Effects of the air layer of an idealized superhydrophobic surface on the slip length and skin-friction drag

The anisotropy of the slip length and its effect on the skin-friction drag are numerically investigated for a turbulent channel flow with an idealized superhydro-phobic surface having an air layer, where the idealized air-water interface is flat and does not contain the surface-tension effect. Inside the air layer, both the shear-driven flow and recirculating flow with zero net mass flow rate are considered. With increasing air-layer thickness, the slip length, slip velocity and percentage of drag reduction increase. It is shown that the slip length is independent of the water flow and depends only on the air-layer geometry. The amount of drag reduction obtained is in between those by the empirical formulae from the streamwise slip only and isotropic slip, indicating that the present air-water interface generates an anisotropic slip, and the streamwise slip length (b(x)) is larger than the spanwise one (b(z)). From the joint probability density function of the slip velocities and velocity gradients at the interface, we confirm the anisotropy of the slip lengths and obtain their relative magnitude (b(x)/b(z) = 4) for the present idealized superhydrophobic surface. It is also shown that the Navier slip model is valid only in the mean sense, and it is generally not applicable to fluctuating quantities.