• Abernathey, R., D. Ferreira, and A. Klocker, 2013: Diagnostics of isopycnal mixing in a circumpolar channel. Ocean Modell., 72, 116, doi:10.1016/j.ocemod.2013.07.004.

    • Search Google Scholar
    • Export Citation
  • Afanasyev, Y. D., S. O. Leary, P. B. Rhines, and E. G. Lindahl, 2012: On the origin of jets in the ocean. Geophys. Astrophys. Fluid Dyn., 106, 113137, doi:10.1080/03091929.2011.562896.

    • Search Google Scholar
    • Export Citation
  • Arbic, B. K., 2000: Generation of mid-ocean eddies: The local baroclinic instability hypothesis. Ph.D. thesis, Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 290 pp.

  • Arbic, B. K., and G. R. Flierl, 2004: Baroclinically unstable geostrophic turbulence in the limits of strong and weak bottom Ekman friction: Application to midocean eddies. J. Phys. Oceanogr., 34, 22572273, doi:10.1175/1520-0485(2004)034<2257:BUGTIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Arbic, B. K., R. B. Scott, G. R. Flierl, A. J. Morten, J. G. Richman, and J. F. Shriver, 2012: Nonlinear cascade of surface oceanic geostrophic kinetic energy in the frequency domain. J. Phys. Oceanogr., 42, 15771600, doi:10.1175/JPO-D-11-0151.1.

    • Search Google Scholar
    • Export Citation
  • Bachman, S., 2012: A diagnostic suite of models for the evaluation of oceanic mesoscale eddy parameterizations. Ph.D. thesis, University of Colorado, 246 pp.

  • Bachman, S., and B. Fox-Kemper, 2013: Eddy parameterization challenge suite I: Eddy spindown. Ocean Modell., 64, 1228, doi:10.1016/j.ocemod.2012.12.003.

    • Search Google Scholar
    • Export Citation
  • Bakas, N. A., and P. J. Ioannou, 2013: On the mechanism underlying the spontaneous emergence of barotropic zonal jets. J. Atmos. Sci., 70, 22512271, doi:10.1175/JAS-D-12-0102.1.

    • Search Google Scholar
    • Export Citation
  • Chen, R., 2013: Energy pathways and structures of oceanic eddies from the ECCO2 state estimate and simplified models. Ph.D. thesis, Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 206 pp.

  • Chen, R., G. R. Flierl, and C. Wunsch, 2014a: A description of local and nonlocal eddy-mean flow interaction in a global eddy-permitting state estimate. J. Phys. Oceanogr., 44, 23362352, doi:10.1175/JPO-D-14-0009.1.

    • Search Google Scholar
    • Export Citation
  • Chen, R., J. L. McClean, S. T. Gille, and A. Griesel, 2014b: Isopycnal eddy diffusivities and critical layers in the Kuroshio Extension from an eddying ocean model. J. Phys. Oceanogr., 44, 21912211, doi:10.1175/JPO-D-13-0258.1.

    • Search Google Scholar
    • Export Citation
  • Chen, R., G. R. Flierl, and C. Wunsch, 2015a: Quantifying and interpreting striations in a subtropical gyre: A spectral perspective. J. Phys. Oceanogr., 45, 387406, doi:10.1175/JPO-D-14-0038.1.

    • Search Google Scholar
    • Export Citation
  • Chen, R., S. T. Gille, J. L. McClean, G. R. Flierl, and A. Griesel, 2015b: A multiwavenumber theory for eddy diffusivities and its application to the southeast Pacific (DIMES) region. J. Phys. Oceanogr., 45, 18771896, doi:10.1175/JPO-D-14-0229.1.

    • Search Google Scholar
    • Export Citation
  • Cox, M., 1987: An eddy-resolving numerical model of the ventilated thermocline: Time dependence. J. Phys. Oceanogr., 17, 10441056, doi:10.1175/1520-0485(1987)017<1044:AERNMO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Danilov, S., and V. M. Gryanik, 2004: Barotropic beta-plane turbulence in a regime with strong zonal jets revisited. J. Atmos. Sci., 61, 22832295, doi:10.1175/1520-0469(2004)061<2283:BBTIAR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Danilov, S., and D. Gurarie, 2004: Scaling, spectra and zonal jets in beta-plane turbulence. Phys. Fluids, 16, 25922603, doi:10.1063/1.1752928.

    • Search Google Scholar
    • Export Citation
  • Davis, A., E. D. Lorenzo, H. Luo, A. Belmadani, N. Maximenko, O. Melnichenko, and N. Schneider, 2014: Mechanisms for the emergence of ocean striations in the North Pacific. Geophys. Res. Lett., 41, 948953, doi:10.1002/2013GL057956.

    • Search Google Scholar
    • Export Citation
  • Dritschel, D. G., and M. E. McIntyre, 2008: Multiple jets as PV staircases: The Phillips effect and the resilience of eddy-transport barriers. J. Atmos. Sci., 65, 855874, doi:10.1175/2007JAS2227.1.

    • Search Google Scholar
    • Export Citation
  • Farrell, B. F., and P. J. Ioannou, 2007: Structure and spacing of jets in barotropic turbulence. J. Atmos. Sci., 64, 36523665, doi:10.1175/JAS4016.1.

    • Search Google Scholar
    • Export Citation
  • Ferrari, R., and C. Wunsch, 2009: Ocean circulation kinetic energy: Reservoirs, sources and sinks. Annu. Rev. Fluid Mech., 41, 253282, doi:10.1146/annurev.fluid.40.111406.102139.

    • Search Google Scholar
    • Export Citation
  • Ferrari, R., and M. Nikurashin, 2010: Suppression of eddy mixing across jets in the Southern Ocean. J. Phys. Oceanogr., 40, 15011519, doi:10.1175/2010JPO4278.1.

    • Search Google Scholar
    • Export Citation
  • Flierl, G. R., and J. Pedlosky, 2007: The nonlinear dynamics of time-dependent subcritical baroclinic currents. J. Phys. Oceanogr., 37, 10011021, doi:10.1175/JPO3034.1.

    • Search Google Scholar
    • Export Citation
  • Galperin, B., H. Nakano, H.-P. Huang, and S. Sukoriansky, 2004: The ubiquitous zonal jets in the atmospheres of giant planets and Earth’s oceans. Geophys. Res. Lett.,31, L13303, doi:10.1029/2004GL019691.

  • Gille, S. T., 2005: Statistical characterization of zonal and meridional ocean wind stress. J. Atmos. Oceanic Technol., 22, 13531372, doi:10.1175/JTECH1789.1.

    • Search Google Scholar
    • Export Citation
  • Gille, S. T., K. Speer, J. R. Ledwell, and A. C. N. Garabato, 2007: Mixing and stirring in the Southern Ocean. Eos, Trans. Amer. Geophys. Union, 88, 382383, doi:10.1029/2007EO390002.

    • Search Google Scholar
    • Export Citation
  • Green, J. S. A., 1970: Transport properties of the large-scale eddies and the general circulation of the atmosphere. Quart. J. Roy. Meteor. Soc., 96, 157185, doi:10.1002/qj.49709640802.

    • Search Google Scholar
    • Export Citation
  • Griesel, A., S. T. Gille, J. Sprintall, J. L. McClean, J. H. LaCasce, and M. E. Maltrud, 2010: Isopycnal diffusivities in the Antarctic Circumpolar Current inferred from Lagrangian floats in an eddying model. J. Geophys. Res.,115, C06006, doi:10.1029/2009JC005821.

  • Hughes, C. W., A. F. Thompson, and C. Wilson, 2010: Identification of jets and mixing barriers from sea level and vorticity measurements using simple statistics. Ocean Modell., 32, 4457, doi:10.1016/j.ocemod.2009.10.004.

    • Search Google Scholar
    • Export Citation
  • Ivchenko, V. O., S. Danilov, and D. Olbers, 2008: Eddies in numerical models of the Southern Ocean. Ocean Modeling in an Eddying Regime, Geophys. Monogr. Ser., Vol. 177, Amer. Geophys. Union, 177–198.

  • Killworth, P. D., 1997: On the parameterization of eddy transfer. Part 1: Theory. J. Mar. Res., 55, 11711197, doi:10.1357/0022240973224102.

    • Search Google Scholar
    • Export Citation
  • Klocker, A., R. Ferrari, and J. H. LaCasce, 2012a: Estimating suppression of eddy mixing by mean flows. J. Phys. Oceanogr., 42, 15661576, doi:10.1175/JPO-D-11-0205.1.

    • Search Google Scholar
    • Export Citation
  • Klocker, A., R. Ferrari, J. H. LaCasce, and S. Merrifield, 2012b: Reconciling float-based and tracer-based estimates of eddy diffusivities. J. Mar. Res., 70, 569602, doi:10.1357/002224012805262743.

    • Search Google Scholar
    • Export Citation
  • Kraichnan, R. H., 1987: Eddy viscosity and diffusivity: Exact formulas and approximations. Complex Syst., 1, 805820.

  • Lilly, D. K., 1969: Numerical simulation of two-dimensional turbulence. Phys. Fluids,12, II-240, doi:10.1063/1.1692444.

  • Maltrud, M., and G. K. Vallis, 1991: Energy spectra and coherent structures in forced two-dimensional and geostrophic turbulence. J. Fluid Mech., 228, 321342.

    • Search Google Scholar
    • Export Citation
  • Maximenko, N. A., B. Bang, and H. Sasaki, 2005: Observational evidence of alternating zonal jets in the world ocean. Geophys. Res. Lett.,32, L12607, doi:10.1029/2005GL022728.

  • Maximenko, N. A., O. V. Melnichenko, P. P. Niiler, and H. Sasaki, 2008: Stationary mesoscale jet-like features in the ocean. Geophys. Res. Lett.,35, L08603, doi:10.1029/2008GL033267.

  • Menemenlis, D., J. Campin, P. Heimbach, C. Hill, T. Lee, A. Nguyen, M. Schodlock, and H. Zhang, 2008: ECCO2: High resolution global ocean and sea ice data synthesis. Mercator Ocean Quarterly Newsletter, No. 31, Mercator Ocean, Ramonville Saint-Agne, France, 1321. [Available online at http://ecco2.org/manuscripts/reports/ECCO2_Mercator.pdf.]

  • Monahan, A. H., 2012: The temporal autocorrelation structure of sea surface winds. J. Climate, 25, 66846700, doi:10.1175/JCLI-D-11-00698.1.

    • Search Google Scholar
    • Export Citation
  • Nakano, H., and H. Hasumi, 2005: A series of zonal jets embedded in the broad zonal flows in the Pacific obtained in eddy-permitting ocean general circulation models. J. Phys. Oceanogr., 35, 474488, doi:10.1175/JPO2698.1.

    • Search Google Scholar
    • Export Citation
  • Panetta, R. L., 1993: Zonal jets in wide baroclinically unstable regions: Persistence and scale selection. J. Atmos. Sci., 50, 20732106, doi:10.1175/1520-0469(1993)050<2073:ZJIWBU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Pedlosky, J., 1987: Geophysical Fluid Dynamics. Springer-Verlag, 710 pp.

  • Plumb, R. A., and J. D. Mahlman, 1987: The zonally averaged transport characteristics of the GFDL general circulation/transport model. J. Atmos. Sci., 44, 298327, doi:10.1175/1520-0469(1987)044<0298:TZATCO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Rhines, P. B., 1975: Waves and turbulence on a beta-plane. J. Fluid Mech., 69, 417443, doi:10.1017/S0022112075001504.

  • Richards, K. J., N. A. Maximenko, F. O. Bryan, and H. Sasaki, 2006: Zonal jets in the Pacific Ocean. Geophys. Res. Lett.,33, L03605, doi:10.1029/2005GL024645.

  • Rypina, I. I., I. Kamenkovich, P. Berloff, and L. J. Pratt, 2012: Eddy-induced particle dispersion in the near-surface North Atlantic. J. Phys. Oceanogr., 42, 22062228, doi:10.1175/JPO-D-11-0191.1.

    • Search Google Scholar
    • Export Citation
  • Schlax, M. G., and D. B. Chelton, 2008: The influence of mesoscale eddies on the detection of quasi-zonal jets in the ocean. Geophys. Res. Lett.,35, L24602, doi:10.1029/2008GL035998.

  • Schlax, M. G., D. B. Chelton, and M. H. Freilich, 2001: Sampling errors in wind fields constructed from single and tandem Scatterometer datasets. J. Atmos. Oceanic Technol., 18, 10141036, doi:10.1175/1520-0426(2001)018<1014:SEIWFC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Shuckburgh, E., and P. Haynes, 2003: Diagnosing transport and mixing using a tracer-based coordinate system. Phys. Fluids, 15, 3342, doi:10.1063/1.1610471.

    • Search Google Scholar
    • Export Citation
  • Smith, K. S., 2007: The geography of linear baroclinic instability in Earth’s oceans. J. Mar. Res., 65, 655683, doi:10.1357/002224007783649484.

    • Search Google Scholar
    • Export Citation
  • Srinivasan, K., and W. R. Young, 2012: Zonostrophic instability. J. Atmos. Sci., 69, 16331656, doi:10.1175/JAS-D-11-0200.1.

  • Srinivasan, K., and W. R. Young, 2014: Reynolds stress and eddy diffusivity of β-plane shear flows. J. Atmos. Sci., 71, 21692185, doi:10.1175/JAS-D-13-0246.1.

    • Search Google Scholar
    • Export Citation
  • Sukoriansky, S., N. Dikovskaya, and B. Galperin, 2007: On the arrest of inverse energy cascade and the Rhines scale. J. Atmos. Sci., 64, 33123327, doi:10.1175/JAS4013.1.

    • Search Google Scholar
    • Export Citation
  • Thompson, A. F., 2008: The atmospheric ocean: Eddies and jets in the Antarctic Circumpolar Current. Philos. Trans. Roy. Soc. London, A366, 45294541, doi:10.1098/rsta.2008.0196.

    • Search Google Scholar
    • Export Citation
  • Thompson, A. F., 2010: Jet formation and evolution in baroclinic turbulence with simple topography. J. Phys. Oceanogr., 40, 257278, doi:10.1175/2009JPO4218.1.

    • Search Google Scholar
    • Export Citation
  • Thompson, A. F., and K. J. Richards, 2011: Low frequency variability of Southern Ocean jets. J. Geophys. Res.,116, C09022, doi:10.1029/2010JC006749.

  • Venaille, A., G. K. Vallis, and K. S. Smith, 2011: Baroclinic turbulence in the ocean: Analysis with primitive equation and quasigeostrophic simulations. J. Phys. Oceanogr., 41, 16051623, doi:10.1175/JPO-D-10-05021.1.

    • Search Google Scholar
    • Export Citation
  • Williams, G. P., 1978: Planetary circulations: 1. Barotropic representation of Jovian and terrestrial turbulence. J. Atmos. Sci., 35, 13991426, doi:10.1175/1520-0469(1978)035<1399:PCBROJ>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Woods, N. W., 2013: Physical controls on copepod aggregations in the Gulf of Maine. Ph.D. thesis, Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 213 pp.

  • Xu, C., X. Shang, and R. X. Huang, 2011: Estimate of global eddy energy generation/dissipation rate from altimetry data. Ocean Dyn., 61, 525541, doi:10.1007/s10236-011-0377-8.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 174 85 10
PDF Downloads 99 43 11

The Contribution of Striations to the Eddy Energy Budget and Mixing: Diagnostic Frameworks and Results in a Quasigeostrophic Barotropic System with Mean Flow

View More View Less
  • 1 Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California
  • | 2 Massachusetts Institute of Technology, Cambridge, Massachusetts
Restricted access

Abstract

Low-frequency oceanic motions have banded structures termed “striations.” Since these striations embedded in large-scale gyre flows can have large amplitudes, the authors investigated the effect of mean flow on their directions as well as their contribution to energetics and mixing using a β-plane, barotropic, quasigeostrophic ocean model. In spite of the model simplicity, striations are always found to exist regardless of the imposed barotropic mean flow. However, their properties are sensitive to the mean flow. Rhines jets move with the mean flow and are not necessarily striations. If the meridional component of the mean flow is large, Rhines jets become high-frequency motions; low-frequency striations still exist, but they are nonzonal, have small magnitudes, and contribute little to energetics and mixing. Otherwise, striations are zonal, dominated by Rhines jets, and contribute significantly to energetics and mixing. This study extends the theory of β-plane, barotropic turbulence, driven by white noise forcing at small scales, to include the effect of a constant mean flow. Theories developed in this study, based upon the Galilean invariance property, illustrate that the barotropic mean flow has no effect on total mixing rates, but does affect the energy cascades in the frequency domain. Diagnostic frameworks developed here can be useful to quantify the striations’ contribution to energetics and mixing in the ocean and more realistic models. A novel diagnostic formula is applied to estimating eddy diffusivities.

Corresponding author address: Ru Chen, Scripps Institution of Oceanography, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0230. E-mail: ruchen@alum.mit.edu

Abstract

Low-frequency oceanic motions have banded structures termed “striations.” Since these striations embedded in large-scale gyre flows can have large amplitudes, the authors investigated the effect of mean flow on their directions as well as their contribution to energetics and mixing using a β-plane, barotropic, quasigeostrophic ocean model. In spite of the model simplicity, striations are always found to exist regardless of the imposed barotropic mean flow. However, their properties are sensitive to the mean flow. Rhines jets move with the mean flow and are not necessarily striations. If the meridional component of the mean flow is large, Rhines jets become high-frequency motions; low-frequency striations still exist, but they are nonzonal, have small magnitudes, and contribute little to energetics and mixing. Otherwise, striations are zonal, dominated by Rhines jets, and contribute significantly to energetics and mixing. This study extends the theory of β-plane, barotropic turbulence, driven by white noise forcing at small scales, to include the effect of a constant mean flow. Theories developed in this study, based upon the Galilean invariance property, illustrate that the barotropic mean flow has no effect on total mixing rates, but does affect the energy cascades in the frequency domain. Diagnostic frameworks developed here can be useful to quantify the striations’ contribution to energetics and mixing in the ocean and more realistic models. A novel diagnostic formula is applied to estimating eddy diffusivities.

Corresponding author address: Ru Chen, Scripps Institution of Oceanography, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0230. E-mail: ruchen@alum.mit.edu
Save