Investigation of turbulent flows over superhydrophobic surfaces with oscillatory slip length

Superhydrophobic surfaces have been widely studied for the purposes of drag reduction; the formation of an air film on the surface allows for a slip boundary condition, greatly decreasing the wall friction and thus the overall friction drag. Experimental results of patterned superhydrophobic surfaces, with dynamic pressure control allowing for oscillation of the individual air films, show an even further drag reduction. In addition, it has been observed that under such conditions, strong oscillatory velocities are induced in the streamwise direction, reminiscent of a Stokes boundary layer (Wang and Gharib, Bull. Am. Phys. Soc. 2018). We present a numerical study that isolates two possible factors that we believe may be contributing to the significant drag reduction. We utilize direct numerical simulations (DNS) to study the effects of (1) slip boundary condition with slip length oscillating in time and (2) oscillating streamwise wall boundary condition with nonzero bulk flow, revealing the foundational interplay between effective slip length, oscillations of slip length, and reduction of drag.