Parameterization of Submesoscale Mixed Layer Restratification under Sea Ice

Kalyan Shrestha aSchool of Oceanography, University of Washington, Seattle, Washington

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Georgy E. Manucharyan aSchool of Oceanography, University of Washington, Seattle, Washington

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Abstract

Commonly used parameterization of mixed layer instabilities in general circulation models was developed for temperate oceans and does not take into account the presence of sea ice in any way. However, the ice–ocean drag provides a strong mechanical coupling between the sea ice and the surface ocean currents and hence may affect mixed layer restratification processes. Here we use idealized simulations of mixed layer instabilities to demonstrate that the sea ice dramatically suppresses the eddy-driven overturning in the mixed layer by dissipating the eddy kinetic energy generated during instabilities. Considering the commonly used viscous-plastic sea ice rheology, we developed an improvement to the existing mixed layer overturning parameterization, making it explicitly dependent on sea ice concentration. Below the critical sea ice concentration of about 0.68, the internal sea ice stresses are very weak and the conventional parameterization holds. At higher concentrations, the sea ice cover starts acting as a nearly immobile surface lid, inducing strong dissipation of submesoscale eddies and reducing the intensity of the restratification streamfunction up to a factor of 4 for a fully ice-covered ocean. Our findings suggest that climate projection models might be exaggerating the restratification processes under sea ice, which could contribute to biases in mixed layer depth, salinity, ice–ocean heat fluxes, and sea ice cover.

© 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: Kalyan Shrestha, kalyansh@uw.edu

Abstract

Commonly used parameterization of mixed layer instabilities in general circulation models was developed for temperate oceans and does not take into account the presence of sea ice in any way. However, the ice–ocean drag provides a strong mechanical coupling between the sea ice and the surface ocean currents and hence may affect mixed layer restratification processes. Here we use idealized simulations of mixed layer instabilities to demonstrate that the sea ice dramatically suppresses the eddy-driven overturning in the mixed layer by dissipating the eddy kinetic energy generated during instabilities. Considering the commonly used viscous-plastic sea ice rheology, we developed an improvement to the existing mixed layer overturning parameterization, making it explicitly dependent on sea ice concentration. Below the critical sea ice concentration of about 0.68, the internal sea ice stresses are very weak and the conventional parameterization holds. At higher concentrations, the sea ice cover starts acting as a nearly immobile surface lid, inducing strong dissipation of submesoscale eddies and reducing the intensity of the restratification streamfunction up to a factor of 4 for a fully ice-covered ocean. Our findings suggest that climate projection models might be exaggerating the restratification processes under sea ice, which could contribute to biases in mixed layer depth, salinity, ice–ocean heat fluxes, and sea ice cover.

© 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: Kalyan Shrestha, kalyansh@uw.edu

Supplementary Materials

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  • Abernathey, R. P., J. Marshall, and D. Ferreira, 2011: The dependence of southern ocean meridional overturning on wind stress. J. Phys. Oceanogr., 41, 22612278, https://doi.org/10.1175/JPO-D-11-023.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Abernathey, R. P., I. Cerovecki, P. R. Holland, E. Newsom, M. Mazloff, and L. D. Talley, 2016: Water-mass transformation by sea ice in the upper branch of the southern ocean overturning. Nat. Geosci., 9, 596601, https://doi.org/10.1038/ngeo2749.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Andrews, D. G., J. R. Holton, and C. B. Leovy, 1987: Middle Atmosphere Dynamics. International Geophysical Series, Vol. 40, Academic Press, 489 pp.

    • Search Google Scholar
    • Export Citation
  • Bachman, S. D., and J. R. Taylor, 2016: Numerical simulations of the equilibrium between eddy-induced restratification and vertical mixing. J. Phys. Oceanogr., 46, 919935, https://doi.org/10.1175/JPO-D-15-0110.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bachman, S. D., J. R. Taylor, K. A. Adams, and P. J. Hosegood, 2017: Mesoscale and submesoscale effects on mixed layer depth in the Southern Ocean. J. Phys. Oceanogr., 47, 21732188, https://doi.org/10.1175/JPO-D-17-0034.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Biddle, L. C., and S. Swart, 2020: The observed seasonal cycle of submesoscale processes in the Antarctic marginal ice zone. J. Geophys. Res. Oceans, 125, e2019JC015587, https://doi.org/10.1029/2019JC015587.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Boccaletti, G., R. Ferrari, and B. Fox-Kemper, 2007: Mixed layer instabilities and restratification. J. Phys. Oceanogr., 37, 22282250, https://doi.org/10.1175/JPO3101.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brenner, S., L. Rainville, J. Thomson, and C. Lee, 2020: The evolution of a shallow front in the Arctic marginal ice zone. Elem. Sci. Anth., 8, 17, https://doi.org/10.1525/elementa.413.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brink, K. H., and D. A. Cherian, 2013: Instability of an idealized tidal mixing front: Symmetric instabilities and frictional effects. J. Mar. Res., 71, 425450, https://doi.org/10.1357/002224013812587582.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Buckley, J. R., T. Gammelsrod, J. A. Johannessen, O. M. Johannessen, and L. P. Roed, 1979: Upwelling: Oceanic structure at the edge of the Arctic ice pack in winter. Science, 203, 165167, https://doi.org/10.1126/science.203.4376.165.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Callies, J., R. Ferrari, J. Klymak, and J. Gula, 2015: Seasonality in submesoscale turbulence. Nat. Commun., 6, 6862, https://doi.org/10.1038/ncomms7862.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, S.-H., C.-J. Chen, and J. A. Lerczak, 2019: On baroclinic instability over continental shelves: Testing the utility of Eady-type models. J. Phys. Oceanogr., 50, 333, https://doi.org/10.1175/JPO-D-19-0175.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cohanim, K., K. X. Zhao, and A. L. Stewart, 2021: Dynamics of eddies generated by sea ice leads. J. Phys. Oceanogr., 51, 30713092, https://doi.org/10.1175/JPO-D-20-0169.1.

    • Search Google Scholar
    • Export Citation
  • Csanady, G. T., 2001: Air-Sea Interaction: Laws and Mechanisms. Cambridge University Press, 248 pp.

  • Damsgaard, A., A. Adcroft, and O. Sergienko, 2018: Application of discrete element methods to approximate sea ice dynamics. J. Adv. Model. Earth Syst., 10, 22282244, https://doi.org/10.1029/2018MS001299.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Davy, R., and S. Outten, 2020: The Arctic surface climate in CMIP6: Status and developments since CMIP5. J. Climate, 33, 80478068, https://doi.org/10.1175/JCLI-D-19-0990.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • du Plessis, M., S. Swart, I. J. Ansorge, A. Mahadevan, and A. F. Thompson, 2019: Southern ocean seasonal restratification delayed by submesoscale wind–front interactions. J. Phys. Oceanogr., 49, 10351053, https://doi.org/10.1175/JPO-D-18-0136.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Eady, E. T., 1949: Long waves and cyclone waves. Tellus, 1, 3352, https://doi.org/10.3402/tellusa.v1i3.8507.

  • 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
  • Fox-Kemper, B., and R. Ferrari, 2008: Parameterization of mixed layer eddies. Part II: Prognosis and impact. J. Phys. Oceanogr., 38, 11661179, https://doi.org/10.1175/2007JPO3788.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fox-Kemper, B., R. Ferrari, and R. Hallberg, 2008: Parameterization of mixed layer eddies. Part I: Theory and diagnosis. J. Phys. Oceanogr., 38, 11451165, https://doi.org/10.1175/2007JPO3792.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fox-Kemper, B., and Coauthors, 2011: Parameterization of mixed layer eddies. III: Implementation and impact in global ocean climate simulations. Ocean Modell., 39, 6178, https://doi.org/10.1016/j.ocemod.2010.09.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gallaher, S. G., 2019: The importance of capturing late melt season sea ice conditions for modeling the western Arctic Ocean boundary layer. Elem. Sci. Anth., 7, 53, https://doi.org/10.1525/elementa.391.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gallaher, S. G., T. P. Stanton, W. J. Shaw, S. T. Cole, J. M. Toole, J. P. Wilkinson, T. Maksym, and B. Hwang, 2016: Evolution of a Canada basin ice ocean boundary layer and mixed layer across a developing thermodynamically forced marginal ice zone. J. Geophys. Res. Oceans, 121, 62236250, https://doi.org/10.1002/2016JC011778.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Garrett, C. J. R., and J. W. Loder, 1981: Dynamical aspects of shallow sea fronts. Philos. Trans. Roy. Soc., A302, 563581, https://doi.org/10.1098/rsta.1981.0183.

    • Search Google Scholar
    • Export Citation
  • Gent, P. R., and J. C. McWilliams, 1990: Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20, 150155, https://doi.org/10.1175/1520-0485(1990)020<0150:IMIOCM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Giddy, I., S. Swart, M. du Plessis, A. F. Thompson, and S.-A. Nicholson, 2021: Stirring of sea-ice meltwater enhances submesoscale fronts in the Southern Ocean. J. Geophys. Res. Oceans, 126, e2020JC016814, https://doi.org/10.1029/2020JC016814.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gula, J., M. J. Molemaker, and J. C. McWilliams, 2016: Topographic generation of submesoscale centrifugal instability and energy dissipation. Nat. Commun., 7, 12811, https://doi.org/10.1038/ncomms12811.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gupta, M., J. Marshall, H. Song, J.‐M. Campin, and G. Meneghello, 2020: Sea‐ice melt driven by ice‐ocean stresses on the mesoscale. J. Geophys. Res. Oceans, 125, e2020JC016404, https://doi.org/10.1029/2020JC016404.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Haine, T. W. N., and J. Marshall, 1998: Gravitational, symmetric, and baroclinic instability of the ocean mixed layer. J. Phys. Oceanogr., 28, 634658, https://doi.org/10.1175/1520-0485(1998)028<0634:GSABIO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Herman, A., 2016: Discrete-element bonded-particle sea ice model design, version 1.3 a–Model description and implementation. Geosci. Model Dev., 9, 12191241, https://doi.org/10.5194/gmd-9-1219-2016.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hibler, W. D. I., 1979: A dynamic thermodynamic sea ice model. J. Phys. Oceanogr., 9, 815846, https://doi.org/10.1175/1520-0485(1979)009<0815:ADTSIM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hopkins, M. A., 2004: A discrete element Lagrangian sea ice model. Eng. Comput., 21, 409421, https://doi.org/10.1108/02644400410519857.

  • Horvat, C., and E. Tziperman, 2018: Understanding melting due to ocean eddy heat fluxes at the edge of sea-ice floes. Geophys. Res. Lett., 45, 97219730, https://doi.org/10.1029/2018GL079363.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Horvat, C., and Coauthors, 2019: Estimating the sea ice floe size distribution using satellite altimetry: Theory, climatology, and model comparison. Cryosphere, 13, 28692885, https://doi.org/10.5194/tc-13-2869-2019.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Klein, P., and G. Lapeyre, 2009: The oceanic vertical pump induced by mesoscale and submesoscale turbulence. Annu. Rev. Mar. Sci., 1, 351375, https://doi.org/10.1146/annurev.marine.010908.163704.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Krishfield, R., A. Toole, A. Proshutinsky, and M.-L. Timmermans, 2008: Automated ice-tethered profilers for seawater observations under pack ice in all seasons. J. Atmos. Oceanic Technol., 25, 20912105, https://doi.org/10.1175/2008JTECHO587.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Langleben, M. P., 1982: Water drag coefficient of first-year sea ice. J. Geophys. Res., 87, 573578, https://doi.org/10.1029/JC087iC01p00573.

  • Langmuir, I., 1938: Surface motion of water induced by wind. Science, 87, 119123, https://doi.org/10.1126/science.87.2250.119.

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lemieux, J.-F., B. Tremblay, J. Sedlacek, P. Tupper, S. Thomas, D. Huard, and J.-P. Auclair, 2010: Improving the numerical convergence of viscous-plastic sea ice models with the Jacobian-free Newton-Krylov method. J. Comput. Phys., 229, 28402852, https://doi.org/10.1016/j.jcp.2009.12.011.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Losch, M., D. Menemenlis, P. Heimbach, J.-M. Campin, and C. Hill, 2010: On the formulation of sea-ice models. Part 1: Effects of different solver implementations and parameterizations. Ocean Modell., 33, 129144, https://doi.org/10.1016/j.ocemod.2009.12.008.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lu, K., T. Weingartner, S. Danielson, P. Winsor, E. Dobbins, K. Martini, and H. Statscewich, 2015: Lateral mixing across ice meltwater fronts of the Chukchi Sea shelf. Geophys. Res. Lett., 42, 67546761, https://doi.org/10.1002/2015GL064967.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mahadevan, A., E. D’Asaro, C. Lee, and M. J. Perry, 2012: Eddy-driven stratification initiates North Atlantic spring phytoplankton blooms. Science, 337, 5458, https://doi.org/10.1126/science.1218740.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Manucharyan, G. E., and M. L. Timmermans, 2013: Generation and separation of mesoscale eddies from surface ocean fronts. J. Phys. Oceanogr., 43, 25452562, https://doi.org/10.1175/JPO-D-13-094.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Manucharyan, G. E., and A. F. Thompson, 2017: Submesoscale sea ice-ocean interactions in marginal ice zones. J. Geophys. Res. Oceans, 122, 94559475, https://doi.org/10.1002/2017JC012895.

    • 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
  • McIntosh, P. C., and T. J. McDougall, 1996: Isopycnal averaging and the residual mean circulation. J. Phys. Oceanogr., 26, 16551660, https://doi.org/10.1175/1520-0485(1996)026<1655:IAATRM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., 2016: Submesoscale currents in the ocean. Proc. Roy. Soc., A472, 132, https://doi.org/10.1098/rspa.2016.0117.

  • McWilliams, J. C., 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
  • Melville, W. K., 1996: The role of surface-wave breaking in air-sea interaction. Annu. Rev. Fluid Mech., 28, 279321, https://doi.org/10.1146/annurev.fl.28.010196.001431.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mensa, J. A., and M. L. Timmermans, 2017: Characterizing the seasonal cycle of upper-ocean flows under multi-year sea ice. Ocean Modell., 113, 115130, https://doi.org/10.1016/j.ocemod.2017.03.009.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Molemaker, M., J. McWilliams, and M. K. Dewar, 2015: Submesoscale instability and generation of mesoscale anticyclones near a separation of the California Undercurrent. J. Phys. Oceanogr., 45, 613629, https://doi.org/10.1175/JPO-D-13-0225.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Notz, D., and S. Community, 2020: Arctic sea ice in CMIP6. Geophys. Res. Lett., 47, e2019GL086749, https://doi.org/10.1029/2019GL086749.

  • Ou, H. W., 1984: Geostrophic adjustment: A mechanism for frontogenesis? J. Phys. Oceanogr., 14, 9941000, https://doi.org/10.1175/1520-0485(1984)014<0994:GAAMFF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ou, H. W., and A. L. Gordon, 1986: Spin-down of baroclinic eddies under sea ice. J. Geophys. Res., 91, 76237630, https://doi.org/10.1029/JC091iC06p07623.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Perovich, D. K., 2003: Thin and thinner: Sea ice mass balance measurements during SHEBA. J. Geophys. Res., 108, 8050, https://doi.org/10.1029/2001JC001079.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pope, S., 2000: Turbulent Flows. Cambridge University Press, 802 pp.

  • Renault, L., J. C. McWilliams, and J. Gula, 2018: Dampening of submesoscale currents by air-sea stress coupling in the Californian upwelling system. Sci. Rep., 8, 13388, https://doi.org/10.1038/s41598-018-31602-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Roach, L. A., J. Dorr, C. R. Holmes, F. Massonnet, E. W. Blockley, D. Notz, and C. M. Bitz, 2020: Antarctic sea ice in CMIP6. Geophys. Res. Lett., 47, e2019GL086729, https://doi.org/10.1029/2019GL086729.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rothrock, D. A., 1975: The mechanical behavior of pack ice. Annu. Rev. Earth Planet. Sci., 3, 317342, https://doi.org/10.1146/annurev.ea.03.050175.001533.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sallée, J.-B., R. J. Matear, S. R. Rintoul, and A. Lenton, 2012: Localized subduction of anthropogenic carbon dioxide in the southern hemisphere oceans. Nat. Geosci., 5, 579584, https://doi.org/10.1038/ngeo1523.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shrestha, K., W. Anderson, and J. Kuehl, 2018: Langmuir turbulence in coastal zones: Structure and length scales. J. Phys. Oceanogr., 48, 10891115, https://doi.org/10.1175/JPO-D-17-0067.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smith, G. C., and Coauthors, 2019: Polar ocean observations: A critical gap in the observing system and its effect on environmental predictions from hours to a season. Front. Mar. Sci., 6, 429, https://doi.org/10.3389/fmars.2019.00429.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Spall, M. A., 1997: Baroclinic jets in confluent flow. J. Phys. Oceanogr., 27, 10541071, https://doi.org/10.1175/1520-0485(1997)027<1054:BJICF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stone, P. H., 1970: On non-geostrophic baroclinic stability: Part II. J. Atmos. Sci., 27, 721726, https://doi.org/10.1175/1520-0469(1970)027<0721:ONGBSP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stroeve, J. C., M. C. Serreze, M. M. Holland, J. E. Kay, J. Malanik, and A. P. Barrett, 2012: The Arctic’s rapidly shrinking sea ice cover: A research synthesis. Climatic Change, 110, 10051027, https://doi.org/10.1007/s10584-011-0101-1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Su, Z., J. Wang, P. Klein, A. F. Thompson, and D. Menemenlis, 2018: Ocean submesoscales as a key component of the global heat budget. Nat. Commun., 9, 775, https://doi.org/10.1038/s41467-018-02983-w.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Swart, S., M. D. du Plessis, A. F. Thompson, L. C. Biddle, I. Giddy, T. Linders, M. Mohrmann, and S.-A. Nicholson, 2020: Submesoscale fronts in the Antarctic marginal ice zone and their response to wind forcing. Geophys. Res. Lett., 47, e2019GL086649, https://doi.org/10.1029/2019GL086649.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tandon, A., and C. Garrett, 1995: Geostrophic adjustment and restratification of a mixed layer with horizontal gradients above a stratified layer. J. Phys. Oceanogr., 25, 22292241, https://doi.org/10.1175/1520-0485(1995)025<2229:GAAROA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thomas, L. N., 2008: Formation of intrathermocline eddies at ocean fronts by wind-driven destruction of potential vorticity. Dyn. Atmos. Oceans, 45, 252273, https://doi.org/10.1016/j.dynatmoce.2008.02.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thomas, L. N., and P. B. Rhines, 2002: Nonlinear stratified spin-up. J. Fluid Mech., 473, 211244, https://doi.org/10.1017/S0022112002002367.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thomas, L. N., and C. M. Lee, 2005: Intensification of ocean fronts by down-front winds. J. Phys. Oceanogr., 35, 10861102, https://doi.org/10.1175/JPO2737.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thomas, L. N., and R. Ferrari, 2008: Friction, frontogenesis, and the stratification of the surface mixed layer. J. Phys. Oceanogr., 38, 25012518, https://doi.org/10.1175/2008JPO3797.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thompson, A., A. Lazar, C. Buckingham, A. Naveira Garabato, G. Damerell, and K. Heywood, 2016: Open-ocean submesoscale motions: A full seasonal cycle of mixed layer instabilities from gliders. J. Phys. Oceanogr., 46, 12851307, https://doi.org/10.1175/JPO-D-15-0170.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thompson, L., 2000: Ekman layers and two-dimensional frontogenesis in the upper ocean. J. Geophys. Res., 105, 64376451, https://doi.org/10.1029/1999JC900336.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tietsche, S., and Coauthors, 2014: Seasonal to interannual Arctic sea ice predictability in current global climate models. Geophys. Res. Lett., 41, 10351043, https://doi.org/10.1002/2013GL058755.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tilling, R. L., A. Ridout, and A. Shepherd, 2018: Estimating arctic sea ice thickness and volume using CryoSat-2 radar altimeter data. Adv. Space Res., 62, 12031225, https://doi.org/10.1016/j.asr.2017.10.051.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Timmermans, M. L., S. Cole, and J. Toole, 2012: Horizontal density structure and restratification of the Arctic Ocean surface layer. J. Phys. Oceanogr., 42, 659668, https://doi.org/10.1175/JPO-D-11-0125.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Toole, J. M., R. A. Krishfield, M. L. Timmermans, and A. Proshutinsky, 2011: The ice-tethered profiler: Argo of the Arctic. Oceanography, 24, 126135, https://doi.org/10.5670/oceanog.2011.64.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Toyota, T., S. Takatsuji, and M. Nakayama, 2006: Characteristics of sea ice floe size distribution in the seasonal ice zone. Geophys. Res. Lett., 33, L02616, https://doi.org/10.1029/2005GL024556.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Turner, A. K., K. J. Peterson, and D. Bolintineanu, 2021: Geometric remapping of particle distributions in the discrete element model for sea ice (DEMSI v0.0). Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2021-199.

    • Search Google Scholar
    • Export Citation
  • Wenegrat, J. O., and M. J. McPhaden, 2016: Wind, waves, and fronts: Frictional effects in a generalized Ekman model. J. Phys. Oceanogr., 46, 371394, https://doi.org/10.1175/JPO-D-15-0162.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wenegrat, J. O., L. N. Thomas, J. Gula, and J. C. McWilliams, 2018: Effects of the submesoscale on the potential vorticity budget of ocean mode waters. J. Phys. Oceanogr., 48, 21412165, https://doi.org/10.1175/JPO-D-17-0219.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Williams, G. P., and J. B. Robinson, 1974: Generalized Eady waves with Ekman pumping. J. Atmos. Sci., 31, 17681776, https://doi.org/10.1175/1520-0469(1974)031<1768:GEWWEP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhan, P., A. C. Subramanian, F. Yao, A. R. Kartadikaria, D. Guo, and I. Hoteit, 2016: The eddy kinetic energy budget in the Red Sea. J. Geophys. Res. Oceans, 121, 4732, https://doi.org/10.1002/2015JC011589.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, J., and W. D. I. Hibler, 1997: On an efficient numerical method for modeling sea ice dynamics. J. Geophys. Res., 102, 86918702, https://doi.org/10.1029/96JC03744.

    • Crossref
    • Search Google Scholar
    • Export Citation
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