Forcing Space: An Alternative to Regime Diagrams for Predicting Characteristics of Turbulence in the Ocean Surface Mixing Layer

Ann E. Gargett aInstitute of Ocean Sciences, Sidney, British Columbia, Canada
bOld Dominion University, Norfolk, Virginia

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Abstract

Various forms of regime diagrams have become an accepted means of identifying the dominant type of forcing of turbulence in the ocean surface layer. However, all of the proposed forms share a number of issues, demonstrated here, that make them an imperfect tool for this purpose. Instead, I suggest a forcing space consisting of surface buoyancy flux (usually dominated by surface heat flux) and a growth rate defined as the inverse of a theoretical time scale for growth of Langmuir circulations in an unstratified water column. Using coastal data, it is demonstrated that, provided forcing conditions are roughly constant for several hours, location in the upper half-plane of this forcing space predicts organizational characteristics of observed turbulence that range in a systematic way between those of “pure” convection and those of full depth Langmuir circulations. In this upper half-plane, where a convective scale velocity exists and the surface Stokes drift velocity can be computed, allowing calculation of a Stokes scale velocity, a linear combination of the two scale velocities provides a consistent estimate of observed rms turbulent vertical velocity. Time dependence is nevertheless a frequent characteristic of ocean surface layer forcing, if only because of the (usually large) diurnal variation in surface heat flux. It is shown that the time scale of response of surface layer turbulence to time variable forcing depends on whether the major change is due to wind/wave or buoyancy forcing. Relevant modeling studies are suggested.

© 2022 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: Ann Gargett, gargettann@gmail.com

Abstract

Various forms of regime diagrams have become an accepted means of identifying the dominant type of forcing of turbulence in the ocean surface layer. However, all of the proposed forms share a number of issues, demonstrated here, that make them an imperfect tool for this purpose. Instead, I suggest a forcing space consisting of surface buoyancy flux (usually dominated by surface heat flux) and a growth rate defined as the inverse of a theoretical time scale for growth of Langmuir circulations in an unstratified water column. Using coastal data, it is demonstrated that, provided forcing conditions are roughly constant for several hours, location in the upper half-plane of this forcing space predicts organizational characteristics of observed turbulence that range in a systematic way between those of “pure” convection and those of full depth Langmuir circulations. In this upper half-plane, where a convective scale velocity exists and the surface Stokes drift velocity can be computed, allowing calculation of a Stokes scale velocity, a linear combination of the two scale velocities provides a consistent estimate of observed rms turbulent vertical velocity. Time dependence is nevertheless a frequent characteristic of ocean surface layer forcing, if only because of the (usually large) diurnal variation in surface heat flux. It is shown that the time scale of response of surface layer turbulence to time variable forcing depends on whether the major change is due to wind/wave or buoyancy forcing. Relevant modeling studies are suggested.

© 2022 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: Ann Gargett, gargettann@gmail.com
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  • Banner, M. L., A. V. Babanin, and I. R. Young, 2000: Breaking probability for dominant waves on the sea surface. J. Phys. Oceanogr., 30, 31453160, https://doi.org/10.1175/1520-0485(2000)030<3145:BPFDWO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Battjes, J. A., T. J. Zitman, and L. H. Holthuusen, 1987: A reanalysis of the spectra observed in JONSWAP. J. Phys. Oceanogr., 17, 12881295, https://doi.org/10.1175/1520-0485(1987)017<1288:AROTSO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Belcher, S. E., and Coauthors, 2012: A global perspective on Langmuir turbulence in the ocean surface boundary layer. Geophys. Res. Lett., 39, L18605, https://doi.org/10.1029/2012GL052932.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bidlot, J.-F., 2020: Official IFS documentation CY47R1—Part VII: ECMWF Wave Model. ECMWF, 114 pp., http://dx.doi.org/10.21957/31drbygag.

    • Search Google Scholar
    • Export Citation
  • Clarke, A. J., and S. Van Gorder, 2018: The relationship of near-surface flow, Stokes drift and the wind stress. J. Geophys. Res. Oceans, 123, 46804692, https://doi.org/10.1029/2018JC014102.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Craik, A. D. 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
  • Etling, D., and R. A. Brown, 1993: Roll vortices in the planetary boundary layer: A review. Bound.-Layer Meteor., 65, 215248, https://doi.org/10.1007/BF00705527.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fairall, C. W., E. F. Bradley, J. E. Hare, A. A. Grachev, and J. B. Edson, 2003: Bulk parameterization of air-sea fluxes: Updates and verification for the COARE algorithm. J. Climate, 16, 571591, https://doi.org/10.1175/1520-0442(2003)016%3C0571:BPOASF%3E2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Forristall, G. Z., 1981: Measurements of a saturated range in ocean wave spectra. J. Geophys. Res., 86, 80758084, https://doi.org/10.1029/JC086iC09p08075.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gargett, A. E., and J. R. Wells, 2007: Langmuir turbulence in shallow water: Part I. Observations. J. Fluid Mech., 576, 2761, https://doi.org/10.1017/S0022112006004575.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gargett, A. E., and C. E. Grosch, 2014: Turbulence process domination under the combined forcings of wind stress, the Langmuir vortex force, and surface cooling. J. Phys. Oceanogr., 44, 4467, https://doi.org/10.1175/JPO-D-13-021.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gargett, A. E., and D. J. Savidge, 2020: Winds, waves and turbulence on a shallow continental shelf during passage of a tropical storm. J. Phys. Oceanogr., 50, 1341134, https://doi.org/10.1175/JPO-D-20-0024.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gargett, A. E., J. R. Wells, A. E. Tejada-Martínez, and C. E. Grosch, 2004: Langmuir supercells: A mechanism for sediment resuspension and transport in shallow seas. Science, 306, 19251928, https://doi.org/10.1126/science.1100849.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grant, A. L., and S. E. Belcher, 2009: Characteristics of Langmuir turbulence in the ocean mixed layer. J. Phys. Oceanogr., 39, 18711887, https://doi.org/10.1175/2009JPO4119.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grosch, C. E., and A. E. Gargett, 2016: Why do LES of Langmuir supercells not include rotation? J. Phys. Oceanogr., 46, 35953597, https://doi.org/10.1175/JPO-D-16-0092.1.

    • 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
  • Kenyon, K. E., 1969: Stokes drift for random gravity waves. J. Geophys. Res., 74, 69916994, https://doi.org/10.1029/JC074i028p06991.

  • Leibovich, S., 1977: Convective instability of stably stratified water in the ocean. J. Fluid Mech., 82, 561581, https://doi.org/10.1017/S0022112077000846.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Li, M., C. Garrett, and E. Skyllingstad, 2004: A regime diagram for classifying turbulent eddies in the upper ocean. Deep-Sea Res. I, 52, 259278, https://doi.org/10.1016/j.dsr.2004.09.004.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 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
  • Min, H. S., and Y. Noh, 2004: Influence of the surface heating on Langmuir circulation. J. Phys. Oceanogr., 34, 26302641, https://doi.org/10.1175/JPOJPO-2654.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Phillips, O. M., 1958: The equilibrium range in the spectrum of wind-generated waves. J. Fluid Mech., 4, 426434, https://doi.org/10.1017/S0022112058000550.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Resio, D. T., C. E. Long, and C. L. Vincent, 2004: The equilibrium-range constant in wind-generated wave spectra. J. Geophys. Res., 109, CO1018, https://doi.org/10.1029/2003JC001788.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Romero, L., and W. K. Melville, 2010: Numerical modeling of fetch-limited waves in the Gulf of Tehuantepec. J. Phys. Oceanogr., 40, 466486, https://doi.org/10.1175/2009JPO4128.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Skyllingstad, E. D., 2000: Scales of Langmuir circulation generated using a large-eddy simulation model. Spill Sci. Technol. Bull., 6, 239246, https://doi.org/10.1016/S1353-2561(01)00042-1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smith, J. A., 1996: Observations of Langmuir circulation, waves, and the mixed layer. The Air-Sea Interface: Radio and Acoustic Sensing, Turbulence, and Wave Dynamics, M. A. Donelan, W. Hui and W. J. Plant, Eds., University of Toronto Press, 613622.

    • Search Google Scholar
    • Export Citation
  • Toba, Y., 1973: Local balance in the air-sea boundary process. J. Oceanogr. Soc. Japan, 29, 209220, https://doi.org/10.1007/BF02108528.

  • Walker, R., A. E. Tejada-Martínez, and C. E. Grosch, 2016: Large-eddy simulation of a coastal ocean under the combined effect of surface heat fluxes and full-depth Langmuir circulation. J. Phys. Oceanogr., 42, 24112436, https://doi.org/10.1175/JPO-D-15-0168.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yoshikawa, Y., Y. Baba, H. Mizutani, T. Kubo, and C. Shimoda, 2018: Observed features of Langmuir turbulence forced by misaligned wind and waves under destabilizing buoyancy force. J. Phys. Oceanogr., 48, 27372759, https://doi.org/10.1175/JPO-D-18-0038.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
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