The effect of slip and surface texture on turbulence over superhydrophobic surfaces

Abstract

<jats:p>Superhydrophobic surfaces are able to entrap gas pockets in between surface roughness elements when submerged in water. These entrapped gas pockets give these surfaces the potential to reduce drag due to the overlying flow being able to locally slip over the gas pockets, resulting in a mean slip at the surface. In this work we assess the separate effects that surface slip and surface texture have on turbulence over superhydrophobic surfaces. We show that the direct effect of surface slip does not modify the dynamics of the overlying turbulence, which remains canonical or smooth-wall like. The surface drag is governed by the difference between two virtual origins, the virtual origin of the mean flow and the virtual origin experienced by the overlying turbulence, in an extension of the theory from Luchini, Manzo &amp; Pozzi (<jats:italic>J. Fluid Mech.</jats:italic>, vol. 228, 1991, pp. 87–109) for riblets. Streamwise slip deepens the virtual origin of the mean flow, while spanwise slip deepens the virtual origin perceived by the overlying turbulence. Drag reduction is then proportional to the difference between the two virtual origins. We decompose the near-wall flow into background-turbulence and texture-coherent components, and show that the background-turbulence component experiences the surface as homogeneous slip lengths. The validity of the slip-length model can then be extended to larger texture size <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018009096_inline1" /><jats:tex-math>$L^{+}$</jats:tex-math></jats:alternatives></jats:inline-formula> than thought in previous studies. For <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018009096_inline2" /><jats:tex-math>$L^{+}\gtrsim 25$</jats:tex-math></jats:alternatives></jats:inline-formula>, however, we observe that a nonlinear interaction with the texture-coherent flow develops that alters the dynamics of the background turbulence, exhibiting a modified distribution of turbulent energy across length scales. This has the effect of reducing the velocity increment <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0022112018009096_inline3" /><jats:tex-math>$\unicode[STIX]{x0394}U^{+}$</jats:tex-math></jats:alternatives></jats:inline-formula> compared to that predicted using homogeneous slip lengths and sets the upper limit of applicability of slip-length models.</jats:p>