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Numerical study of effect of wave phase on Reynolds stresses and turbulent kinetic energy in Langmuir turbulence

Published online by Cambridge University Press:  07 October 2020

Anqing Xuan Open the ORCID record for Anqing Xuan [Opens in a new window] ,
Bing-Qing Deng Open the ORCID record for Bing-Qing Deng [Opens in a new window]  and
Lian Shen Open the ORCID record for Lian Shen [Opens in a new window]
Anqing Xuan
Affiliation:
Department of Mechanical Engineering and Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN55455, USA
Bing-Qing Deng
Affiliation:
Department of Mechanical Engineering and Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN55455, USA
Lian Shen*
Affiliation:
Department of Mechanical Engineering and Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN55455, USA
*
†Email address for correspondence: [email protected]
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Abstract

The dynamics of Reynolds stresses and turbulent kinetic energy (TKE) in Langmuir turbulence are analysed using data of large-eddy simulations with the wave phase resolved. It is found that the streamwise and spanwise Reynolds normal stresses and the Reynolds shear stress vary appreciably with the wave phase, while the vertical normal stress is only weakly dependent on the wave phase. Budget analyses indicate that the production due to wave straining and the effects associated with turbulence pressure are the dominant mechanisms for the wave-phase variation of Reynolds stresses. The accumulative effect of wave–turbulence interactions on TKE is then investigated using the Lagrangian average. It is discovered that the energy transfer from wave to turbulence is contributed by two mechanisms. The first mechanism is the turbulence production by the Lagrangian mean wave shearing and the mean shear stress, which is consistent with the traditional wave-phase-averaged model. The second mechanism, which is not accounted for in previous studies, is the correlation between the wave-phase variation of the Reynolds shear stress and the wave orbital shearing. A model is proposed for the second mechanism. Comparison of the frequency spectrum with Craik–Leibovich simulation results shows that the correlation effect can affect the turbulence fluctuations at time scales around the wave period, indicating the importance of this effect on Reynolds stresses and TKE.

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 904 , 10 December 2020 , A17
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Andrews, D. G. & Mcintyre, M. E. 1978 An exact theory of nonlinear waves on a Lagrangian-mean flow. J. Fluid Mech. 89 (4), 609–646.CrossRefGoogle Scholar
Ardhuin, F. & Jenkins, A. D. 2006 On the interaction of surface waves and upper ocean turbulence. J. Phys. Oceanogr. 36 (3), 551–557.CrossRefGoogle Scholar
Belcher, S. E., Grant, A. L. M., Hanley, K. E., Fox-Kemper, B., Van Roekel, L., Sullivan, P. P., Large, W. G., Brown, A., Hines, A., Calvert, D., et al. 2012 A global perspective on Langmuir turbulence in the ocean surface boundary layer. Geophys. Res. Lett. 39 (18), L18605.CrossRefGoogle Scholar
Bou-Zeid, E., Meneveau, C. & Parlange, M. 2005 A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys. Fluids 17 (2), 025105.CrossRefGoogle Scholar
Chapman, D. R. 1979 Computational aerodynamics development and outlook. AIAA J. 17 (12), 1293–1313.CrossRefGoogle Scholar
Chen, B., Yang, D., Meneveau, C. & Chamecki, M. 2016 Effects of swell on transport and dispersion of oil plumes within the ocean mixed layer. J. Geophys. Res. 121 (5), 3564–3578.CrossRefGoogle Scholar
Choi, H. & Moin, P. 2012 Grid-point requirements for large eddy simulation: Chapman's estimates revisited. Phys. Fluids 24 (1), 011702.CrossRefGoogle Scholar
Craik, A. D. D. 1977 The generation of Langmuir circulations by an instability mechanism. J. Fluid Mech. 81 (2), 209–223.CrossRefGoogle Scholar
Craik, A. D. D. & Leibovich, S. 1976 A rational model for Langmuir circulations. J. Fluid Mech. 73 (3), 401–426.CrossRefGoogle Scholar
D'Asaro, E. A. 2001 Turbulent vertical kinetic energy in the ocean mixed layer. J. Phys. Oceanogr. 31 (12), 3530–3537.2.0.CO;2>CrossRefGoogle Scholar
D'Asaro, E. A. 2014 Turbulence in the upper-ocean mixed layer. Annu. Rev. Mater. Sci. 6, 101–115.CrossRefGoogle ScholarPubMed
Deng, B.-Q., Yang, Z., Xuan, A. & Shen, L. 2019 Influence of Langmuir circulations on turbulence in the bottom boundary layer of shallow water. J. Fluid Mech. 861, 275–308.CrossRefGoogle Scholar
Fan, Y. & Griffies, S. M. 2014 Impacts of parameterized Langmuir turbulence and nonbreaking wave mixing in global climate simulations. J. Clim. 27 (12), 4752–4775.CrossRefGoogle Scholar
Fujiwara, Y., Yoshikawa, Y. & Matsumura, 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 (8), 1691–1708.CrossRefGoogle Scholar
Grant, A. L. M. & Belcher, S. E. 2009 Characteristics of Langmuir turbulence in the ocean mixed layer. J. Phys. Oceanogr. 39 (8), 1871–1887.CrossRefGoogle Scholar
Guo, X. & Shen, L. 2010 Interaction of a deformable free surface with statistically steady homogeneous turbulence. J. Fluid Mech. 658, 33–62.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
Guo, X. & Shen, L. 2014 Numerical study of the effect of surface wave on turbulence underneath. Part 2. Eulerian and Lagrangian properties of turbulence kinetic energy. J. Fluid Mech. 744, 250–272.CrossRefGoogle Scholar
Harcourt, R. R. 2013 A second-moment closure model of Langmuir turbulence. J. Phys. Oceanogr. 43 (4), 673–697.CrossRefGoogle Scholar
Harcourt, R. R. & D'Asaro, E. A. 2008 Large-eddy simulation of Langmuir turbulence in pure wind seas. J. Phys. Oceanogr. 38 (7), 1542–1562.CrossRefGoogle Scholar
Holm, D. D. 1996 The ideal Craik–Leibovich equations. Physica D 98 (2–4), 415–441.CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2008 Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids 20 (10), 101511.CrossRefGoogle Scholar
Jiang, J.-Y. & Street, R. L. 1991 Modulated flows beneath wind-ruffled, mechanically generated water waves. J. Geophys. Res. 96 (C2), 2711–2721.CrossRefGoogle Scholar
Jiang, J.-Y., Street, R. L. & Klotz, S. P. 1990 A study of wave–turbulence interaction by use of a nonlinear water wave decomposition technique. J. Geophys. Res. 95 (C9), 16037–16054.CrossRefGoogle Scholar
Kawamura, T. 2000 Numerical investigation of turbulence near a sheared air–water interface. Part 2: Interaction of turbulent shear flow with surface waves. J. Mar. Sci. Technol. 5 (4), 161–175.CrossRefGoogle Scholar
Kitaigorodskii, S. A., Donelan, M. A., Lumley, J. L. & Terray, E. A. 1983 Wave–turbulence interactions in the upper ocean. Part II. Statistical characteristics of wave and turbulent components of the random velocity field in the marine surface layer. J. Phys. Oceanogr. 13 (11), 1988–1999.2.0.CO;2>CrossRefGoogle Scholar
Kukulka, T., Plueddemann, A. J., Trowbridge, J. H. & Sullivan, P. P. 2009 Significance of Langmuir circulation in upper ocean mixing: comparison of observations and simulations. Geophys. Res. Lett. 36 (10), L10603.CrossRefGoogle Scholar
Leibovich, S. 1977 Convective instability of stably stratified water in the ocean. J. Fluid Mech. 82 (3), 561–581.CrossRefGoogle Scholar
Leibovich, S. 1980 On wave–current interaction theories of Langmuir circulations. J. Fluid Mech. 99 (4), 715–724.CrossRefGoogle Scholar
Lewis, D. M. 2005 A simple model of plankton population dynamics coupled with a LES of the surface mixed layer. J. Theor. Biol. 234 (4), 565–591.CrossRefGoogle ScholarPubMed
Li, M. 2000 Estimating horizontal dispersion of floating particles in wind-driven upper ocean. Spill Sci. Technol. B 6 (3–4), 255–261.CrossRefGoogle Scholar
Li, M., Garrett, C. & Skyllingstad, E. 2005 A regime diagram for classifying turbulent large eddies in the upper ocean. Deep-Sea Res. I 52 (2), 259–278.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1953 Mass transport in water waves. Phil. Trans. R. Soc. Lond. A 245 (903), 535–581.Google Scholar
Longuet-Higgins, M. S. 1986 Eulerian and Lagrangian aspects of surface waves. J. Fluid Mech. 173, 683–707.CrossRefGoogle Scholar
Lumley, J. L. 1975 Pressure–strain correlation. Phys. Fluids 18 (6), 750–750.CrossRefGoogle Scholar
Lumley, J. L. & Terray, E. A. 1983 Kinematics of turbulence convected by a random wave field. J. Phys. Oceanogr. 13 (11), 2000–2007.2.0.CO;2>CrossRefGoogle Scholar
Magnaudet, J. & Thais, L. 1995 Orbital rotational motion and turbulence below laboratory wind water waves. J. Geophys. Res. 100 (C1), 757–771.CrossRefGoogle Scholar
McWilliams, J. C. & Sullivan, P. P. 2000 Vertical mixing by Langmuir circulations. Spill Sci. Technol. B 6 (3–4), 225–237.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
Meneveau, C., Lund, T. S. & Cabot, W. H. 1996 A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319, 353–385.CrossRefGoogle Scholar
Noh, Y., Kang, I. S., Herold, M. & Raasch, S. 2006 Large eddy simulation of particle settling in the ocean mixed layer. Phys. Fluids 18 (8), 085109.CrossRefGoogle Scholar
Pearson, B. C., Grant, A. L. M. & Polton, J. A. 2019 Pressure–strain terms in Langmuir turbulence. J. Fluid Mech. 880, 5–31.CrossRefGoogle Scholar
Phillips, O. M. 1977 The Dynamics of the Upper Ocean, 2nd edn. Cambridge University Press.Google Scholar
Polton, J. A. & Belcher, S. E. 2007 Langmuir turbulence and deeply penetrating jets in an unstratified mixed layer. J. Geophys. Res. 112 (C9), C09020.CrossRefGoogle Scholar
Porté-Agel, F., Meneveau, C. & Parlange, M. B. 2000 A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer. J. Fluid Mech. 415, 261–284.CrossRefGoogle Scholar
Rabe, T. J., Kukulka, T., Ginis, I., Hara, T., Reichl, B. G., D'Asaro, E. A., Harcourt, R. R. & Sullivan, P. P. 2014 Langmuir turbulence under Hurricane Gustav (2008). J. Phys. Oceanogr. 45 (3), 657–677.CrossRefGoogle Scholar
Rashidi, M., Hetsroni, G. & Banerjee, S. 1992 Wave–turbulence interaction in free-surface channel flows. Phys. Fluids A 4 (12), 2727–2738.CrossRefGoogle Scholar
Rye, H. 2000 Probable effects of Langmuir circulation observed on oil slicks in the field. Spill Sci. Technol. B 6 (3–4), 263–271.CrossRefGoogle Scholar
Shen, L., Zhang, X., Yue, D. K. P. & Triantafyllou, G. S. 1999 The surface layer for free-surface turbulent flows. J. Fluid Mech. 386, 167–212.CrossRefGoogle Scholar
Shrestha, K., Anderson, W., Tejada-Martínez, A. & Kuehl, J. 2019 Orientation of coastal-zone Langmuir cells forced by wind, wave and mean current at variable obliquity. J. Fluid Mech. 879, 716–743.CrossRefGoogle Scholar
Skyllingstad, E. D. & Denbo, D. W. 1995 An ocean large-eddy simulation of Langmuir circulations and convection in the surface mixed layer. J. Geophys. Res. 100 (C5), 8501–8522.CrossRefGoogle Scholar
Speziale, C. G., Sarkar, S. & Gatski, T. B. 1991 Modelling the pressure–strain correlation of turbulence: an invariant dynamical systems approach. J. Fluid Mech. 227, 245–272.CrossRefGoogle Scholar
Sullivan, P. P. & McWilliams, J. C. 2010 Dynamics of winds and currents coupled to surface waves. Annu. Rev. Fluid Mech. 42, 19–42.CrossRefGoogle Scholar
Sullivan, P. P. & McWilliams, J. C. 2019 Langmuir turbulence and filament frontogenesis in the oceanic surface boundary layer. J. Fluid Mech. 879, 512–553.CrossRefGoogle Scholar
Teixeira, M. A. C. & Belcher, S. E. 2002 On the distortion of turbulence by a progressive surface wave. J. Fluid Mech. 458, 229–267.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
Thais, L. & Magnaudet, J. 1996 Turbulent structure beneath surface gravity waves sheared by the wind. J. Fluid Mech. 328, 313–344.CrossRefGoogle Scholar
Thorpe, S. A. 2004 Langmuir circulation. Annu. Rev. Fluid Mech. 36, 55–79.CrossRefGoogle Scholar
Thorpe, S. A., Osborn, T. R., Farmer, D. M. & Vagle, S. 2003 Bubble clouds and Langmuir circulation: observations and models. J. Phys. Oceanogr. 33 (9), 2013–2031.2.0.CO;2>CrossRefGoogle Scholar
Townsend, A. A. 1998 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Van Roekel, L. P., Fox-Kemper, B., Sullivan, P. P., Hamlington, P. E. & Haney, S. R. 2012 The form and orientation of Langmuir cells for misaligned winds and waves. J. Geophys. Res. 117, C05001.CrossRefGoogle Scholar
Veron, F., Melville, W. K. & Lenain, L. 2009 Measurements of ocean surface turbulence and wave–turbulence interactions. J. Phys. Oceanogr. 39 (9), 2310–2323.CrossRefGoogle Scholar
Wang, P. & Özgökmen, T. M. 2018 Langmuir circulation with explicit surface waves from moving-mesh modeling. Geophys. Res. Lett. 45 (1), 216–226.CrossRefGoogle Scholar
Xuan, A., Deng, B.-Q. & Shen, L. 2019 Study of wave effect on vorticity in Langmuir turbulence using wave-phase-resolved large-eddy simulation. J. Fluid Mech. 875, 173–224.CrossRefGoogle Scholar
Xuan, A. & Shen, L. 2019 A conservative scheme for simulation of free-surface turbulent and wave flows. J. Comput. Phys. 378, 18–43.CrossRefGoogle Scholar
Yang, D., Chamecki, M. & Meneveau, C. 2014 Inhibition of oil plume dilution in Langmuir ocean circulation. Geophys. Res. Lett. 41 (5), 1632–1638.CrossRefGoogle Scholar
Zhou, H. 1999 Numerical simulation of Langmuir circulations in a wavy domain and its comparison with the Craik–Leibovich theory. PhD thesis, Stanford University.Google Scholar