rayleigh wave surfaces with different wave slopes and material properties to study turbulence flow properties in the vicinity of compliant surfaces. The results show a very different pattern to the airy wave cases, which can guide the future design of surface actuators and explore a nonlocal technique to perform flow control.