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.