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

Di Yang, Lian Shen

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27 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)58-103
Number of pages46
JournalJournal of Fluid Mechanics
StatePublished - May 25 2017

Bibliographical note

Publisher Copyright:
© 2017 Cambridge University Press.


  • Key words turbulent boundary layers
  • turbulence simulation
  • wind-wave interactions


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