Upper Ocean Turbulence from High-Resolution 3D Simulations

Patrice Klein Laboratoire de Physique des Océans, IFREMER/CNRS, Brest, France

Search for other papers by Patrice Klein in
Current site
Google Scholar
PubMed
Close
,
Bach Lien Hua Laboratoire de Physique des Océans, IFREMER/CNRS, Brest, France

Search for other papers by Bach Lien Hua in
Current site
Google Scholar
PubMed
Close
,
Guillaume Lapeyre Laboratoire de Météorologie Dynamique/IPSL, Ecole Normale Supérieure/CNRS, Paris, France

Search for other papers by Guillaume Lapeyre in
Current site
Google Scholar
PubMed
Close
,
Xavier Capet Institute of Geophysics and Planetary Physics, University of California, Los Angleles, Los Angeles, California

Search for other papers by Xavier Capet in
Current site
Google Scholar
PubMed
Close
,
Sylvie Le Gentil Laboratoire de Physique des Océans, IFREMER/CNRS, Brest, France

Search for other papers by Sylvie Le Gentil in
Current site
Google Scholar
PubMed
Close
, and
Hideharu Sasaki Earth Simulator Center, JAMSTEC, Yokohama, Japan

Search for other papers by Hideharu Sasaki in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

The authors examine the turbulent properties of a baroclinically unstable oceanic flow using primitive equation (PE) simulations with high resolution (in both horizontal and vertical directions). Resulting dynamics in the surface layers involve large Rossby numbers and significant vortical asymmetries. Furthermore, the ageostrophic divergent motions associated with small-scale surface frontogenesis are shown to significantly alter the nonlinear transfers of kinetic energy and consequently the time evolution of the surface dynamics. Such impact of the ageostrophic motions explains the emergence of the significant cyclone–anticyclone asymmetry and of a strong restratification in the upper layers, which are not allowed by the quasigeostrophic (QG) or surface quasigeostrophic (SQG) theory. However, despite this strong ageostrophic character, some of the main surface properties are surprisingly still close to the surface quasigeostrophic equilibrium. They include a noticeable shallow (≈k−2) velocity spectrum as well as a conspicuous local spectral relationship between surface kinetic energy, sea surface height, and density variance over a large range of scales (from 400 to 4 km). Furthermore, surface velocities can be remarkably diagnosed from only the surface density using SQG relations. This suggests that the validity of some specific SQG relations extends to dynamical regimes with large Rossby numbers. The interior dynamics, on the other hand, strongly differ from the surface dynamics, involving a small Rossby number, a steep (≈k−4) velocity spectrum, and a somewhat steeper density spectrum. The compensation of the surface restratification by a destratification at depth confirms a connection between the surface and the interior induced by the small-scale divergent motions.

Corresponding author address: P. Klein, LPO, IFREMER, BP 70, 29280 Plouzané, France. Email: pklein@ifremer.fr

Abstract

The authors examine the turbulent properties of a baroclinically unstable oceanic flow using primitive equation (PE) simulations with high resolution (in both horizontal and vertical directions). Resulting dynamics in the surface layers involve large Rossby numbers and significant vortical asymmetries. Furthermore, the ageostrophic divergent motions associated with small-scale surface frontogenesis are shown to significantly alter the nonlinear transfers of kinetic energy and consequently the time evolution of the surface dynamics. Such impact of the ageostrophic motions explains the emergence of the significant cyclone–anticyclone asymmetry and of a strong restratification in the upper layers, which are not allowed by the quasigeostrophic (QG) or surface quasigeostrophic (SQG) theory. However, despite this strong ageostrophic character, some of the main surface properties are surprisingly still close to the surface quasigeostrophic equilibrium. They include a noticeable shallow (≈k−2) velocity spectrum as well as a conspicuous local spectral relationship between surface kinetic energy, sea surface height, and density variance over a large range of scales (from 400 to 4 km). Furthermore, surface velocities can be remarkably diagnosed from only the surface density using SQG relations. This suggests that the validity of some specific SQG relations extends to dynamical regimes with large Rossby numbers. The interior dynamics, on the other hand, strongly differ from the surface dynamics, involving a small Rossby number, a steep (≈k−4) velocity spectrum, and a somewhat steeper density spectrum. The compensation of the surface restratification by a destratification at depth confirms a connection between the surface and the interior induced by the small-scale divergent motions.

Corresponding author address: P. Klein, LPO, IFREMER, BP 70, 29280 Plouzané, France. Email: pklein@ifremer.fr

Save
  • Abraham, E. R., C. S. Law, P. W. Boyd, S. J. Lavender, M. T. Maldonado, and A. R. Bowle, 2000: Importance of stirring in the development of an iron-fertilized phytoplankton bloom. Nature, 407 , 727730.

    • Search Google Scholar
    • Export Citation
  • Andrews, D. G., and B. J. Hoskins, 1978: Energy spectra predicted by semi-geostrophic theories of frontogenesis. J. Atmos. Sci., 35 , 509512.

    • Search Google Scholar
    • Export Citation
  • Blumen, W., 1978: Uniform potential vorticity flow. Part I: Theory of wave interactions and two-dimensional turbulence. J. Atmos. Sci., 35 , 774783.

    • Search Google Scholar
    • Export Citation
  • Boccaletti, G., R. Ferrari, and B. Fox-Kemper, 2007: Mixed layer instabilities and restratification. J. Phys. Oceanogr., 37 , 22282250.

    • Search Google Scholar
    • Export Citation
  • Boyd, J. P., 1992: The energy spectrum of fronts: Time evolution of shocks in Burgers’ equation. J. Atmos. Sci., 49 , 128139.

  • Capet, X., P. Klein, B. Hua, G. Lapeyre, and J. C. McWilliams, 2008a: Surface kinetic energy transfer in surface quasi-geostrophic flows. J. Fluid Mech., 604 , 165174.

    • Search Google Scholar
    • Export Citation
  • Capet, X., J. C. McWilliams, M. J. Molemaker, and A. F. Shchepetkin, 2008b: Mesoscale to submesoscale transition in the California current system. Part II: Frontal processes. J. Phys. Oceanogr., 38 , 4464.

    • Search Google Scholar
    • Export Citation
  • Capet, X., J. C. McWilliams, M. J. Molemaker, and A. F. Shchepetkin, 2008c: Mesoscale to submesoscale transition in the California current system. Part III: Energy balance and flux. J. Phys. Oceanogr., in press.

    • Search Google Scholar
    • Export Citation
  • Charney, J., 1971: Geostrophic turbulence. J. Atmos. Sci., 28 , 10871095.

  • Haine, T. W., and J. Marshall, 1998: Gravitational, symmetric, and baroclinic instability of the ocean mixed layer. J. Phys. Oceanogr., 28 , 634658.

    • Search Google Scholar
    • Export Citation
  • Hakim, G. J., C. Snyder, and D. J. Muraki, 2002: A new surface model for cyclone–anticyclone asymmetry. J. Atmos. Sci., 59 , 24052420.

    • Search Google Scholar
    • Export Citation
  • Held, I. M., and V. D. Larichev, 1996: A scaling theory for horizontally homogeneous, baroclinically unstable flow on a beta plane. J. Atmos. Sci., 53 , 946952.

    • Search Google Scholar
    • Export Citation
  • Held, I. M., R. T. Pierrehumbert, S. T. Garner, and K. L. Swanson, 1995: Surface quasi-geostrophic dynamics. J. Fluid Mech., 282 , 120.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., 1975: The geostrophic momentum approximation and the semigeostrophic equations. J. Atmos. Sci., 32 , 233242.

  • Hua, B. L., 1994: Skewness of the generalized centrifugal force divergence for a joint normal distribution of strain and vorticity components. Phys. Fluids, A6 , 32003202.

    • Search Google Scholar
    • Export Citation
  • Hua, B. L., and D. B. Haidvogel, 1986: Numerical simulations of the vertical structure of quasigeostrophic turbulence. J. Atmos. Sci., 43 , 29232936.

    • Search Google Scholar
    • Export Citation
  • Hua, B. L., J. C. McWilliams, and P. Klein, 1998: Lagrangian accelerations in geostrophic turbulence. J. Fluid Mech., 366 , 87108.

  • Hurlburt, H. E., and P. J. Hogan, 2000: Impact of 1/8° to 1/64° resolution on Gulf Stream model-data comparisons in basin-scale subtropical Atlantic Ocean models. Dyn. Atmos. Oceans, 32 , 283329.

    • Search Google Scholar
    • Export Citation
  • Isern-Fontanet, J., B. Chapron, G. Lapeyre, and P. Klein, 2006: Potential use of microwave sea surface temperatures for the estimation of ocean currents. Geophys. Res. Lett., 33 .L24608, doi:10.1029/2006GL027801.

    • Search Google Scholar
    • Export Citation
  • Juckes, M., 1994: Quasigeostrophic dynamics of the tropopause. J. Atmos. Sci., 51 , 27562768.

  • Karsten, R., H. Jones, and J. Marshall, 2002: The role of eddy transfer in setting the stratification and transport of a circumpolar current. J. Phys. Oceanogr., 32 , 3954.

    • Search Google Scholar
    • Export Citation
  • Klein, P., A. Tréguier, and B. L. Hua, 1998: Three-dimensional stirring of thermohaline fronts. J. Mar. Res., 56 , 589612.

  • Lapeyre, G., and P. Klein, 2006: Dynamics of the upper oceanic layers in terms of surface quasigeostrophy theory. J. Phys. Oceanogr., 36 , 165176.

    • Search Google Scholar
    • Export Citation
  • Lapeyre, G., P. Klein, and B. L. Hua, 2006: Oceanic restratification by surface frontogenesis. J. Phys. Oceanogr., 36 , 15771590.

  • Large, W. G., S. C. Doney, and J. C. McWilliams, 1994: Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization. Rev. Geophys., 32 , 363403.

    • Search Google Scholar
    • Export Citation
  • Larichev, V. D., and I. M. Held, 1995: Eddy amplitudes and fluxes in a homogeneous model of fully developed baroclinic instability. J. Phys. Oceanogr., 25 , 22852297.

    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., 1984: The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech., 146 , 2143.

  • McWilliams, J. C., 1985: Submesoscale coherent vortices in the ocean. Rev. Geophys., 23 , 165182.

  • McWilliams, J. C., 1989: Statistical properties of decaying geostrophic turbulence. J. Fluid Mech., 198 , 199230.

  • Rhines, P. B., 1979: Geostrophic turbulence. Annu. Rev. Fluid Mech., 11 , 404441.

  • Rivière, P., A-M. Tréguier, and P. Klein, 2004: Effects of bottom friction on nonlinear equilibration of an oceanic baroclinic jet. J. Phys. Oceanogr., 34 , 416432.

    • Search Google Scholar
    • Export Citation
  • Salmon, R. S., 1980: Baroclinic instability and geostrophic turbulence. Geophys. Astrophys. Fluid Dyn., 15 , 167211.

  • Scott, R. K., 2006: Local and nonlocal advection of a passive scalar. Phys. Fluids, 56 , 122125.

  • Shchepetkin, A. F., 2008: Computational kernel algorithms for fine-scale, multi-process, long-time oceanic simulations. Handbook of Numerical Analysis: Special Volume: Computational Methods for the Atmosphere and the Oceans, R. Teman and J. Tribbia, Eds., in press.

    • Search Google Scholar
    • Export Citation
  • Shchepetkin, A. F., and J. C. McWilliams, 2005: The regional oceanic modeling system (ROMS): A split-explicit, free-surface, topography-following-coordinate ocean model. Ocean Modell., 9 , 347404.

    • Search Google Scholar
    • Export Citation
  • Siegel, A., J. B. Weiss, J. Toomre, J. C. McWilliams, P. S. Berloff, and I. Yavneh, 2001: Eddies and vortices in ocean basin dynamics. Geophys. Res. Lett., 28 , 31833186.

    • Search Google Scholar
    • Export Citation
  • Smith, K. S., and G. K. Vallis, 2001: The scales and equilibration of midocean eddies: Freely evolving flow. J. Phys. Oceanogr., 31 , 554571.

    • Search Google Scholar
    • Export Citation
  • Snyder, C., W. C. Skamarock, and R. Rotunno, 1991: A comparison of primitive-equation and semigeostrophic simulations of baroclinic waves. J. Atmos. Sci., 48 , 21792194.

    • Search Google Scholar
    • Export Citation
  • Thomas, L. N., 2005: Destruction of potential vorticity by winds. J. Phys. Oceanogr., 35 , 24572466.

  • Tulloch, R., and K. S. Smith, 2006: A theory for the atmospheric energy spectrum: Depth-limited temperature anomalies at the tropopause. Proc. Natl. Acad. Sci. USA, 103 , 1469014694.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 1420 405 48
PDF Downloads 1079 287 19