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

Effect of texture randomization on the slip and interfacial robustness in turbulent flows over superhydrophobic surfaces