Slope Dependent Turbulence over Two-dimensional Wavy Surfaces

Abstract: 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 attempt to develop a bottom up understanding of the mechanisms underlying turbulence generation and transport, particularly within the region of the turbulent boundary layer (TBL) affected by the surface. We relate surface characteristics with turbulence generation mechanisms, Reynolds stress transport and the resulting drag increase. To this end, we perform 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, $Re_{\tau}=180$, with different mean surface slopes, $\zeta$ (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 generation occurs in the leeward and windward side of the wave. In contrast, the spanwise variance is produced through pressure-rate-of-strain mechanism, primarily, along the windward side of the wave for flows with very little flow separation. We also observe significant dispersion effects in the production structure.