Nonlocal Transport and Implied Viscosity and Diffusivity throughout the Boundary Layer in LES of the Southern Ocean with Surface Waves

William G. Large National Center for Atmospheric Research, Boulder, Colorado

Search for other papers by William G. Large in
Current site
Google Scholar
PubMed
Close
,
Edward G. Patton National Center for Atmospheric Research, Boulder, Colorado

Search for other papers by Edward G. Patton in
Current site
Google Scholar
PubMed
Close
, and
Peter P. Sullivan National Center for Atmospheric Research, Boulder, Colorado

Search for other papers by Peter P. Sullivan in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Observations from the Southern Ocean Flux Station provide a wide range of wind, buoyancy, and wave (Stokes) forcing for large-eddy simulation (LES) of deep Southern Ocean boundary layers. Almost everywhere there is a nonzero angle Ω between the shear and the stress vectors. Also, with unstable forcing there is usually a depth where there is stable stratification, but zero buoyancy flux and often a number of depths above where there is positive flux, but neutral stratification. These features allow nonlocal transports of buoyancy and of momentum to be diagnosed, using either the Eulerian or Lagrangian shear. The resulting profiles of nonlocal diffusivity and viscosity are quite similar when scaled according to Monin–Obukhov similarity theory in the surface layer, provided the Eulerian shear is used. Therefore, a composite shape function is constructed that may be generally applicable. In contrast, the deeper boundary layer appears to be too decoupled from the Stokes component of the Lagrangian shear. The nonlocal transports can be dominant. The diagnosed across-shear momentum flux is entirely nonlocal and is highly negatively correlated with the across-shear component of the wind stress, just as nonlocal and surface buoyancy fluxes are related. Furthermore, in the convective limit the scaling coefficients become essentially identical, with some consistency with atmospheric experience. The nonlocal contribution to the along-shear momentum flux is proportional to (1 − cosΩ) and is always countergradient, but is unrelated to the aligned wind stress component.

© 2019 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: W. G. Large, wily@ucar.edu

Abstract

Observations from the Southern Ocean Flux Station provide a wide range of wind, buoyancy, and wave (Stokes) forcing for large-eddy simulation (LES) of deep Southern Ocean boundary layers. Almost everywhere there is a nonzero angle Ω between the shear and the stress vectors. Also, with unstable forcing there is usually a depth where there is stable stratification, but zero buoyancy flux and often a number of depths above where there is positive flux, but neutral stratification. These features allow nonlocal transports of buoyancy and of momentum to be diagnosed, using either the Eulerian or Lagrangian shear. The resulting profiles of nonlocal diffusivity and viscosity are quite similar when scaled according to Monin–Obukhov similarity theory in the surface layer, provided the Eulerian shear is used. Therefore, a composite shape function is constructed that may be generally applicable. In contrast, the deeper boundary layer appears to be too decoupled from the Stokes component of the Lagrangian shear. The nonlocal transports can be dominant. The diagnosed across-shear momentum flux is entirely nonlocal and is highly negatively correlated with the across-shear component of the wind stress, just as nonlocal and surface buoyancy fluxes are related. Furthermore, in the convective limit the scaling coefficients become essentially identical, with some consistency with atmospheric experience. The nonlocal contribution to the along-shear momentum flux is proportional to (1 − cosΩ) and is always countergradient, but is unrelated to the aligned wind stress component.

© 2019 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: W. G. Large, wily@ucar.edu
Save
  • Belcher, S., and Coauthors, 2012: A global perspective on mixing in the ocean surface boundary layer. J. Geophys. Res., 39, L18605, https://doi.org/10.1029/2012GL052932.

    • Search Google Scholar
    • Export Citation
  • Berg, J., J. Mann, and E. Patton, 2013: Lidar-observed stress vectors and veer in the atmospheric boundary layer. J. Atmos. Oceanic Technol., 30, 19611969, https://doi.org/10.1175/JTECH-D-12-00266.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Berrisford, P., and Coauthors, 2011: The ERA-Interim Archive: Version 2.0. ERA Rep. Series 1, 23 pp., https://www.ecmwf.int/en/elibrary/8174-era-interim-archive-version-20.

  • Bretherton, C., and S. Park, 2009: A new moist turbulence parameterization in the Community Atmosphere Model. J. Climate, 84, 34223448, https://doi.org/10.1175/2008JCLI2556.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brown, A., and A. Grant, 1997: Non-local mixing of momentum in the convective boundary layer. Bound.-Layer Meteor., 84, 122, https://doi.org/10.1023/A:1000388830859.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Burchard, H., and Coauthors, 2008: Observational and numerical modeling methods for quantifying coastal ocean turbulence and mixing. Prog. Oceanogr., 76, 399442, https://doi.org/10.1016/j.pocean.2007.09.005.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Canuto, V., F. Minotti, C. Ronchi, M. Ypma, and O. Zeman, 1994: Second-order closure PBL model with new third-order moments: Comparison with LES data. J. Atmos. Sci., 51, 16051618, https://doi.org/10.1175/1520-0469(1994)051<1605:SOCPMW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Canuto, V., Y. Cheng, and A. Howard, 2007: Non-local ocean mixing model and a new plume model for deep convection. Ocean Modell., 16, 2846, https://doi.org/10.1016/j.ocemod.2006.07.003.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cheng, Y., V. Canuto, and A. Howard, 2002: An improved model for the turbulent PBL. J. Atmos. Sci., 59, 15501565, https://doi.org/10.1175/1520-0469(2002)059<1550:AIMFTT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Craik, A., 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
  • Danabasoglu, G., S. Bates, B. Briegleb, S. Jayne, M. Jochum, W. Large, S. Peacock, and S. Yeager, 2012: The CCSM4 ocean component. J. Climate, 25, 13611389, https://doi.org/10.1175/JCLI-D-11-00091.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Deardorff, J., 1966: The counter-gradient heat flux in the atmosphere and in the laboratory. J. Atmos. Sci., 23, 503506, https://doi.org/10.1175/1520-0469(1966)023<0503:TCGHFI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Deardorff, J., 1972: Theoretical expression for the countergradient vertical heat flux. J. Geophys. Res., 77, 59005904, https://doi.org/10.1029/JC077i030p05900.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Downes, S., and Coauthors, 2014: An assessment of Southern Ocean water masses and sea ice during 1988-2007 in a suite of interannual CORE-II simulations. Ocean Modell., 18, 6794, https://doi.org/10.1016/j.ocemod.2015.07.022.

    • Search Google Scholar
    • Export Citation
  • DuVivier, A., W. Large, and R. Small, 2018: Argo observations of the deep mixing band in the Southern Ocean: A salinity modeling challenge. J. Geophys. Res. Oceans, 123, 75997617, https://doi.org/10.1029/2018JC014275.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Frech, M., and L. Mahrt, 1995: A two-scale mixing formulation for the atmospheric boundary layer. Bound.-Layer Meteor., 73, 91104, https://doi.org/10.1007/BF00708931.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grant, A., and S. 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
  • Harcourt, R., 2013: A second-moment closure model of Langmuir turbulence. J. Phys. Oceanogr., 43, 673697, https://doi.org/10.1175/JPO-D-12-0105.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Harcourt, R., 2015: An improved second-moment closure model of Langmuir turbulence. J. Phys. Oceanogr., 45, 84103, https://doi.org/10.1175/JPO-D-14-0046.1

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Harcourt, R., and E. 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
  • Högström, U., 1988: Non-dimensional wind and temperature profiles in the atmospheric surface layer. Bound.-Layer Meteor., 42, 5578, https://doi.org/10.1007/BF00119875.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holtslag, A., and C.-H. Moeng, 1991: Eddy diffusivity and counter gradient transport in the convective atmospheric boundary layer. J. Atmos. Oceanic Technol., 48, 16901698, https://doi.org/10.1175/1520-0469(1991)048<1690:EDACTI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Holtslag, A., and B. Boville, 1993: Local versus nonlocal boundary-layer diffusion in a global climate model. J. Climate, 6, 18251842, https://doi.org/10.1175/1520-0442(1993)006<1825:LVNBLD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kantha, L., and C. Clayson, 1994: An improved mixed layer model for geophysical applications. J. Geophys. Res., 99, 25 23525 266, https://doi.org/10.1029/94JC02257.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Keller, L., and A. Friedmann, 1924: Differentialgleichungen fur die turbulente bewegung einer kompressiblen flussigkeit. Proceedings of the First International Congress on Applied Mechanics, Waltman, 395405.

    • Search Google Scholar
    • Export Citation
  • Kraus, E., and J. Turner, 1967: A one-dimensional model of the seasonal thermocline, II. The general theory and its consequences. Tellus, 19, 98105, https://doi.org/10.3402/tellusa.v19i1.9753.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Large, W., J. McWilliams, and S. Doney, 1994: Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization. J. Atmos. Sci., 32, 363403, https://doi.org/10.1029/94RG01872.

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lesieur, M., 1997: Turbulence in Fluids. 3rd ed. Fluid Mechanics and Its Applications, Vol. 84, Kluwer Academic, 563 pp.

  • Li, Q., and B. Fox-Kemper, 2017: Assessing the effects of Langmuir turbulence on the entrainment buoyancy flux in the ocean surface boundary layer. J. Phys. Oceanogr., 47, 28632886, https://doi.org/10.1175/JPO-D-17-0085.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mailhot, J., and R. Benoit, 1982: A finite-element model of the atmospheric boundary layer suitable for use with numerical weather prediction models. J. Atmos. Sci., 39, 22492266, https://doi.org/10.1175/1520-0469(1982)039<2249:AFEMOT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McWilliams, J., 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
  • Mellor, G., and T. Yamada, 1982: Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys., 20, 851875, https://doi.org/10.1029/RG020i004p00851.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Moeng, C.-H., 1984: A large-eddy simulation model for the study of planetary boundary-layer turbulence. J. Atmos. Sci., 41, 20522062, https://doi.org/10.1175/1520-0469(1984)041<2052:ALESMF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Moeng, C.-H., and J. C. Wyngaard, 1989: Evaluation of turbulent transport and dissipation closures in second-order modeling. J. Atmos. Sci., 46, 23112330, https://doi.org/10.1175/1520-0469(1989)046<2311:EOTTAD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Monin, A., and A. Obukhov, 1954: Basic laws of turbulent mixing in the surface layer of the atmosphere. Tr. Geofiz. Inst., Akad. Nauk SSSR, 24 (151), 163187.

    • Search Google Scholar
    • Export Citation
  • Noh, Y., W. Cheon, S. Hong, and S. Raasch, 2003: Improvement of the K-Profile Model for the planetary boundary layer based on large eddy simulation data. Bound.-Layer Meteor., 107, 401427, https://doi.org/10.1023/A:1022146015946.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Noh, Y., H. 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
  • O’Brien, J., 1970: A note on the vertical structure of the eddy exchange coefficient in the planetary boundary layer. Rev. Geophys., 27, 12131215, https://doi.org/10.1175/1520-0469(1970)027<1213:ANOTVS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Park, S., 2014: A unified convection scheme (UNICON). Part I: Formulation. J. Atmos. Sci., 71, 39023930, https://doi.org/10.1175/JAS-D-13-0233.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Price, J., R. Weller, and R. Pinkel, 1986: Diurnal cycling: Observations and models of the upper ocean’s response to diurnal heating, cooling and wind mixing. J. Geophys. Res., 91, 84118427, https://doi.org/10.1029/JC091iC07p08411.

    • 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
  • Sallée, J., E. Shuckburgh, N. Bruneau, A. Meijers, T. Bracegirdle, and Z. Wang, 2013: Assessment of southern ocean mixed-layer depths in CMIP5 models: Historical bias and forcing response. J. Geophys. Res. Oceans, 110, 18451862, https://doi.org/10.1002/jgrc.20157.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schultz, E., S. Josey, and R. Verein, 2012: First air-sea flux mooring measurements in the Southern Ocean. Geophys. Res. Lett., 39, L16606, https://doi.org/10.1029/2012GL052290.

    • Search Google Scholar
    • Export Citation
  • Siebesma, A., P. Soares, and J. Teixeira, 2007: A combined eddy-diffusivity mass-flux approach for the convective boundary layer. J. Atmos. Sci., 64, 12301248, https://doi.org/10.1175/JAS3888.1

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smyth, W., E. Skylingstad, G. Crawford, and H. Wijesekera, 2002: Nonlocal fluxes and stokes drift effects in the K-profile parameterization. Ocean Dyn., 52, 104115, https://doi.org/10.1007/s10236-002-0012-9.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sullivan, P., J. McWilliams, and C. Moeng, 1994: A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows. Bound.-Layer Meteor., 71, 247276, https://doi.org/10.1007/BF00713741.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sullivan, P., J. McWilliams, and W. Melville, 2004: The oceanic boundary layer driven by wave breaking with stochastic variability. Part 1. Direct numerical simulations. J. Fluid Mech., 507, 143174, https://doi.org/10.1017/S002211200700897X

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sullivan, P., J. McWilliams, and W. Melville, 2007: Surface gravity wave effects in the oceanic boundary layer: Large-eddy simulation with vortex force and stochastic breakers. J. Fluid Mech., 593, 405452, https://doi.org/10.1017/S002211200700897X.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tan, Z., C. Kaul, K. Pressel, Y. Cohen, T. Schneider, and J. Teixeira, 2018: An extended eddy-diffusivity mass-flux scheme for unified representation of subgrid-scale turbulence and convection. J. Adv. Model. Earth Syst., 10, 770800, https://doi.org/10.1002/2017MS001162.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tolman, H., 2002: User manual and system documentation of WAVEWATCH-III version 2.22. Tech. rep., NOAA/NWS/NCEP/MMAB Tech. Note 222, 133 pp., https://polar.ncep.noaa.gov/mmab/papers/tn222/MMAB_222.pdf.

  • Troen, I., and L. Mahrt, 1986: A simple model of the atmospheric boundary layer: Sensitivity to surface evaporation. Bound.-Layer Meteor., 37, 129148, https://doi.org/10.1007/BF00122760.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • van Roekel, L., B. Fox-Kemper, P. Sullivan, P. Hamlington, and S. Haney, 2012: The form and orientation of Langmuir cells for misaligned winds and waves. J. Geophys. Res., 117, C05001, https://doi.org/10.1029/2011JC007516.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • van Roekel, L., and Coauthors, 2018: The KPP boundary layer scheme: Revisiting its formulation and benchmarking one-dimensional ocean simulations relative to LES. J. Adv. Model. Earth Syst., 10, 26472685, https://doi.org/10.1029/2018MS001336.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, D., J. McWilliams, and W. Large, 1998: Large eddy simulation of the diurnal cycle of deep equatorial turbulence. J. Phys. Oceanogr., 28, 129148, https://doi.org/10.1175/1520-0485(1998)028<0129:LESOTD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Weijer, W., and Coauthors, 2012: The Southern Ocean and its climate in CCSM4. J. Climate, 25, 26522675, https://doi.org/10.1175/JCLI-D-11-00302.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wyngaard, J., 1982: Lectures on the planetary boundary layer. Mesoscale Meteorology—Theories, Observations and Models, D. Lilly and T. Gal-Chen, Eds., NATO ASI Series C, Vol. 114, D. Reidel, 603650.

    • Search Google Scholar
    • Export Citation
  • Wyngaard, J. C., 2010: Turbulence in the Atmosphere. Cambridge University Press, 406 pp.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 468 156 24
PDF Downloads 360 83 18