Enhanced drag-reduction over superhydrophobic surfaces with sinusoidal textures: A DNS study

•Flow over superhydrophobic sinusoidal textures induce secondary-flow leading to SSL.•Vortex stretching alters secondary vortices effecting skin-frictional drag levels.•Cross-stream fluctuations are damped for sinusoidal SHS compared to straight ridges.•Near-wall streaks are skewed in the spanwise direction by Stokes transverse strain. Direct Numerical Simulation (DNS) studies of a fully developed turbulent channel flow are performed with sinusoidal surface texture to assess its ability to enhance turbulent skin-frictional drag reductions over superhydrophobic surfaces (SHS). The streamwise sinusoidal microgroove structure generates asymmetric secondary flows to induce an in-plane stationary distribution of spanwise velocity that oscillates in the streamwise direction. The transverse motions over a sinusoidal texture behave analogously to an existing drag-reduction technique by spanwise wall oscillations. The friction-drag levels and slip-lengths are precisely quantified for various streamwise wavelength configurations, and an optimum wavelength for the maximum reduction in turbulent drag is determined. The response of the near-wall turbulent structures to the sinusoidal microgrooves is also analysed. The transverse Stokes strain generates spanwise tilting in the near-wall streaks for large wavelengths, inducing an apparent drop in the wall-normal ejections and sweeps, thereby reducing the turbulent contribution to the wall-shear-stress. The transverse shear strain above the sinusoidal microgroove is demonstrated to be resembling a Stokes spatial layer (SSL), by comparing with existing analytical solutions of strain profiles for wall-forcing by spanwise spatial oscillations.