Nonlocality of the slip length operator for scalar and momentum transport in turbulent flow over superhydrophobic surfaces

Simulation of superhydrophobic surfaces (SHS) commonly utilizes a slip length boundary condition, relating slip velocity to wall-normal velocity gradient. In the Stokes flow limit, this effect can be shown to only depend on local velocity gradients at the wall; at finite Reynolds numbers, we find that nonlocal effects emerge. We investigate both scalar and momentum transport using the macroscopic forcing method to construct nonlocal eddy diffusivity, eddy viscosity, and slip kernels for turbulent channel flow over pattern-resolved SHS. The importance of nonlocality in these operators is assessed using the Reynolds-averaged representations for mean scalar and velocity fields.