Direct-simulation-based study of turbulent flow over various waving boundaries

Di Yang, Lian Shen

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112 Scopus citations


We use direct numerical simulation of stress-driven turbulent Couette flows over waving surfaces to study turbulence in the vicinity of water waves. Mechanistic study is performed through systematic investigation of different wavy surface conditions including plane progressive Airy and Stokes waves with and without wind-induced surface drift, as well as stationary wavy walls and vertically waving walls for comparison. Two different wave steepness values ak = 0.1 and 0.25 are considered, where a is the wave amplitude and k is the wavenumber. For effects of wave age, defined as the ratio between the wave phase speed c and the turbulence friction velocity u*, we consider three values, namely c/u* = 2, 14 and 25, corresponding to slow, intermediate and fast waves, respectively. Detailed analysis of turbulence structure and statistics shows their dependence on the above-mentioned parameters. Our result agrees with previous measurement and simulation results and reveals many new features unreported in the literature. Over progressive waves, although no apparent flow separation is found in mean flow, considerable intermittent separations in instantaneous flow are detected in slow waves with large steepness. The near-surface coherent vortical structures are examined. We propose two conceptual vortex structure models: quasi-streamwise and reversed horseshoe vortices for slow waves and bent quasi-streamwise vortices for intermediate and fast waves. Detailed examination of Reynolds stress with quadrant analysis, turbulent kinetic energy (TKE) and TKE budget with a focus on production shows large variation with wave phase; analysis shows that the variation is highly dependent on wave age and wave nonlinearity. Comparison between Airy waves and Stokes waves indicates that although the nonlinearity of surface water waves is a high-order effect compared with the wave age and wave steepness, it still makes an appreciable difference to the turbulence structure. The effect of wave nonlinearity on surface pressure distribution causes substantial difference in the wave growth rate. Wind-induced surface drift can cause a phase shift in the downstream direction and a reduction in turbulence intensity; this effect is appreciable for slow waves but negligible for intermediate and fast waves. In addition to providing detailed information on the turbulence field in the vicinity of wave surfaces, the results obtained in this study suggest the importance of including wave dynamics in the study of wind-wave interaction.

Original languageEnglish (US)
Pages (from-to)131-180
Number of pages50
JournalJournal of Fluid Mechanics
StatePublished - May 10 2010

Bibliographical note

Funding Information:
This research is supported by the Office of Naval Research. The Young Investigator award to LS is gratefully acknowledged. We would like to thank the referees for their valuable comments that provided us significant help to improve the previous version of this paper.


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