Direct numerical simulation of scalar transport in turbulent flows over progressive surface waves

The transport of passive scalars in turbulent flows over progressive water waves is studied using direct numerical simulation. A combined pseudo-spectral and finite-difference scheme on a wave-surface-fitted grid is used to simulate the flow and scalar fields above the wave surface. Three representative wave ages (i.e. wave-to-wind speed ratios) are considered, corresponding to slow, intermediate and fast wind-waves, respectively. For each wave condition, four Schmidt numbers are considered for the scalar transport. The presence of progressive surface waves is found to induce significant wave-phase-correlated variation to the scalar field, with the phase dependence varying with the wave age. The time- and plane-averaged profiles of the scalar over waves of various ages exhibit similar vertical structures as those found in turbulence over a flat wall, but with the von Kármán constant and effective wave surface roughness for the mean scalar profile exhibiting considerable variation with the wave age. The profiles of the root-mean-square scalar fluctuations and the horizontal scalar flux exhibit good scaling in the viscous sublayer that agrees with the scaling laws previously reported for flat-wall turbulence, but with noticeable wave-induced variation in the viscous wall region. The profiles of the vertical scalar flux in the viscous sublayer exhibit apparent discrepancies from the reported scaling law for flat-wall turbulence, due to a negative vertical flux region above the windward face of the wave crest. Direct observation and quadrant-based conditional averages indicate that the wave-dependent distributions of the scalar fluctuations and fluxes are highly correlated with the coherent vortical structures in the turbulence, which exhibit clear wave-dependent characteristics in terms of both shape and preferential location.