An Idealized Model Study of Eddy Energetics in the Western Boundary “Graveyard”

Zhibin Yang Key Laboratory of Physical Oceanography and Frontiers Science Center for Deep Ocean Multispheres and Earth System, Ocean University of China, Qingdao, China
College of Oceanography, Hohai University, Nanjing, China
Centre for Ocean and Atmospheric Sciences, School of Environmental Sciences, University of East Anglia, Norwich, United Kingdom
Department of Atmospheric and Oceanic Sciences and Institute of Atmospheric Sciences, Fudan University, Shanghai, China

Search for other papers by Zhibin Yang in
Current site
Google Scholar
PubMed
Close
,
Xiaoming Zhai Centre for Ocean and Atmospheric Sciences, School of Environmental Sciences, University of East Anglia, Norwich, United Kingdom

Search for other papers by Xiaoming Zhai in
Current site
Google Scholar
PubMed
Close
,
David P. Marshall Department of Physics, University of Oxford, Oxford, United Kingdom

Search for other papers by David P. Marshall in
Current site
Google Scholar
PubMed
Close
, and
Guihua Wang Department of Atmospheric and Oceanic Sciences and Institute of Atmospheric Sciences, Fudan University, Shanghai, China
CMA-FDU Joint Laboratory of Marine Meteorology, Fudan University, Shanghai, China

Search for other papers by Guihua Wang in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Recent studies show that the western boundary acts as a “graveyard” for westward-propagating ocean eddies. However, how the eddy energy incident on the western boundary is dissipated remains unclear. Here we investigate the energetics of eddy–western boundary interaction using an idealized MIT ocean circulation model with a spatially variable grid resolution. Four types of model experiments are conducted: 1) single eddy cases, 2) a sea of random eddies, 3) with a smooth topography, and 4) with a rough topography. We find significant dissipation of incident eddy energy at the western boundary, regardless of whether the model topography at the western boundary is smooth or rough. However, in the presence of rough topography, not only the eddy energy dissipation rate is enhanced, but more importantly, the leading process for removing eddy energy in the model switches from bottom frictional drag as in the case of smooth topography to viscous dissipation in the ocean interior above the rough topography. Further analysis shows that the enhanced eddy energy dissipation in the experiment with rough topography is associated with greater anticyclonic, ageostrophic instability (AAI), possibly as a result of lee wave generation and nonpropagating form drag effect.

© 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: Xiaoming Zhai, xiaoming.zhai@uea.ac.uk

Abstract

Recent studies show that the western boundary acts as a “graveyard” for westward-propagating ocean eddies. However, how the eddy energy incident on the western boundary is dissipated remains unclear. Here we investigate the energetics of eddy–western boundary interaction using an idealized MIT ocean circulation model with a spatially variable grid resolution. Four types of model experiments are conducted: 1) single eddy cases, 2) a sea of random eddies, 3) with a smooth topography, and 4) with a rough topography. We find significant dissipation of incident eddy energy at the western boundary, regardless of whether the model topography at the western boundary is smooth or rough. However, in the presence of rough topography, not only the eddy energy dissipation rate is enhanced, but more importantly, the leading process for removing eddy energy in the model switches from bottom frictional drag as in the case of smooth topography to viscous dissipation in the ocean interior above the rough topography. Further analysis shows that the enhanced eddy energy dissipation in the experiment with rough topography is associated with greater anticyclonic, ageostrophic instability (AAI), possibly as a result of lee wave generation and nonpropagating form drag effect.

© 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: Xiaoming Zhai, xiaoming.zhai@uea.ac.uk
Save
  • Alford, M. H., A. Y. Shcherbina, and M. C. Gregg, 2013: Observations of near-inertial gravity waves radiating from a frontal jet. J. Phys. Oceanogr., 43, 12251239, https://doi.org/10.1175/JPO-D-12-0146.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Arbic, B. K., and Coauthors, 2009: Estimates of bottom flows and bottom boundary layer dissipation of the oceanic general circulation from global high-resolution models. J. Geophys. Res., 114, C02024, https://doi.org/10.1029/2008JC005072.

    • Search Google Scholar
    • Export Citation
  • Bell, T., 1975a: Lee waves in stratified flows with simple harmonic time dependence. J. Fluid Mech., 67, 705722, https://doi.org/10.1017/S0022112075000560.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bell, T., 1975b: Topographically generated internal waves in the open ocean. J. Geophys. Res., 80, 320327, https://doi.org/10.1029/JC080i003p00320.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brannigan, L., D. P. Marshall, A. C. N. Garabato, and A. J. G. Nurser, 2015: The seasonal cycle of submesoscale flows. Ocean Modell., 92, 6984, https://doi.org/10.1016/j.ocemod.2015.05.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chelton, D. B., M. G. Schlax, R. M. Samelson, and R. A. de Szoeke, 2007: Global observations of large oceanic eddies. Geophys. Res. Lett., 34, L15606, https://doi.org/10.1029/2007GL030812.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Clément, L., E. Frajka-Williams, K. Sheen, J. Brearley, and A. N. Garabato, 2016: Generation of internal waves by eddies impinging on the western boundary of the North Atlantic. J. Phys. Oceanogr., 46, 10671079, https://doi.org/10.1175/JPO-D-14-0241.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dewar, W. K., and A. M. Hogg, 2010: Topographic inviscid dissipation of balanced flow. Ocean Modell., 32, 113, https://doi.org/10.1016/j.ocemod.2009.03.007.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Duhaut, T. H., and D. N. Straub, 2006: Wind stress dependence on ocean surface velocity: Implications for mechanical energy input to ocean circulation. J. Phys. Oceanogr., 36, 202211, https://doi.org/10.1175/JPO2842.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Eden, C., and R. J. Greatbatch, 2008: Diapycnal mixing by mesoscale eddies. Ocean Modell., 23, 113120, https://doi.org/10.1016/j.ocemod.2008.04.006.

    • Crossref
    • 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, https://doi.org/10.1146/annurev.fluid.40.111406.102139.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gill, A. E., J. Green, and A. J. Simmons, 1974: Energy partition in large-scale ocean circulation and production of mid-ocean eddies. Deep-Sea Res. Oceanogr. Abstr., 21, 499528, https://doi.org/10.1016/0011-7471(74)90010-2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Goff, J. A., and T. H. Jordan, 1988: Stochastic modeling of seafloor morphology: Inversion of sea beam data for second-order statistics. J. Geophys. Res., 93, 13 58913 608, https://doi.org/10.1029/JB093iB11p13589.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Huang, R. X., 2005: Available potential energy in the world’s oceans. J. Mar. Res., 63, 141158, https://doi.org/10.1357/0022240053693770.

  • Huang, R. X., 2010: Ocean Circulation: Wind-Driven and Thermohaline Processes. Cambridge University Press, 806 pp.

    • Crossref
    • Export Citation
  • Hughes, C. W., and C. Wilson, 2008: Wind work on the geostrophic ocean circulation: An observational study of the effect of small scales in the wind stress. J. Geophys. Res., 113, C02016, https://doi.org/10.1029/2007JC004371.

    • Search Google Scholar
    • Export Citation
  • Jansen, M. F., and I. M. Held, 2014: Parameterizing subgrid-scale eddy effects using energetically consistent backscatter. Ocean Modell., 80, 3648, https://doi.org/10.1016/j.ocemod.2014.06.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jansen, M. F., A. J. Adcroft, R. Hallberg, and I. M. Held, 2015: Parameterization of eddy fluxes based on a mesoscale energy budget. Ocean Modell., 92, 2841, https://doi.org/10.1016/j.ocemod.2015.05.007.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Klymak, J. M., 2018: Nonpropagating form drag and turbulence due to stratified flow over large-scale abyssal hill topography. J. Phys. Oceanogr., 48, 23832395, https://doi.org/10.1175/JPO-D-17-0225.1.

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lee, D., and P. Niiler, 1998: The inertial chimney: The near-inertial energy drainage from the ocean surface to the deep layer. J. Geophys. Res., 103, 75797591, https://doi.org/10.1029/97JC03200.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mak, J., J. R. Maddison, D. P. Marshall, and D. R. Munday, 2018: Implementation of a geometrically informed and energetically constrained mesoscale eddy parameterization in an ocean circulation model. J. Phys. Oceanogr., 48, 23632382, https://doi.org/10.1175/JPO-D-18-0017.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, D. P., and A. J. Adcroft, 2010: Parameterization of ocean eddies: Potential vorticity mixing, energetics and Arnold’s first stability theorem. Ocean Modell., 32, 188204, https://doi.org/10.1016/j.ocemod.2010.02.001.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, D. P., J. R. Maddison, and P. S. Berloff, 2012: A framework for parameterizing eddy potential vorticity fluxes. J. Phys. Oceanogr., 42, 539557, https://doi.org/10.1175/JPO-D-11-048.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, J., A. Adcroft, C. Hill, L. Perelman, and C. Heisey, 1997: A finite-volume, incompressible Navier-Stokes model for studies of the ocean on parallel computers. J. Geophys. Res., 102, 57535766, https://doi.org/10.1029/96JC02775.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., 2003: Diagnostic force balance and its limits. Nonlinear Processes in Geophysical Fluid Dynamics, O. V. Fuentes, J. Sheinbaum, and J. Ochoa, Eds., Kluwer, 287–304.

    • Crossref
    • Export Citation
  • McWilliams, J. C., and I. Yavneh, 1998: Fluctuation growth and instability associated with a singularity in the balanced equations. Phys. Fluids, 10, 25872596, https://doi.org/10.1063/1.869772.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., M. J. Molemaker, and I. Yavneh, 2004: Ageostrophic, anticyclonic instability of a geostrophic, barotropic boundary current. Phys. Fluids, 16, 37203725, https://doi.org/10.1063/1.1785132.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Molemaker, M. J., J. C. McWilliams, and I. Yavneh, 2005: Baroclinic instability and loss of balance. J. Phys. Oceanogr., 35, 15051517, https://doi.org/10.1175/JPO2770.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Müller, P., J. C. McWilliams, and M. J. Molemaker, 2005: Routes to dissipation in the ocean: The 2D/3D turbulence conundrum. Marine Turbulence, H. B. J. Simpson and J. Sündermann, Eds., Cambridge University Press, 397–405.

  • Nagai, T., A. Tandon, E. Kunze, and A. Mahadevan, 2015: Spontaneous generation of near-inertial waves by the Kuroshio Front. J. Phys. Oceanogr., 45, 23812406, https://doi.org/10.1175/JPO-D-14-0086.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Naveira Garabato, A. C., and Coauthors, 2019: Rapid mixing and exchange of deep-ocean waters in an abyssal boundary current. Proc. Natl. Acad. Sci. USA, 116, 13 23313 238, https://doi.org/10.1073/pnas.1904087116.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nikurashin, M., and R. Ferrari, 2010a: Radiation and dissipation of internal waves generated by geostrophic flows impinging on small-scale topography: Theory. J. Phys. Oceanogr., 40, 10551074, https://doi.org/10.1175/2009JPO4199.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nikurashin, M., and R. Ferrari, 2010b: Radiation and dissipation of internal waves generated by geostrophic flows impinging on small-scale topography: Application to the Southern Ocean. J. Phys. Oceanogr., 40, 20252042, https://doi.org/10.1175/2010JPO4315.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nikurashin, M., G. K. Vallis, and A. Adcroft, 2013: Routes to energy dissipation for geostrophic flows in the Southern Ocean. Nat. Geosci., 6, 4851, https://doi.org/10.1038/ngeo1657.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Oort, A., S. Ascher, S. Levitus, and J. Peixóto, 1989: New estimates of the available potential energy in the World Ocean. J. Geophys. Res., 94, 31873200, https://doi.org/10.1029/JC094iC03p03187.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Oort, A., L. Anderson, and J. Peixóto, 1994: Estimates of the energy cycle of the oceans. J. Geophys. Res., 99, 76657688, https://doi.org/10.1029/93JC03556.

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

    • Crossref
    • Export Citation
  • Saenko, O., X. Zhai, W. Merryfield, and W. Lee, 2012: The combined effect of tidally and eddy-driven diapycnal mixing on the large-scale ocean circulation. J. Phys. Oceanogr., 42, 526538, https://doi.org/10.1175/JPO-D-11-0122.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sen, A., R. B. Scott, and B. K. Arbic, 2008: Global energy dissipation rate of deep-ocean low-frequency flows by quadratic bottom boundary layer drag: Computations from current-meter data. Geophys. Res. Lett., 35, L09606, https://doi.org/10.1029/2008GL033407.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shakespeare, C. J., and A. M. Hogg, 2017: Spontaneous surface generation and interior amplification of internal waves in a regional-scale ocean model. J. Phys. Oceanogr., 47, 811826, https://doi.org/10.1175/JPO-D-16-0188.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shakespeare, C. J., and A. M. Hogg, 2018: The life cycle of spontaneously generated internal waves. J. Phys. Oceanogr., 48, 343359, https://doi.org/10.1175/JPO-D-17-0153.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Staquet, C., and J. Sommeria, 2002: Internal gravity waves: From instabilities to turbulence. Annu. Rev. Fluid Mech., 34, 559593, https://doi.org/10.1146/annurev.fluid.34.090601.130953.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stöber, U., M. Walter, C. Mertens, and M. Rhein, 2008: Mixing estimates from hydrographic measurements in the deep western boundary current of the North Atlantic. Deep-Sea Res. I, 55, 721736, https://doi.org/10.1016/j.dsr.2008.03.006.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Teague, W. J., M. J. Carron, and P. J. Hogan, 1990: A comparison between the generalized digital environmental model and Levitus climatologies. J. Geophys. Res., 95, 71677183, https://doi.org/10.1029/JC095iC05p07167.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thomas, L., J. Taylor, R. Ferrari, and T. Joyce, 2013: Symmetric instability in the Gulf Stream. Deep-Sea Res II., 91, 96110, https://doi.org/10.1016/j.dsr2.2013.02.025.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • von Storch, J. S., C. Eden, I. Fast, H. Haak, D. Hernández-Deckers, E. Maier-Reimer, J. Marotzke, and D. Stammer, 2012: An estimate of the Lorenz energy cycle for the world ocean based on the 1/10° STORM/NCEP simulation. J. Phys. Oceanogr., 42, 21852205, https://doi.org/10.1175/JPO-D-12-079.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Walter, M., C. Mertens, and M. Rhein, 2005: Mixing estimates from a large-scale hydro-graphic survey in the North Atlantic. Geophys. Res. Lett., 32, L13605, https://doi.org/10.1029/2005GL022471.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, P., J. McWilliams, and Z. Kizner, 2012: Ageostrophic instability in rotating shallow water. J. Fluid Mech., 712, 327353, https://doi.org/10.1017/jfm.2012.422.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, Y., and A. L. Stewart, 2018: Eddy dynamics over continental slopes under retrograde winds: Insights from a model inter-comparison. Ocean Modell., 121, 118, https://doi.org/10.1016/j.ocemod.2017.11.006.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wenegrat, J. O., J. Callies, and L. N. Thomas, 2018: Submesoscale baroclinic instability in the bottom boundary layer. J. Phys. Oceanogr., 48, 25712592, https://doi.org/10.1175/JPO-D-17-0264.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Williams, P. D., T. W. Haine, and P. L. Read, 2008: Inertia–gravity waves emitted from balanced flow: Observations, properties, and consequences. J. Atmos. Sci., 65, 35433556, https://doi.org/10.1175/2008JAS2480.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wunsch, C., 1998: The work done by the wind on the oceanic general circulation. J. Phys. Oceanogr., 28, 23322340, https://doi.org/10.1175/1520-0485(1998)028<2332:TWDBTW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xu, C., X. Zhai, and X.-D. Shang, 2016: Work done by atmospheric winds on mesoscale ocean eddies. Geophys. Res. Lett., 43, 12 17412 180, https://doi.org/10.1002/2016GL071275.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhai, X., and R. J. Greatbatch, 2007: Wind work in a model of the northwest Atlantic Ocean. Geophys. Res. Lett., 34, L04606, https://doi.org/10.1029/2006GL028907.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhai, X., and D. P. Marshall, 2013: Vertical eddy energy fluxes in the North Atlantic subtropical and subpolar gyres. J. Phys. Oceanogr., 43, 95103, https://doi.org/10.1175/JPO-D-12-021.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhai, X., H. L. Johnson, and D. P. Marshall, 2010: Significant sink of ocean-eddy energy near western boundaries. Nat. Geosci., 3, 608612, https://doi.org/10.1038/ngeo943.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhai, X., H. L. Johnson, D. P. Marshall, and C. Wunsch, 2012: On the wind power input to the ocean general circulation. J. Phys. Oceanogr., 42, 13571365, https://doi.org/10.1175/JPO-D-12-09.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, Z., Y. Zhang, W. Wang, and R. X. Huang, 2013: Universal structure of mesoscale eddies in the ocean. Geophys. Res. Lett., 40, 36773681, https://doi.org/10.1002/grl.50736.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 292 0 0
Full Text Views 468 195 17
PDF Downloads 462 147 14