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

Published online by Cambridge University Press:  18 December 2019

A. E. Tejada-Martínez Open the ORCID record for A. E. Tejada-Martínez [Opens in a new window] ,
A. Hafsi ,
C. Akan ,
M. Juha  and
F. Veron Open the ORCID record for F. Veron [Opens in a new window]
A. E. Tejada-Martínez*
Affiliation:
Civil and Environmental Engineering, University of South Florida, Tampa, FL 33620, USA
A. Hafsi
Affiliation:
Civil and Environmental Engineering, University of South Florida, Tampa, FL 33620, USA
C. Akan
Affiliation:
College of Computing, Engineering and Construction, University of North Florida, Jacksonville, FL 32224, USA
M. Juha
Affiliation:
Programa de Ingeniería Mecánica, Universidad de La Sabana, Chía 140013, Cundinamarca, Colombia
F. Veron
Affiliation:
College of Earth, Ocean and Environment, University of Delaware, Newark, DE 19762, USA
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Geophysical and Geological Flows: Air/sea interactions Mixing: Turbulent mixing Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 885 , 25 February 2020 , A5
Copyright
© 2019 Cambridge University Press

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References

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, 1–16.CrossRefGoogle Scholar
Craik, A. D. D. & Leibovich, S. 1976 A rational model for Langmuir circulations. J. Fluid Mech. 73, 401–426.CrossRefGoogle Scholar
D’Asaro, E. A. 2001 Turbulent vertical kinetic energy in the ocean mixed layer. J. Phys. Oceanogr. 31, 3530–3537.2.0.CO;2>CrossRefGoogle Scholar
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, 1691–1708.CrossRefGoogle Scholar
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, 44–67.CrossRefGoogle Scholar
Gargett, A. E. & Wells, J. R. 2007 Langmuir turbulence in shallow water. Part 1. Observations. J. Fluid Mech. 576, 27–61.CrossRefGoogle Scholar
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, 558–587.CrossRefGoogle Scholar
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, 40–56.Google Scholar
Holm, D. D. 1996 The ideal Craik–Leibovich equations. Physica D 98, 415–441.Google Scholar
Kenney, B. C. 1993 Observations of coherent bands of algae in a surface shear layer. Limnol. Oceanogr. 38, 1059–1067.CrossRefGoogle Scholar
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, 1–20.Google Scholar
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, 646–687.CrossRefGoogle Scholar
Langmuir, I. 1938 Surface motion of water induced by wind. Science 87, 119–123.CrossRefGoogle ScholarPubMed
Leibovich, S. 1983 The form and dynamics of Langmuir circulations. Annu. Rev. Fluid Mech. 15, 391–427.CrossRefGoogle Scholar
Li, M. & Garrett, C. 1993 Cell merging and the jet/downwelling ratio in Langmuir circulation. J. Mar. Res. 51, 737–769.CrossRefGoogle Scholar
McWilliams, J. C., Sullivan, P. P. & Moeng, C.-H. 1997 Langmuir turbulence in the ocean. J. Fluid Mech. 334, 1–30.CrossRefGoogle Scholar
Melville, W. K., Shear, R. & Veron, F. 1988 Laboratory measurements of the generation and evolution of Langmuir circulations. J. Fluid Mech. 364, 31–58.CrossRefGoogle Scholar
Phillips, O. M. 1977 The Dynamics of the Upper Ocean. Cambridge University Press.Google Scholar
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, 493–503.CrossRefGoogle Scholar
Smith, C. R. & Metzler, S. P. 1983 The characteristics of low speed streaks in the near-wall region. J. Fluid Mech. 129, 27–54.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Tejada-Martínez, A. E. & Grosch, C. E. 2007 Langmuir turbulence in shallow water. Part 2. Large-eddy simulation. J. Fluid Mech. 576, 63–108.CrossRefGoogle Scholar
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, 115–142.CrossRefGoogle Scholar
Texeira, M. A. C. & Belcher, S. E. 2002 On the distortion of turbulence by a progressive wave. J. Fluid Mech. 458, 229–267.CrossRefGoogle Scholar
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, 1715–1735.CrossRefGoogle Scholar
Veron, F. & Melville, W. K. 2001 Experiments on the stability and transition of wind-driven water surfaces. J. Fluid Mech. 446, 22–65.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar