  Superhydrophobic surfaces demonstrate promising potential for skin friction
reduction in naval and hydrodynamic applications. Recent developments of
superhydrophobic surfaces aiming for scalable applications use random
distribution of roughness, such as spray coating and etched process. However,
most of previous analyses of the interaction between flows and superhydrophobic
surfaces studied periodic geometries that are economically feasible only in
lab-scale experiments. We conduct direct numerical simulations of turbulent
flows over randomly patterned interfaces considering a range of texture widths
$w^+\approx 4-26$, and solid fractions $\phi_s=11\%$ to $25\%$. Slip and
no-slip boundary conditions are implemented in a pattern, modeling the presence
of gas-liquid interfaces and solid elements. Our results indicate that slip of
randomly distributed textures under turbulent flows are about $30\%$ less than
those of surfaces with aligned features of the same size. In the small texture
size limit $w^+\approx 4$, the slip length of the randomly distributed textures
in turbulent flows is well described by a previously introduced Stokes flow
solution of randomly distributed shear-free holes. By comparing DNS results for
patterned slip and no-slip boundary against the corresponding homogenized slip
length boundary conditions, we show that turbulent flows over randomly
distributed posts can be represented by an isotropic slip length in streamwise
and spanwise direction. The average pressure fluctuation on gas pocket is
similar to that of the aligned features with the same texture size and gas
fraction, but the maximum interface deformation at the leading edge of the
roughness element is about twice larger when the textures are randomly
distributed.
