• Abkar, M., H. J. Bae, and P. Moin, 2016: Minimum-dissipation scalar transport model for large-eddy simulation of turbulent flows. Phys. Rev. Fluids, 1, 041701, https://doi.org/10.1103/PhysRevFluids.1.041701.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Andrews, D. G., and M. McIntyre, 1978: An exact theory of nonlinear waves on a Lagrangian-mean flow. J. Fluid Mech., 89, 609646, https://doi.org/10.1017/S0022112078002773.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Besard, T., C. Foket, and B. De Sutter, 2018: Effective extensible programming: Unleashing Julia on GPUs. IEEE Trans. Parallel Distrib. Syst., 30, 827841, https://doi.org/10.1109/TPDS.2018.2872064.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bezanson, J., S. Karpinski, V. B. Shah, and A. Edelman, 2012: Julia: A fast dynamic language for technical computing. arXiv, 27 pp., https://arxiv.org/abs/1209.5145.

    • Search Google Scholar
    • Export Citation
  • Bühler, O., 2014: Waves and Mean Flows. 2nd ed. Cambridge University Press, 374 pp.

  • Craik, A. D., and S. Leibovich, 1976: A rational model for Langmuir circulations. J. Fluid Mech., 73, 401426, https://doi.org/10.1017/S0022112076001420.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • D’Asaro, E. A., J. Thomson, A. Shcherbina, R. Harcourt, M. Cronin, M. Hemer, and B. Fox-Kemper, 2014: Quantifying upper ocean turbulence driven by surface waves. Geophys. Res. Lett., 41, 102107, https://doi.org/10.1002/2013GL058193.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fan, Y., I. Ginis, and T. Hara, 2009: The effect of wind–wave–current interaction on air–sea momentum fluxes and ocean response in tropical cyclones. J. Phys. Oceanogr., 39, 10191034, https://doi.org/10.1175/2008JPO4066.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grare, L., W. L. Peirson, H. Branger, J. W. Walker, J.-P. Giovanangeli, and V. Makin, 2013: Growth and dissipation of wind-forced, deep-water waves. J. Fluid Mech., 722, 550, https://doi.org/10.1017/jfm.2013.88.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Harcourt, R. R., and E. A. D’Asaro, 2008: Large-eddy simulation of Langmuir turbulence in pure wind seas. J. Phys. Oceanogr., 38, 15421562, https://doi.org/10.1175/2007JPO3842.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hasselmann, K., 1970: Wave-driven inertial oscillations. Geophys. Astrophys. Fluid Dyn., 1, 463502, https://doi.org/10.1080/03091927009365783.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holm, D. D., 1996: The ideal Craik-Leibovich equations. Physica D, 98, 415441, https://doi.org/10.1016/0167-2789(96)00105-4.

  • Huang, N. E., 1979: On surface drift currents in the ocean. J. Fluid Mech., 91, 191208, https://doi.org/10.1017/S0022112079000112.

  • Kukulka, T., A. J. Plueddemann, J. H. Trowbridge, and P. P. Sullivan, 2010: Rapid mixed layer deepening by the combination of Langmuir and shear instabilities: A case study. J. Phys. Oceanogr., 40, 23812400, https://doi.org/10.1175/2010JPO4403.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Large, W. G., E. G. Patton, A. K. DuVivier, P. P. Sullivan, and L. Romero, 2019: Similarity theory in the surface layer of large-eddy simulations of the wind-, wave-, and buoyancy-forced southern ocean. J. Phys. Oceanogr., 49, 21652187, https://doi.org/10.1175/JPO-D-18-0066.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Leibovich, S., 1977: On the evolution of the system of wind drift currents and Langmuir circulations in the ocean. Part I. Theory and averaged current. J. Fluid Mech., 79, 715743, https://doi.org/10.1017/S002211207700041X.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Leibovich, S., 1980: On wave-current interaction theories of Langmuir circulations. J. Fluid Mech., 99, 715724, https://doi.org/10.1017/S0022112080000857.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Longuet-Higgins, M. S., 1953: Mass transport in water waves. Philos. Trans. Roy. Soc. London, 245A, 535581, https://doi.org/10.1098/rsta.1953.0006.

    • Search Google Scholar
    • Export Citation
  • Longuet-Higgins, M. S., 1969: A nonlinear mechanism for the generation of sea waves. Proc. Roy. Soc. London, 311A, 371389, https://doi.org/10.1098/rspa.1969.0123.

    • Search Google Scholar
    • Export Citation
  • Longuet-Higgins, M. S., 1986: Eulerian and Lagrangian aspects of surface waves. J. Fluid Mech., 173, 683707, https://doi.org/10.1017/S0022112086001325.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mcintyre, M., 1981: On the ‘wave momentum’ myth. J. Fluid Mech., 106, 331347, https://doi.org/10.1017/S0022112081001626.

  • McWilliams, J. C., P. P. Sullivan, and C.-H. Moeng, 1997: Langmuir turbulence in the ocean. J. Fluid Mech., 334, 130, https://doi.org/10.1017/S0022112096004375.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Melville, W. K., 1996: The role of surface-wave breaking in air-sea interaction. Annu. Rev. Fluid Mech., 28, 279321, https://doi.org/10.1146/annurev.fl.28.010196.001431.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Noh, Y., H. S. Min, and S. Raasch, 2004: Large-eddy simulation of the ocean mixed layer: The effects of wave breaking and Langmuir circulation. J. Phys. Oceanogr., 34, 720735, https://doi.org/10.1175/1520-0485(2004)034<0720:LESOTO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pearson, B., 2018: Turbulence-induced anti-Stokes flow and the resulting limitations of large-eddy simulation. J. Phys. Oceanogr., 48, 117122, https://doi.org/10.1175/JPO-D-17-0208.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Phillips, O., 1985: Spectral and statistical properties of the equilibrium range in wind-generated gravity waves. J. Fluid Mech., 156, 505531, https://doi.org/10.1017/S0022112085002221.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pollard, R. T., 1970: Surface waves with rotation: An exact solution. J. Geophys. Res., 75, 58955898, https://doi.org/10.1029/JC075i030p05895.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Polton, J. A., and S. E. Belcher, 2007: Langmuir turbulence and deeply penetrating jets in an unstratified mixed layer. J. Geophys. Res., 112, C09020, https://doi.org/10.1029/2007JC004205.

    • Search Google Scholar
    • Export Citation
  • Rozema, W., H. J. Bae, P. Moin, and R. Verstappen, 2015: Minimum-dissipation models for large-eddy simulation. Phys. Fluids, 27, 085107, https://doi.org/10.1063/1.4928700.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schumann, U., and R. A. Sweet, 1988: Fast Fourier transforms for direct solution of Poisson’s equation with staggered boundary conditions. J. Comput. Phys., 75, 123137, https://doi.org/10.1016/0021-9991(88)90102-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Seshasayanan, K., and B. Gallet, 2019: Surface gravity waves propagating in a rotating frame: The Ekman-Stokes instability. Phys. Rev. Fluids, 4, 104802, https://doi.org/10.1103/PhysRevFluids.4.104802.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Skyllingstad, E. D., and D. W. Denbo, 1995: An ocean large-eddy simulation of Langmuir circulations and convection in the surface mixed layer. J. Geophys. Res., 100, 85018522, https://doi.org/10.1029/94JC03202.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stokes, G. G., 1847: On the theory of oscillatory waves. Trans. Cambridge Philos. Soc., 8, 441455.

  • Sullivan, P. P., and J. C. McWilliams, 2010: Dynamics of winds and currents coupled to surface waves. Annu. Rev. Fluid Mech., 42, 1942, https://doi.org/10.1146/annurev-fluid-121108-145541.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sullivan, P. P., L. Romero, J. C. McWilliams, and W. K. Melville, 2012: Transient evolution of Langmuir turbulence in ocean boundary layers driven by hurricane winds and waves. J. Phys. Oceanogr., 42, 19591980, https://doi.org/10.1175/JPO-D-12-025.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Suzuki, N., and B. Fox-Kemper, 2016: Understanding Stokes forces in the wave-averaged equations. J. Geophys. Res. Oceans, 121, 35793596, https://doi.org/10.1002/2015JC011566.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ursell, F., and G. Deacon, 1950: On the theoretical form of ocean swell on a rotating earth. Geophys. J. Int., 6, 18, https://doi.org/10.1111/j.1365-246X.1950.tb02968.x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Verstappen, R., 2018: How much eddy dissipation is needed to counterbalance the nonlinear production of small, unresolved scales in a large-eddy simulation of turbulence? Comput. Fluids, 176, 276284, https://doi.org/10.1016/j.compfluid.2016.12.016.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vreugdenhil, C. A., and J. R. Taylor, 2018: Large-eddy simulations of stratified plane Couette flow using the anisotropic minimum-dissipation model. Phys. Fluids, 30, 085104, https://doi.org/10.1063/1.5037039.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wagner, G. L., 2016: On the coupled evolution of oceanic internal waves and quasi-geostrophic flow. Ph.D. thesis, University of California, San Diego, 216 pp.

  • Yang, D., B. Chen, M. Chamecki, and C. Meneveau, 2015: Oil plumes and dispersion in Langmuir, upper-ocean turbulence: Large-eddy simulations and K-profile parameterization. J. Geophys. Res. Oceans, 120, 47294759, https://doi.org/10.1002/2014JC010542.

    • Crossref
    • Search Google Scholar
    • Export Citation
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Near-Inertial Waves and Turbulence Driven by the Growth of Swell

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  • 1 Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts
  • | 2 Integrated Applied Mathematics and Mechanical Engineering, University of New Hampshire, Durham, New Hampshire
  • | 3 Service de Physique de l’Etat Condense, Commissariat á l’Energie Atomique Saclay, CNRS UMR 3680, Universitè Paris-Saclay, Saint-Aubin, France
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Abstract

Between 5% and 25% of the total momentum transferred between the atmosphere and ocean is transmitted via the growth of long surface gravity waves called “swell.” In this paper, we use large-eddy simulations to show that swell-transmitted momentum excites near-inertial waves and drives turbulent mixing that deepens a rotating, stratified, turbulent ocean surface boundary layer. We find that swell-transmitted currents are less effective at producing turbulence and mixing the boundary layer than currents driven by an effective surface stress. Overall, however, the differences between swell-driven and surface-stress-driven boundary layers are relatively minor. In consequence, our results corroborate assumptions made in Earth system models that neglect the vertical structure of swell-transmitted momentum fluxes and instead parameterize all air–sea momentum transfer processes with an effective surface stress.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Gregory L. Wagner, wagner.greg@gmail.com

Abstract

Between 5% and 25% of the total momentum transferred between the atmosphere and ocean is transmitted via the growth of long surface gravity waves called “swell.” In this paper, we use large-eddy simulations to show that swell-transmitted momentum excites near-inertial waves and drives turbulent mixing that deepens a rotating, stratified, turbulent ocean surface boundary layer. We find that swell-transmitted currents are less effective at producing turbulence and mixing the boundary layer than currents driven by an effective surface stress. Overall, however, the differences between swell-driven and surface-stress-driven boundary layers are relatively minor. In consequence, our results corroborate assumptions made in Earth system models that neglect the vertical structure of swell-transmitted momentum fluxes and instead parameterize all air–sea momentum transfer processes with an effective surface stress.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Gregory L. Wagner, wagner.greg@gmail.com
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