Direct measurement of slip length operator and eddy viscosity fields for turbulent flows over superhydrophobic surfaces

Superhydrophobic surfaces (SHS) are textured hydrophobic surfaces which have the ability to trap air pockets when immersed in water. This can result in significant drag reduction, due to substantially lower viscosity of air resulting in large effective slip velocity at the interface. Past studies model this slip velocity in terms of a homogenized Navier slip boundary condition with a slip length relating the wall slip velocity to the wall-normal velocity gradient. In this study, we seek to understand the effects of superhydrophobic surfaces in the context of momentum mixing. We use the macroscopic forcing method (Mani and Park, Phys. Rev. Fluids, 2021) to compute the eddy viscosity of a turbulent channel over SHS, implemented as both a pattern-resolved boundary condition and homogenized slip length boundary condition. We present key differences in the mixing behavior of both boundary conditions through quantification of their implications on the near-wall eddy viscosity. In addition, we compute the fully generalized slip length operator to assess the nonlocal effects of SHS patterning.