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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Agarwal, N., E. Ryzhov, D. Kondrashov, and P. Berloff, 2021: Correlation-based flow decomposition and statistical analysis of the eddy forcing. J. Fluid Mech., 924, A5, https://doi.org/10.1017/jfm.2021.604.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Aluie, H., 2019: Convolutions on the sphere: Commutation with differential operators. Int. J. Geomath., 10, 9, https://doi.org/10.1007/s13137-019-0123-9.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Aluie, H., M. Hecht, and G. K. Vallis, 2018: Mapping the energy cascade in the North Atlantic Ocean: The coarse-graining approach. J. Phys. Oceanogr., 48, 225244, https://doi.org/10.1175/JPO-D-17-0100.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bachman, S. D., and B. Fox-Kemper, 2013: Eddy parameterization challenge suite I: Eady spindown. Ocean Modell., 64, 1228, https://doi.org/10.1016/j.ocemod.2012.12.003.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bachman, S. D., B. Fox-Kemper, and F. O. Bryan, 2015: A tracer-based inversion method for diagnosing eddy-induced diffusivity and advection. Ocean Modell., 86, 114, https://doi.org/10.1016/j.ocemod.2014.11.006.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bachman, S. D., B. Fox-Kemper, and B. Pearson, 2017: A scale-aware subgrid model for quasi-geostrophic turbulence. J. Geophys. Res. Oceans, 122, 15291554, https://doi.org/10.1002/2016JC012265.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bachman, S. D., B. Fox-Kemper, and F. O. Bryan, 2020: A diagnosis of anisotropic eddy diffusion from a high-resolution global ocean model. J. Adv. Model. Earth Syst., 12, e2019MS001904, https://doi.org/10.1029/2019MS001904.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Berloff, P., E. Ryzhov, and I. Shevchenko, 2021: On dynamically unresolved oceanic mesoscale motions. J. Fluid Mech., 920, A41, https://doi.org/10.1017/jfm.2021.477.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bleck, R., 2002: An oceanic general circulation model framed in hybrid isopycnic-Cartesian coordinates. Ocean Modell., 4, 5588, https://doi.org/10.1016/S1463-5003(01)00012-9.

    • 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.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Danabasoglu, G., and J. C. McWilliams, 1995: Sensitivity of the global ocean circulation to parameterizations of mesoscale tracer transports. J. Climate, 8, 29672987, https://doi.org/10.1175/1520-0442(1995)008<2967:SOTGOC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Eden, C., and R. J. Greatbatch, 2008: Towards a mesoscale eddy closure. Ocean Modell., 20, 223239, https://doi.org/10.1016/j.ocemod.2007.09.002.

  • Ferrari, R., and M. Nikurashin, 2010: Suppression of eddy diffusivity across jets in the southern ocean. J. Phys. Oceanogr., 40, 15011519, https://doi.org/10.1175/2010JPO4278.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ferrari, R., J. C. McWilliams, V. M. Canuto, and M. Dubovikov, 2008: Parameterization of eddy fluxes near oceanic boundaries. J. Climate, 21, 27702789, https://doi.org/10.1175/2007JCLI1510.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fox-Kemper, B., R. Ferrari, and J. Pedlosky, 2003: On the indeterminacy of rotational and divergent eddy fluxes. J. Phys. Oceanogr., 33, 478–483, https://doi.org/10.1175/1520-0485(2003)033<0478:OTIORA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Garabato, A. C. N., X. Yu, J. Callies, R. Barkan, K. L. Polzin, E. E. Frajka-Williams, C. E. Buckingham, and S. M. Griffies, 2022: Kinetic energy transfers between mesoscale and submesoscale motions in the open ocean’s upper layers. J. Phys. Oceanogr., 52, 7597, https://doi.org/10.1175/JPO-D-21-0099.1.

    • Crossref
    • 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
  • Gent, P. R., J. Willebrand, T. J. McDougall, and J. C. McWilliams, 1995: Parameterizing eddy-induced tracer transports in ocean circulation models. Ocean Modell., 25, 463474, https://doi.org/10.1175/1520-0485(1995)025<0463:PEITTI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gent, P. R., A. P. Craig, C. M. Bitz, and J. W. Weatherly, 2002: Parameterization improvements in an eddy-permitting ocean model for climate. J. Climate, 15, 14471459, https://doi.org/10.1175/1520-0442(2002)015<1447:PIIAEP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • George, T. M., G. E. Manucharyan, and A. F. Thompson, 2021: Deep learning to infer eddy heat fluxes from sea surface height patterns of mesoscale turbulence. Nat. Commun., 12, 800, https://doi.org/10.1038/s41467-020-20779-9.

    • Crossref
    • 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.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Griesel, A., S. T. Gille, J. Sprintall, J. L. McClean, and M. E. Maltrud, 2009: Assessing eddy heat flux and its parameterization: A wavenumber perspective from a 1/10° ocean simulation. Ocean Modell., 29, 248260, https://doi.org/10.1016/j.ocemod.2009.05.004.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Griffies, S. M., 1998: The Gent–McWilliams skew flux. J. Phys. Oceanogr., 28, 831841, https://doi.org/10.1175/1520-0485(1998)028<0831:TGMSF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Haigh, M., and P. Berloff, 2021: On co-existing diffusive and anti-diffusive tracer transport by oceanic mesoscale eddies. Ocean Modell., 168, 101909, https://doi.org/10.1016/j.ocemod.2021.101909.

    • Crossref
    • Export Citation
  • Haigh, M., L. Sun, I. Shevchenko, and P. Berloff, 2020: Tracer-based estimates of eddy-induced diffusivities. Deep-Sea Res. I, 160, 103264, https://doi.org/10.1016/j.dsr.2020.103264.

    • Crossref
    • Export Citation
  • Haigh, M., L. Sun, J. C. McWilliams, and P. Berloff, 2021a: On eddy transport in the ocean. Part I: The diffusion tensor. Ocean Modell., 164, 101831, https://doi.org/10.1016/j.ocemod.2021.101831.

    • Crossref
    • Export Citation
  • Haigh, M., L. Sun, J. C. McWilliams, and P. Berloff, 2021b: On eddy transport in the ocean. Part II: The advection tensor. Ocean Modell., 165, 101845, https://doi.org/10.1016/j.ocemod.2021.101845.

    • Crossref
    • Export Citation
  • Hewitt, H. T., and Coauthors, 2020: Resolving and parameterising the ocean mesoscale in Earth system models. Curr. Climate Change Rep., 6, 137152, https://doi.org/10.1007/s40641-020-00164-w.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jayne, S. R., and J. Marotzke, 2002: The oceanic eddy heat transport. J. Phys. Oceanogr., 32, 3328–3345, https://doi.org/10.1175/1520-0485(2002)032<3328:TOEHT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kamenkovich, I., and Z. Garraffo, 2022: Importance of mesoscale currents in AMOC pathways and timescales. J. Phys. Oceanogr., 52, 16131628, https://doi.org/10.1175/JPO-D-21-0244.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kamenkovich, I., I. I. Rypina, and P. Berloff, 2015: Properties and origins of the anisotropic eddy-induced transport in the North Atlantic. J. Phys. Oceanogr., 45, 778791, https://doi.org/10.1175/JPO-D-14-0164.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kamenkovich, I., Z. Garraffo, R. Pennel, and R. A. Fine, 2017: Importance of mesoscale eddies and mean circulation in ventilation of the Southern Ocean. J. Geophys. Res. Oceans, 122, 27242741, https://doi.org/10.1002/2016JC012292.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kamenkovich, I., P. Berloff, M. Haigh, L. Sun, and Y. Lu, 2021: Complexity of mesoscale eddy diffusivity in the ocean. Geophys. Res. Lett., 48, e2020GL091719, https://doi.org/10.1029/2020GL091719.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Klocker, A., and R. Abernathey, 2014: Global patterns of mesoscale eddy properties and diffusivities. J. Phys. Oceanogr., 44, 10301046, https://doi.org/10.1175/JPO-D-13-0159.1.

    • Crossref
    • 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, https://doi.org/10.1175/JPO-D-11-0205.1.

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kuhlbrodt, T., R. S. Smith, Z. Wang, and J. M. Gregory, 2012: The influence of eddy parameterizations on the transport of the Antarctic circumpolar current in coupled climate models. Ocean Modell., 5253, 18, https://doi.org/10.1016/j.ocemod.2012.04.006.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • LaCasce, J. H., 2008: Statistics from Lagrangian observations. Prog. Oceanogr., 77, 129, https://doi.org/10.1016/j.pocean.2008.02.002.

  • Ledwell, J. R., A. J. Watson, and C. S. Law, 1998: Mixing of a tracer in the pycnocline. J. Geophys. Res., 103, 21 49921 529, https://doi.org/10.1029/98JC01738.

    • Search Google Scholar
    • Export Citation
  • Leonard, A., 1997: Large-eddy simulation of chaotic convection and beyond. 35th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA, 1–8, https://doi.org/10.2514/6.1997-204.

    • Crossref
    • Export Citation
  • Li, Z., Y. Chao, and J. C. McWilliams, 2006: Computation of the stream function and velocity potential for limited and irregular domains. Mon. Wea. Rev., 134, 33843394, https://doi.org/10.1175/MWR3249.1.

    • Search Google Scholar
    • Export Citation
  • Lumpkin, R., A.-M. Treguier, and K. Speer, 2002: Lagrangian eddy scales in the northern Atlantic Ocean. J. Phys. Oceanogr., 32, 24252440, https://doi.org/10.1175/1520-0485-32.9.2425.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Maddison, J. R., D. P. Marshall, and J. Shipton, 2015: On the dynamical influence of ocean eddy potential vorticity fluxes. Ocean Modell., 92, 169182, https://doi.org/10.1016/j.ocemod.2015.06.003.

    • Search Google Scholar
    • Export Citation
  • Mak, J., D. Marshall, J. Maddison, and S. Bachman, 2017: Emergent eddy saturation from an energy constrained eddy parameterisation. Ocean Modell., 112, 125138, https://doi.org/10.1016/j.ocemod.2017.02.007.

    • 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, J., and G. Shutts, 1981: A note on rotational and divergent eddy fluxes. J. Phys. Oceanogr., 11, 16771680, https://doi.org/10.1175/1520-0485(1981)011<1677:ANORAD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, J., and K. Speer, 2012: Closure of the meridional overturning circulation through Southern Ocean upwelling. Nat. Geosci., 5, 171180, https://doi.org/10.1038/ngeo1391.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Meijers, A. J. S., 2014: The Southern Ocean in the Coupled Model Intercomparison Project phase 5. Philos. Trans. Roy. Soc., A372, 20130296, https://doi.org/10.1098/rsta.2013.0296.

    • Crossref
    • Export Citation
  • Mensa, J. A., Z. Garraffo, A. Griffa, T. M. Özgökmen, A. Haza, and M. Veneziani, 2013: Seasonality of the submesoscale dynamics in the Gulf Stream region. Ocean Dyn., 63, 923941, https://doi.org/10.1007/s10236-013-0633-1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Oh, I. S., V. Zhurbas, and W. Park, 2000: Estimating horizontal diffusivity in the East Sea (Sea of Japan) and the northwest Pacific from satellite-tracked drifter data. J. Geophys. Res., 105, 64836492, https://doi.org/10.1029/2000JC900002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Patching, S., 2022: On divergence- and gradient-preserving coarse-graining for finite volume primitive equation ocean models. Ocean Modell., 170, 101941, https://doi.org/10.1016/j.ocemod.2021.101941.

  • Porta Mana, P., and L. Zanna, 2014: Toward a stochastic parameterization of ocean mesoscale eddies. Ocean Modell., 79, 120, https://doi.org/10.1016/j.ocemod.2014.04.002.

    • Search Google Scholar
    • Export Citation
  • Prandtl, L., 1925: Bericht über untersuchungen zur ausgebildeten turbulenz. Z. Angew. Math. Mech., 5, 136139, https://doi.org/10.1002/zamm.19250050212.

    • Search Google Scholar
    • Export Citation
  • Pratt, L., R. Barkan, and I. Rypina, 2016: Scalar flux kinematics. Fluids, 1, 27, https://doi.org/10.3390/fluids1030027.

  • Qian, Y.-K., S. Peng, and C.-X. Liang, 2019: Reconciling Lagrangian diffusivity and effective diffusivity in contour-based coordinates. J. Phys. Oceanogr., 49, 15211539, https://doi.org/10.1175/JPO-D-18-0251.1.

    • Search Google Scholar
    • Export Citation
  • Redi, M., 1982: Oceanic isopycnal mixing by coordinate rotation. Ocean Modell., 12, 11541158, https://doi.org/10.1175/1520-0485(1982)012<1154:OIMBCR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Riha, S., and C. Eden, 2011: Lagrangian and Eulerian lateral diffusivities in zonal jets. Ocean Modell., 39, 114124, https://doi.org/10.1016/j.ocemod.2011.02.002.

    • Search Google Scholar
    • Export Citation
  • Rypina, I. I., L. J. Pratt, and M. S. Lozier, 2011: Near-surface transport pathways in the North Atlantic Ocean: Looking for throughput from the subtropical to the subpolar gyre. Ocean Modell., 41, 911925, https://doi.org/10.1175/2011JPO4498.1.

    • Search Google Scholar
    • Export Citation
  • 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, https://doi.org/10.1175/JPO-D-11-0191.1.

    • Search Google Scholar
    • Export Citation
  • Ryzhov, E. A., and P. Berloff, 2022: On transport tensor of dynamically unresolved oceanic mesoscale eddies. J. Fluid Mech., 939, A7, https://doi.org/10.1017/jfm.2022.169.

    • Search Google Scholar
    • Export Citation
  • Sallée, J.-B., K. Speer, R. Morrow, and R. Lumpkin, 2008: An estimate of Lagrangian eddy statistics and diffusion in the mixed layer of the Southern Ocean. J. Mar. Res., 66, 441463, https://doi.org/10.1357/002224008787157458.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Sun, L., M. Haigh, I. Shevchenko, P. Berloff, and I. Kamenkovich, 2021: On non-uniqueness of the mesoscale eddy diffusivity. J. Fluid Mech., 920, A32, https://doi.org/10.1017/jfm.2021.472.

    • Search Google Scholar
    • Export Citation
  • Taylor, G. I., 1922: Diffusion by continuous movements. Proc. London Math. Soc., s2-20, 196–212, https://doi.org/10.1112/plms/s2-20.1.196.

  • Trias, F. X., F. Dabbagh, A. Gorobets, and C. Oliet, 2020: On a proper tensor-diffusivity model for large-eddy simulation of buoyancy-driven turbulence. Flow Turbul. Combus., 105, 393414, https://doi.org/10.1007/s10494-020-00123-3.

    • Search Google Scholar
    • Export Citation
  • Wagner, P., S. Rühs, F. U. Schwarzkopf, I. M. Koszalka, and A. Biastoch, 2019: Can Lagrangian tracking simulate tracer spreading in a high-resolution ocean general circulation model? J. Phys. Oceanogr., 49, 11411157, https://doi.org/10.1175/JPO-D-18-0152.1.

    • Search Google Scholar
    • Export Citation
  • Waterman, S., N. G. Hogg, and S. R. Jayne, 2011: Eddy–mean flow interaction in the Kuroshio Extension region. J. Phys. Oceanogr., 41, 11821208, https://doi.org/10.1175/2010JPO4564.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, W., and C. Wolfe, 2022: On the vertical structure of oceanic mesoscale tracer diffusivities. J. Adv. Model. Earth Syst., 14, e2021MS002891, https://doi.org/10.1029/2021MS002891.

    • Search Google Scholar
    • Export Citation
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Properties of the Lateral Mesoscale Eddy-Induced Transport in a High-Resolution Ocean Model: Beyond the Flux–Gradient Relation

Yueyang LuaRosenstiel School of Marine, Atmospheric, and Earth Science, University of Miami, Miami, Florida

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Igor KamenkovichaRosenstiel School of Marine, Atmospheric, and Earth Science, University of Miami, Miami, Florida

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Pavel BerloffbDepartment of Mathematics, Imperial College London, London, United Kingdom
cInstitute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia

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Abstract

Lateral mesoscale eddy-induced tracer transport is traditionally represented in coarse-resolution models by the flux–gradient relation. In its most complete form, the relation assumes the eddy tracer flux as a product of the large-scale tracer concentration gradient and an eddy transport coefficient tensor. However, several recent studies reported that the tensor has significant spatiotemporal complexity and is not uniquely defined, that is, it is sensitive to the tracer distributions and to the presence of nondivergent (“rotational”) components of the eddy flux. These issues could lead to significant biases in the representation of the eddy-induced transport. Using a high-resolution tracer model of the Gulf Stream region, we examine the diffusive and advective properties of lateral eddy-induced transport of dynamically passive tracers, reevaluate the utility of the flux–gradient relation, and propose an alternative approach based on modeling the local eddy forcing by a combination of diffusion and generalized eddy-induced advection. Mesoscale eddies are defined by a scale-based spatial filtering, which leads to the importance of new eddy-induced terms, including eddy-mean covariances in the eddy fluxes. The results show that the biases in representing these terms are noticeably reduced by the new approach. A series of targeted simulations in the high-resolution model further demonstrates that the approach outperforms the flux–gradient model in reproducing the stirring and dispersing effect of eddies. Our study indicates potential to upgrade the traditional flux–gradient relation for representing the eddy-induced tracer transport.

© 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: Yueyang Lu, yueyang.lu@miami.edu

Abstract

Lateral mesoscale eddy-induced tracer transport is traditionally represented in coarse-resolution models by the flux–gradient relation. In its most complete form, the relation assumes the eddy tracer flux as a product of the large-scale tracer concentration gradient and an eddy transport coefficient tensor. However, several recent studies reported that the tensor has significant spatiotemporal complexity and is not uniquely defined, that is, it is sensitive to the tracer distributions and to the presence of nondivergent (“rotational”) components of the eddy flux. These issues could lead to significant biases in the representation of the eddy-induced transport. Using a high-resolution tracer model of the Gulf Stream region, we examine the diffusive and advective properties of lateral eddy-induced transport of dynamically passive tracers, reevaluate the utility of the flux–gradient relation, and propose an alternative approach based on modeling the local eddy forcing by a combination of diffusion and generalized eddy-induced advection. Mesoscale eddies are defined by a scale-based spatial filtering, which leads to the importance of new eddy-induced terms, including eddy-mean covariances in the eddy fluxes. The results show that the biases in representing these terms are noticeably reduced by the new approach. A series of targeted simulations in the high-resolution model further demonstrates that the approach outperforms the flux–gradient model in reproducing the stirring and dispersing effect of eddies. Our study indicates potential to upgrade the traditional flux–gradient relation for representing the eddy-induced tracer transport.

© 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: Yueyang Lu, yueyang.lu@miami.edu
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