Direct numerical simulation is used to study the turbulent flow over a smooth wavy
wall undergoing transverse motion in the form of a streamwise travelling wave. The
Reynolds number based on the mean velocity U of the external flow and wall motion
wavelength λ is 10 170; the wave steepness is 2πa/λ = 0.25 where a is the travelling
wave amplitude. A key parameter for this problem is the ratio of the wall motion
phase speed c to U, and results are obtained for c/U in the range of â1.0 to 2.0 at
0.2 intervals. For negative c/U, we find that flow separation is enhanced and a large
drag force is produced. For positive c/U, the results show that as c/U increases from
zero, the separation bubble moves further upstream and away from the wall, and is
reduced in strength. Above a threshold value of c/U ≈ 1, separation is eliminated;
and, relative to small- c/U cases, turbulence intensity and turbulent shear stress are
reduced significantly. The drag force decreases monotonically as c/U increases while the power required for the transverse motion generally increases for large c/U; the
net power input is found to reach a minimum at c/U ≈ 1.2 (for fixed U). The results
obtained in this study provide physical insight into the study of fish-like swimming
mechanisms in terms of drag reduction and optimal propulsive efficiency
