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Large-eddy simulation of small-scale Langmuir circulation and scalar transport

  • A. E. Tejada-Martínez (a1), A. Hafsi (a1), C. Akan (a2), M. Juha (a3) and F. Veron (a4)...

Abstract

Large-eddy simulation (LES) of a wind- and wave-forced water column based on the Craik–Leibovich (C–L) vortex force is used to understand the structure of small-scale Langmuir circulation (LC) and associated Langmuir turbulence. The LES also serves to understand the role of the turbulence in determining molecular diffusive scalar flux from a scalar-saturated air side to the water side and the turbulent vertical scalar flux in the water side. Previous laboratory experiments have revealed that small-scale LC beneath an initially quiescent air–water interface appears shortly after the initiation of wind-driven gravity–capillary waves and provides the laminar–turbulent transition in wind speeds between 3 and $6~\text{m}~\text{s}^{-1}$ . The LES reveals Langmuir turbulence characterized by multiple scales ranging from small bursting eddies at the surface that coalesce to give rise to larger (centimetre-scale) LC over time. It is observed that the smaller scales account for the bulk of the near-surface turbulent vertical scalar flux. Although the contribution of the larger (centimetre-scale) LC to the near-surface turbulent flux increases over time as these scales emerge and become more coherent, the contribution of the smaller scales remains dominant. The growing LC scales lead to increased vertical scalar transport at depths below the interface and thus greater scalar transfer efficiency. Simulations were performed with a fixed wind stress corresponding to a $5~\text{m}~\text{s}^{-1}$ wind speed but with different wave parameters (wavelength and amplitude) in the C–L vortex force. It is observed that longer wavelengths lead to more coherent, larger centimetre-scale LC providing greater contribution to the turbulent vertical scalar flux away from the surface. In all cases, the molecular diffusive scalar flux at the water surface relaxes to the same statistically steady value after transition to Langmuir turbulence occurs, despite the different wave parameters in the C–L vortex force across the simulations. This implies that the small-scale turbulence intensity and the molecular diffusive scalar flux at the surface scale with the wind shear and not with the wave parameters. Furthermore, it is seen that the Langmuir (wave) forcing (provided by the C–L vortex force) is necessary to trigger the turbulence that induces elevated molecular diffusive scalar flux at the water surface relative to wind-driven flow without wave forcing.

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Corresponding author

Email address for correspondence: aetejada@usf.edu

References

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Akan, C., Tejada-Martínez, A. E., Grosch, C. E. & Martinat, G. 2013 Scalar transport in large-eddy simulation of Langmuir turbulence in shallow water. Cont. Shelf Res. 55, 116.
Craik, A. D. D. & Leibovich, S. 1976 A rational model for Langmuir circulations. J. Fluid Mech. 73, 401426.
D’Asaro, E. A. 2001 Turbulent vertical kinetic energy in the ocean mixed layer. J. Phys. Oceanogr. 31, 35303537.
Fujiwara, Y., Yoshikawa, Y. Y. & Matsumara, Y. 2018 A wave-resolving simulation of Langmuir circulations with a nonhydrostatic free-surface model: comparison with Craik–Leibovich theory and an alternative Eulerian view of the driving mechanism. J. Phys. Oceanogr. 48, 16911708.
Gargett, A. E. & Grosch, C. E. 2015 Turbulence process domination under the combined forcings of wind stress, the Langmuir vortex force, and surface cooling. J. Phys. Oceanogr. 44, 4467.
Gargett, A. E. & Wells, J. R. 2007 Langmuir turbulence in shallow water. Part 1. Observations. J. Fluid Mech. 576, 2761.
Guo, X. & Shen, L. 2013 Numerical study of the effect of surface waves on turbulence underneath. Part 1. Mean flow and turbulence vorticity. J. Fluid Mech. 733, 558587.
Hafsi, A., Tejada-Martínez, A. E. & Veron, F. 2017 DNS and measurements of scalar transfer across an air–water interface during inception and growth of Langmuir circulation. Comput. Fluids 58, 4056.
Holm, D. D. 1996 The ideal Craik–Leibovich equations. Physica D 98, 415441.
Kenney, B. C. 1993 Observations of coherent bands of algae in a surface shear layer. Limnol. Oceanogr. 38, 10591067.
Komori, S., Kurose, R., Iwano, K., Ukai, T. & Suzuki, N. 2010 Direct numerical simulation of wind-driven turbulence and scalar transfer at sheared gas–liquid interfaces. J. Turbul. 11, 120.
Kurose, R., Takagaki, N., Kimura, A. & Komori, S. 2016 Direct numerical simulation of turbulent heat transfer across a sheared wind-driven gas–liquid interface. J. Fluid Mech. 804, 646687.
Langmuir, I. 1938 Surface motion of water induced by wind. Science 87, 119123.
Leibovich, S. 1983 The form and dynamics of Langmuir circulations. Annu. Rev. Fluid Mech. 15, 391427.
Li, M. & Garrett, C. 1993 Cell merging and the jet/downwelling ratio in Langmuir circulation. J. Mar. Res. 51, 737769.
McWilliams, J. C., Sullivan, P. P. & Moeng, C.-H. 1997 Langmuir turbulence in the ocean. J. Fluid Mech. 334, 130.
Melville, W. K., Shear, R. & Veron, F. 1988 Laboratory measurements of the generation and evolution of Langmuir circulations. J. Fluid Mech. 364, 3158.
Phillips, O. M. 1977 The Dynamics of the Upper Ocean. Cambridge University Press.
Scott, J. T., Meyer, G. E., Stewart, R. & Walther, E. G. 1969 On the mechanism of Langmuir circulations and their role in epilimnion mixing. Limnol. Oceanogr. 14, 493503.
Smith, C. R. & Metzler, S. P. 1983 The characteristics of low speed streaks in the near-wall region. J. Fluid Mech. 129, 2754.
Takagaki, N., Kurose, R., Tsujimoto, Y., Komori, S. & Takahashi, K. 2015 Effects of turbulent eddies and Langmuir circulations on scalar transfer in a sheared wind-driven liquid flow. Phys. Fluids 27, 016603.
Tejada-Martínez, A. E. & Grosch, C. E. 2007 Langmuir turbulence in shallow water. Part 2. Large-eddy simulation. J. Fluid Mech. 576, 63108.
Tejada-Martínez, A. E., Grosch, C. E., Gargett, A. E., Polton, J. A., Smith, J. A. & MacKinnon, J. A. 2009 A hybrid spectral/finite-difference large-eddy simulator of turbulent processes in the upper ocean. Ocean Model. 30, 115142.
Texeira, M. A. C. & Belcher, S. E. 2002 On the distortion of turbulence by a progressive wave. J. Fluid Mech. 458, 229267.
Tsai, W.-T., Chen, S.-M., Lu, G.-H. & Garbe, C. S. 2013 Characteristics of interfacial signatures on a wind-driven gravity-capillary wave. J. Geophys. Res. 118, 17151735.
Veron, F. & Melville, W. K. 2001 Experiments on the stability and transition of wind-driven water surfaces. J. Fluid Mech. 446, 2265.
Zappa, C. J., McGillis, W. R., Raymond, P. A., Edson, J. B., Hintsa, E. J., Zemmelink, H. J., Dacey, J. W. H. & Ho, D. T. 2007 Environmental turbulent mixing controls on air–water gas exchange in marine and aquatic systems. Geophys. Res. Lett. 34, L10601.
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Large-eddy simulation of small-scale Langmuir circulation and scalar transport

  • A. E. Tejada-Martínez (a1), A. Hafsi (a1), C. Akan (a2), M. Juha (a3) and F. Veron (a4)...

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