The interaction of the overlying turbulent flow with a riblet surface and its impact on drag reduction are analysed. The ‘viscous regime’ of vanishing riblet spacing, in which the drag reduction produced by the riblets is proportional to their size, is reasonably well understood, but this paper focuses on the behaviour for spacingss+≃ 10–20, expressed in wall units, where the viscous regime breaks down and the reduction eventually becomes an increase. Experimental evidence suggests that the two regimes are largely independent, and, based on a re-evaluation of existing data, it is shown that the optimal rib size is collapsed best by the square root of the groove cross-section, ℓg+=Ag+1/2. The mechanism of the breakdown is investigated by systematic DNSs with increasing riblet sizes. It is found that the breakdown is caused by the appearance of long spanwise rollers belowy+≈ 20, with typical streamwise wavelengths λx+≈ 150, that develop from a two-dimensional Kelvin–Helmholtz-like instability of the mean streamwise flow, similar to those over plant canopies and porous surfaces. They account for the drag breakdown, both qualitatively and quantitatively. It is shown that a simplified linear instability model explains the scaling of the breakdown spacing with ℓg+.

The interaction of the overlying turbulent flow with riblets, and its impact on their drag reduction properties are analysed. In the so-called viscous regime of vanishing riblet spacing, the drag reduction is proportional to the riblet size, but for larger riblets the proportionality breaks down, and the drag reduction eventually becomes an increase. It is found that the groove cross section A + g is a better characterization of this breakdown than the riblet spacing, with an optimum A + g 1/2 ≈ 11. It is also found that the breakdown is not associated with the lodging of quasi-streamwise vortices inside the riblet grooves, or with the inapplicability of the Stokes hypothesis to the flow along the grooves, but with the appearance of quasi-two-dimensional spanwise vortices below y + ≈ 30, with typical streamwise wavelengths l

Superhydrophobic surfaces can entrap gas pockets within their grooves when submerged in water. Such a mixed-phase boundary is shown to result in an effective slip velocity on the surface, and has promising potential for drag reduction and energy-saving in hydrodynamic applications. The target flow regime, in most such applications, is a turbulent flow. Previous analyses of this problem involved direct numerical simulations of turbulence with the superhydrophobic surface modelled as a flat boundary, but with a heterogeneous mix of slip and no-slip boundary conditions corresponding to the surface texture. Analysis of the kinematic data from these simulations has helped to establish the magnitude of drag reduction for various texture topologies. The present work is the first investigation that, alongside a kinematic investigation, addresses the robustness of superhydrophobic surfaces by studying the load fields obtain from data from direct numerical simulations (DNS).The key questions at the focus of this work are: does a superhydrophobic surface induce a different pressure field compared to a flat surface? If so, how does this difference scale with system parameters, and when does it become significant that it can deform the air-water interface and potentially rapture the entrapped gas pockets? To this end, we have performed DNS of turbulent channel flows subject to superhydrophobic surfaces over a wide range of texture sizes spanning values from L + = 6 to L + = 155 when expressed in terms of viscous units. The pressure statistics at the wall are decomposed into two contributions: one coherent, caused by the stagnation of slipping flow hitting solid posts, and one time-dependent, caused by overlying turbulence. The results show that the larger texture size intensifies the contribution of stagnation pressure, while the contribution from turbulence is essentially insensitive to L + . The two-dimensional stagnation pressure distribution at the wall and the pressure statistics in the wall-normal direction are found to be self-similar for different L + . The scaling of the induced pressure and the consequent deformations of the air-water interface are analysed. Based on our results, an upper bound on the texture wavelength is quantified that limits the range of robust operation of superhydrophobic surfaces when exposed to high-speed flows. Our results indicate that when the system parameters are expressed in terms of viscous units, the main † Email address for correspondence: alimani@stanford.edu Turbulent pressures over superhydrophobic surfaces 449 parameters controlling the problem are L + and a Weber number based on inner dimensions; We obtain good collapse when all our results are expressed in wall units, independently of the Reynolds number.