Nonlocality of the slip length operator for scalar and momentum transport in turbulent flow 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 substantial effective slip velocity at the interface. Past studies of both laminar and turbulent flows 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 work, we seek to understand the effects of superhydrophobic surfaces in the context of mean scalar and momentum mixing. We use the macroscopic forcing method (Mani and Park, 2021) to compute the generalized eddy viscosity and slip length operators of a turbulent channel over SHS, implemented as both a pattern-resolved boundary condition and homogenized slip length boundary condition, for several pattern sizes and geometries. We present key differences in the mixing behavior of both boundary conditions through quantification of their near-wall eddy viscosity. Analysis of transport in turbulent flow over pattern-resolved surfaces reveals substantial nonlocality in the measured homogenized slip length for both scalar and momentum mixing when the Reynolds and Peclet numbers based on pattern size are finite. We present several metrics to quantify this nonlocality and observe possible trends relating to Reynolds number, texture size, and pattern geometry. The importance of nonlocality in the slip length operator and in the eddy diffusivity operator is demonstrated by examining the impact on Reynolds-averaged solutions for the mean scalar and velocity fields.