Direct numerical simulation of turbulence over two-dimensional waves

Knowledge of turbulent flows over non-flat surfaces is of major practical interest in diverse applications. Significant work continues to be reported in the roughness regime at high Reynolds numbers where the cumulative effect of surface undulations on the averaged and integrated turbulence quantities is well documented. Even for such cases, the surface topology plays an important role for transitional roughness Reynolds numbers that is hard to characterize. In this work, we explore in detail the mechanisms underlying turbulence generation and transport, particularly within the region of the turbulent boundary layer affected by the surface. We relate surface shape with turbulence generation mechanisms and Reynolds stress transport, which has implications to drag increase. We accomplish this using a suite of direct numerical simulations of fully developed turbulent flow between two infinitely wide, two-dimensional sinusoidally wavy surfaces at a friction Reynolds number, Reτ = 180, with different mean surface slopes, ζ (and fixed inner-scaled undulation height, a+ = 13), corresponding to the “waviness” regime. The increase in wave slope enhances near surface turbulent mixing, resulting in increased total drag, higher fraction of form drag, faster approach to isotropy, and thereby modulation of the buffer layer. The primary near-surface streamwise and vertical turbulence production occurs in the leeward and windward sides of the wave, respectively. Furthermore, this production structure shows significant dispersion effects. However, the primary generation process of vertical and spanwise variance occurs through pressure–strain rate mechanism in the windward side.