Passive Tracer Dispersion by Idealized Flows across Rossby Numbers

Madhav Sirohi aInternational Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore, India

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Jim Thomas aInternational Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore, India
bCentre for Applicable Mathematics, Tata Institute of Fundamental Research, Bangalore, India

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Abstract

In this work, we compare and contrast the phenomenological changes in passive tracer dispersion at asymptotically small to O(1) Rossby numbers using idealized two-dimensional flows generated by a two-vertical-mode model. With increasing flow Rossby numbers, we find that the forward flux of tracer variance increases monotonically and the tracer variance spectra show severe depletion of the tracer field, indicating enhanced stirring of the tracer by higher Rossby number flows. On examining the physical structure of the tracer flux and its connection to strain- and vorticity-dominant regions in the flow, we find that a major share of the tracer flux is located in high-shear, strain-dominant regions between coherent vortices at low Rossby numbers, while at higher Rossby numbers, the tracer flux is primarily located in vorticity-dominant regions that are composed of fragmented bits of vorticity. The tracer field is anticorrelated with the tracer flux, i.e., tracer variance is higher in physical regions where tracer flux is lower and vice versa. Our results highlight multiple anisotropic features of submesoscales that enhance tracer dispersion at O(1) Rossby numbers and emphasize the need to take these into account while developing parameterizations for large-scale models.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Jim Thomas, jimthomas.edu@gmail.com

Abstract

In this work, we compare and contrast the phenomenological changes in passive tracer dispersion at asymptotically small to O(1) Rossby numbers using idealized two-dimensional flows generated by a two-vertical-mode model. With increasing flow Rossby numbers, we find that the forward flux of tracer variance increases monotonically and the tracer variance spectra show severe depletion of the tracer field, indicating enhanced stirring of the tracer by higher Rossby number flows. On examining the physical structure of the tracer flux and its connection to strain- and vorticity-dominant regions in the flow, we find that a major share of the tracer flux is located in high-shear, strain-dominant regions between coherent vortices at low Rossby numbers, while at higher Rossby numbers, the tracer flux is primarily located in vorticity-dominant regions that are composed of fragmented bits of vorticity. The tracer field is anticorrelated with the tracer flux, i.e., tracer variance is higher in physical regions where tracer flux is lower and vice versa. Our results highlight multiple anisotropic features of submesoscales that enhance tracer dispersion at O(1) Rossby numbers and emphasize the need to take these into account while developing parameterizations for large-scale models.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Jim Thomas, jimthomas.edu@gmail.com
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  • 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.

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

    • Search Google Scholar
    • Export Citation
  • Busecke, J. J. M., and R. P. Abernathey, 2019: Ocean mesoscale mixing linked to climate variability. Sci. Adv., 5, eaav5014, https://doi.org/10.1126/sciadv.aav5014.

    • Search Google Scholar
    • Export Citation
  • Capet, X., J. C. McWilliams, M. J. Molemaker, and A. F. Shchepetkin, 2008: Mesoscale to submesoscale transition in the California current system. Part I: Flow structure, eddy flux, and observational tests. J. Phys. Oceanogr., 38, 2943, https://doi.org/10.1175/2007JPO3671.1.

    • Search Google Scholar
    • Export Citation
  • Chouksey, A., A. Griesel, M. Chouksey, and C. Eden, 2022: Changes in global ocean circulation due to isopycnal diffusion. J. Phys. Oceanogr., 52, 22192235, https://doi.org/10.1175/JPO-D-21-0205.1.

    • Search Google Scholar
    • Export Citation
  • Clément, L., E. Frajka-Williams, K. L. Sheen, J. A. Brearley, and A. C. 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.

    • Search Google Scholar
    • Export Citation
  • Cole, S. T., and D. L. Rudnick, 2012: The spatial distribution and annual cycle of upper ocean thermohaline structure. J. Geophys. Res., 117, C02027, https://doi.org/10.1029/2011JC007033.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Gnanadesikan, A., M.-A. Pradal, and R. Abernathey, 2015: Isopycnal mixing by mesoscale eddies significantly impacts oceanic anthropogenic Carbon uptake. Geophys. Res. Lett., 42, 42494255, https://doi.org/10.1002/2015GL064100.

    • Search Google Scholar
    • Export Citation
  • Gula, J., M. J. Molemaker, and J. C. McWilliams, 2015: Topographic vorticity generation, submesoscale instability, and vortex street formation in the Gulf Stream. Geophys. Res. Lett., 42, 40544062, https://doi.org/10.1002/2015GL063731.

    • Search Google Scholar
    • Export Citation
  • Holloway, G., and S. S. Kristmannsson, 1984: Stirring and transport of tracer fields by geostrophic turbulence. J. Fluid Mech., 141, 2750, https://doi.org/10.1017/S0022112084000720.

    • Search Google Scholar
    • Export Citation
  • Klein, P., A. M. Treguier, and B. L. Hua, 1998: Three-dimensional stirring of thermohaline fronts. J. Mar. Res., 56, 589612, https://doi.org/10.1357/002224098765213595.

    • Search Google Scholar
    • Export Citation
  • Klymak, J. M., W. Crawford, M. H. Alford, J. A. MacKinnon, and R. Pinkel, 2015: Along-isopycnal variability of spice in the North Pacific. J. Geophys. Res. Oceans, 120, 22872307, https://doi.org/10.1002/2013JC009421.

    • Search Google Scholar
    • Export Citation
  • Kunze, E., J. M. Klymak, R. C. Lien, R. Ferrari, C. M. Lee, M. A. Sundermeyer, and L. Goodman, 2015: Submesoscale water-mass spectra in the Sargasso Sea. J. Phys. Oceanogr., 45, 13251338, https://doi.org/10.1175/JPO-D-14-0108.1.

    • Search Google Scholar
    • Export Citation
  • Lien, R.-C., and T. B. Sanford, 2019: Small-scale potential vorticity in the upper-ocean thermocline. J. Phys. Oceanogr., 49, 18451872, https://doi.org/10.1175/JPO-D-18-0052.1.

    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., 2016: Submesoscale currents in the ocean. Proc. Roy. Soc., A472, 20160177, https://doi.org/10.1098/rspa.2016.0117.

  • Okubo, A., 1970: Horizontal dispersion of floatable particles in the vicinity of velocity singularities such as convergences. Deep-Sea Res. Oceanogr. Abstr., 17, 445454, https://doi.org/10.1016/0011-7471(70)90059-8.

    • Search Google Scholar
    • Export Citation
  • Poje, A. C., T. M. Özgökmen, D. J. Bogucki, and A. D. Kirwan Jr., 2017: Evidence of a forward energy cascade and Kolmogorov self-similarity in submesoscale ocean surface drifter observations. Phys. Fluids, 29, 020701, https://doi.org/10.1063/1.4974331.

    • Search Google Scholar
    • Export Citation
  • Polzin, K. L., and R. Ferrari, 2004: Isopycnal dispersion in NATRE. J. Phys. Oceanogr., 34, 247257, https://doi.org/10.1175/1520-0485(2004)034<0247:IDIN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Ragen, S., M. A. Pradal, and A. Gnanadesikan, 2020: The impact of parameterized lateral mixing on the Antarctic circumpolar current in a coupled climate model. J. Phys. Oceanogr., 50, 965982, https://doi.org/10.1175/JPO-D-19-0249.1.

    • Search Google Scholar
    • Export Citation
  • Samelson, R. M., and C. A. Paulson, 1988: Towed thermistor chain observations of fronts in the subtropical North Pacific. J. Geophys. Res., 93, 22372246, https://doi.org/10.1029/JC093iC03p02237.

    • Search Google Scholar
    • Export Citation
  • Scott, R. K., 2006: Local and nonlocal advection of a passive scalar. Phys. Fluids, 18, 116601, https://doi.org/10.1063/1.2375020.

  • Shcherbina, A. Y., E. A. D’Asaro, C. Lee, J. M. Klymak, M. J. Molemaker, and J. C. McWilliams, 2013: Statistics of vertical vorticity, divergence, and strain in a developed submesoscale turbulence field. Geophys. Res. Lett., 40, 47064711, https://doi.org/10.1002/grl.50919.

    • Search Google Scholar
    • Export Citation
  • Shcherbina, A. Y., and Coauthors, 2015: The LatMix summer campaign: Submesoscale stirring in the upper ocean. Bull. Amer. Meteor. Soc., 96, 12571279, https://doi.org/10.1175/BAMS-D-14-00015.1.

    • Search Google Scholar
    • Export Citation
  • Siegelman, L., P. Klein, P. Rivière, A. F. Thompson, H. S. Torres, M. Flexas, and D. Menemenlis, 2020: Enhanced upward heat transport at deep submesoscale ocean fronts. Nat. Geosci., 13, 5055, https://doi.org/10.1038/s41561-019-0489-1.

    • Search Google Scholar
    • Export Citation
  • Smith, K. S., and R. Ferrari, 2009: The production and dissipation of compensated thermohaline variance by mesoscale stirring. J. Phys. Oceanogr., 39, 24772501, https://doi.org/10.1175/2009JPO4103.1.

    • Search Google Scholar
    • Export Citation
  • Spiro Jaeger, G., J. A. MacKinnon, A. J. Lucas, E. Shroyer, J. Nash, A. Tandon, J. T. Farrar, and A. Mahadevan, 2020: How spice is stirred in the Bay of Bengal. J. Phys. Oceanogr., 50, 26692688, https://doi.org/10.1175/JPO-D-19-0077.1.

    • Search Google Scholar
    • Export Citation
  • Sundermeyer, M. A., D. A. Birch, J. R. Ledwell, M. D. Levine, S. D. Pierce, and B. T. K. Cervantes, 2020: Dispersion in the open ocean seasonal pycnocline at scales of 1–10 km and 1–6 days. J. Phys. Oceanogr., 50, 415437, https://doi.org/10.1175/JPO-D-19-0019.1.

    • Search Google Scholar
    • Export Citation
  • Thiffeault, J.-L., 2012: Using multiscale norms to quantify mixing and transport. Nonlinearity, 25, R1, https://doi.org/10.1088/0951-7715/25/2/R1.

    • Search Google Scholar
    • Export Citation
  • Thomas, J., 2023: Turbulent wave-balance exchanges in the ocean. Proc. Roy. Soc., 479A, 20220565.

  • Thomas, J., and S. Arun, 2020: Near-inertial waves and geostrophic turbulence. Phys. Rev. Fluids, 5, 014801, https://doi.org/10.1103/PhysRevFluids.5.014801.

    • Search Google Scholar
    • Export Citation
  • Thomas, J., and D. Daniel, 2021: Forward flux and enhanced dissipation of geostrophic balanced energy. J. Fluid Mech., 911, A60, https://doi.org/10.1017/jfm.2020.1026.

    • Search Google Scholar
    • Export Citation
  • Thomas, J., and A. Gupta, 2022: Wave-enhanced tracer dispersion. J. Geophys. Res. Oceans, 127, e2020JC017005, https://doi.org/10.1029/2020JC017005.

    • Search Google Scholar
    • Export Citation
  • Thomas, J., and R. Vishnu, 2022: Turbulent transition of a flow from small to O(1) Rossby numbers. J. Phys. Oceanogr., 52, 26092625, https://doi.org/10.1175/JPO-D-21-0270.1.

    • Search Google Scholar
    • Export Citation
  • Thompson, A. F., A. Lazar, C. Buckingham, A. C. Naveira Garabato, G. M. Damerell, and K. J. 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.

    • Search Google Scholar
    • Export Citation
  • Vladoiu, A., R. C. Lien, and E. Kunze, 2022: Two-dimensional wavenumber spectra on the horizontal submesoscale and vertical finescale. J. Phys. Oceanogr., 52, 20092028, https://doi.org/10.1175/JPO-D-21-0111.1.

    • Search Google Scholar
    • Export Citation
  • Weiss, J., 1991: The dynamics of enstrophy transfer in two-dimensional hydrodynamics. Physica D, 48, 273294, https://doi.org/10.1016/0167-2789(91)90088-Q.

    • Search Google Scholar
    • Export Citation
  • Yu, X., A. C. Naveira Garabato, A. P. Martin, C. E. Buckingham, L. Brannigan, and Z. Su, 2019: An annual cycle of submesoscale vertical flow and restratification in the upper ocean. J. Phys. Oceanogr., 49, 14391461, https://doi.org/10.1175/JPO-D-18-0253.1.

    • Search Google Scholar
    • Export Citation
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