Turbulent skin-friction reduction by wavy surfaces

Direct numerical simulations of fully-developed turbulent channel flows with wavy walls are undertaken. The wavy walls, skewed with respect to the mean flow direction, are introduced as a means of emulating a Spatial Stokes Layer (SSL) induced by in-plane wall motion. The transverse shear strain above the wavy wall is shown to be similar to that of a SSL, thereby affecting the turbulent flow, and leading to a reduction in the turbulent skin-friction drag. The pressure- and friction-drag levels are carefully quantified for various flow configurations, exhibiting a combined maximum overall-drag reduction of about 0.5%. The friction-drag reduction is shown to behave approximately quadratically for small wave slopes and then linearly for higher slopes, whilst the pressure-drag penalty increases quadratically. Unlike in the SSL case, there is a region of increased turbulence production over a portion of the wall, above the leeward side of the wave, thus giving rise to a local increase in dissipation. The transverse shear-strain layer is shown to be approximately Reynolds-number independent when the wave geometry is scaled in wall units.