Eddy–Internal Wave Interactions: Stimulated Cascades in Cross-Scale Kinetic Energy and Enstrophy Fluxes

Roy Barkan aPorter School of the Environment and Earth Sciences, Tel Aviv University, Tel Aviv, Israel
bDepartment of Atmospheric and Oceanic Sciences, University of California Los Angeles, Los Angeles, California

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Kaushik Srinivasan bDepartment of Atmospheric and Oceanic Sciences, University of California Los Angeles, Los Angeles, California

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James C. McWilliams bDepartment of Atmospheric and Oceanic Sciences, University of California Los Angeles, Los Angeles, California

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Abstract

The interactions between oceanic mesoscale eddies, submesoscale currents, and internal gravity waves (IWs) are investigated in submesoscale-resolving realistic simulations in the North Atlantic Ocean. Using a novel analysis framework that couples the coarse-graining method in space with temporal filtering and a Helmholtz decomposition, we quantify the effects of the interactions on the cross-scale kinetic energy (KE) and enstrophy fluxes. By systematically comparing solutions with and without IW forcing, we show that externally forced IWs stimulate a reduction in the KE inverse cascade associated with mesoscale rotational motions and an enhancement in the KE forward cascade associated with divergent submesoscale currents, i.e., a “stimulated cascade” process. The corresponding IW effects on the enstrophy fluxes are seasonally dependent, with a stimulated reduction (enhancement) in the forward enstrophy cascade during summer (winter). Direct KE and enstrophy transfers from currents to IWs are also found, albeit with weaker magnitudes compared with the stimulated cascades. We further find that the forward KE and enstrophy fluxes associated with IW motions are almost entirely driven by the scattering of the waves by the rotational eddy field, rather than by wave–wave interactions. This process is investigated in detail in a companion manuscript. Finally, we demonstrate that the stimulated cascades are spatially localized in coherent structures. Specifically, the magnitude and direction of the bidirectional KE fluxes at submesoscales are highly correlated with, and inversely proportional to, divergence-dominated circulations, and the inverse KE fluxes at mesoscales are highly correlated with strain-dominated circulations. The predominantly forward enstrophy fluxes in both seasons are also correlated with strain-dominated flow structures.

© 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: Roy Barkan, rbarkan@tauex.tau.ac.il

Abstract

The interactions between oceanic mesoscale eddies, submesoscale currents, and internal gravity waves (IWs) are investigated in submesoscale-resolving realistic simulations in the North Atlantic Ocean. Using a novel analysis framework that couples the coarse-graining method in space with temporal filtering and a Helmholtz decomposition, we quantify the effects of the interactions on the cross-scale kinetic energy (KE) and enstrophy fluxes. By systematically comparing solutions with and without IW forcing, we show that externally forced IWs stimulate a reduction in the KE inverse cascade associated with mesoscale rotational motions and an enhancement in the KE forward cascade associated with divergent submesoscale currents, i.e., a “stimulated cascade” process. The corresponding IW effects on the enstrophy fluxes are seasonally dependent, with a stimulated reduction (enhancement) in the forward enstrophy cascade during summer (winter). Direct KE and enstrophy transfers from currents to IWs are also found, albeit with weaker magnitudes compared with the stimulated cascades. We further find that the forward KE and enstrophy fluxes associated with IW motions are almost entirely driven by the scattering of the waves by the rotational eddy field, rather than by wave–wave interactions. This process is investigated in detail in a companion manuscript. Finally, we demonstrate that the stimulated cascades are spatially localized in coherent structures. Specifically, the magnitude and direction of the bidirectional KE fluxes at submesoscales are highly correlated with, and inversely proportional to, divergence-dominated circulations, and the inverse KE fluxes at mesoscales are highly correlated with strain-dominated circulations. The predominantly forward enstrophy fluxes in both seasons are also correlated with strain-dominated flow structures.

© 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: Roy Barkan, rbarkan@tauex.tau.ac.il
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  • 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.

    • Search Google Scholar
    • Export Citation
  • Balwada, D., J.-H. Xie, R. Marino, and F. Feraco, 2022: Direct observational evidence of an oceanic dual kinetic energy cascade and its seasonality. Sci. Adv., 8, eabq2566, https://doi.org/10.1126/sciadv.abq2566.

    • Search Google Scholar
    • Export Citation
  • Barkan, R., K. B. Winters, and J. C. McWilliams, 2017: Stimulated imbalance and the enhancement of eddy kinetic energy dissipation by internal waves. J. Phys. Oceanogr., 47, 181198, https://doi.org/10.1175/JPO-D-16-0117.1.

    • Search Google Scholar
    • Export Citation
  • Barkan, R., M. J. Molemaker, K. Srinivasan, J. C. McWilliams, and E. A. D’Asaro, 2019: The role of horizontal divergence in submesoscale frontogenesis. J. Phys. Oceanogr., 49, 15931618, https://doi.org/10.1175/JPO-D-18-0162.1.

    • Search Google Scholar
    • Export Citation
  • Barkan, R., K. Srinivasan, L. Yang, J. C. McWilliams, J. Gula, and C. Vic, 2021: Oceanic mesoscale eddy depletion catalyzed by internal waves. Geophys. Res. Lett., 48, e2021GL094376, https://doi.org/10.1029/2021GL094376.

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

    • Search Google Scholar
    • Export Citation
  • Callies, J., R. Barkan, and A. N. Garabato, 2020: Time scales of submesoscale flow inferred from a mooring array. J. Phys. Oceanogr., 50, 10651086, https://doi.org/10.1175/JPO-D-19-0254.1.

    • Search Google Scholar
    • Export Citation
  • Capet, X., J. C. McWilliams, M. J. Molemaker, and A. F. Shchepetkin, 2008a: Mesoscale to submesoscale transition in the California current system. Part II: Frontal processes. J. Phys. Oceanogr., 38, 4464, https://doi.org/10.1175/2007JPO3672.1.

    • Search Google Scholar
    • Export Citation
  • Capet, X., J. C. McWilliams, M. J. Molemaker, and A. F. Shchepetkin, 2008b: Mesoscale to submesoscale transition in the California Current System. Part III: Energy balance and flux. J. Phys. Oceanogr., 38, 22562269, https://doi.org/10.1175/2008JPO3810.1.

    • Search Google Scholar
    • Export Citation
  • Chaigneau, A., O. Pizarro, and W. Rojas, 2008: Global climatology of near-inertial current characteristics from Lagrangian observations. Geophys. Res. Lett., 35, L13603, https://doi.org/10.1029/2008GL034060.

    • Search Google Scholar
    • Export Citation
  • Charney, J. G., 1971: Geostrophic turbulence. J. Atmos. Sci., 28, 10871095, https://doi.org/10.1175/1520-0469(1971)028<1087:GT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Contreras, M., L. Renault, and P. Marchesiello, 2023: Understanding energy pathways in the Gulf Stream. J. Phys. Oceanogr., 53, 719736, https://doi.org/10.1175/JPO-D-22-0146.1.

    • Search Google Scholar
    • Export Citation
  • Cox, M. R., H. A. Kafiabad, and J. Vanneste, 2023: Inertia-gravity-wave diffusion by geostrophic turbulence: The impact of flow time dependence. J. Fluid Mech., 958, A21, https://doi.org/10.1017/jfm.2023.83.

    • Search Google Scholar
    • Export Citation
  • D’Asaro, E. A., and Coauthors, 2018: Ocean convergence and the dispersion of flotsam. Proc. Natl. Acad. Sci. USA, 115, 11621167, https://doi.org/10.1073/pnas.1718453115.

    • Search Google Scholar
    • Export Citation
  • Dee, D. P., M. Balmaseda, G. Balsamo, R. Engelen, A. J. Simmons, and J.-N. Thépaut, 2014: Toward a consistent reanalysis of the climate system. Bull. Amer. Meteor. Soc., 95, 12351248, https://doi.org/10.1175/BAMS-D-13-00043.1.

    • Search Google Scholar
    • Export Citation
  • Delpech, A., R. Barkan, K. Srinivasan, J. C. McWilliams, B. K. Arbic, O. Q. Siyanbola, and M. C. Buijsman, 2024: Eddy–internal wave interactions and their contribution to cross-scale energy fluxes: A case study in the California current. J. Phys. Oceanogr., 54, 741754, https://doi.org/10.1175/JPO-D-23-0181.1.

    • Search Google Scholar
    • Export Citation
  • Dong, W., O. Bühler, and K. S. Smith, 2020: Frequency diffusion of waves by unsteady flows. J. Fluid Mech., 905, R3, https://doi.org/10.1017/jfm.2020.837.

    • Search Google Scholar
    • Export Citation
  • Dong, W., O. Bühler, and K. S. Smith, 2023: Geostrophic eddies spread near-inertial wave energy to high frequencies. J. Phys. Oceanogr., 53, 13111322, https://doi.org/10.1175/JPO-D-22-0153.1.

    • Search Google Scholar
    • Export Citation
  • Eden, C., F. Pollmann, and D. Olbers, 2019: Numerical evaluation of energy transfers in internal gravity wave spectra of the ocean. J. Phys. Oceanogr., 49, 737749, https://doi.org/10.1175/JPO-D-18-0075.1.

    • Search Google Scholar
    • Export Citation
  • Egbert, G. D., and S. Y. Erofeeva, 2002: Efficient inverse modeling of barotropic ocean tides. J. Atmos. Oceanic Technol., 19, 183204, https://doi.org/10.1175/1520-0426(2002)019<0183:EIMOBO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Egbert, G. D., A. F. Bennett, and M. G. Foreman, 1994: TOPEX/POSEIDON tides estimated using a global inverse model. J. Geophys. Res., 99, 24 82124 852, https://doi.org/10.1029/94JC01894.

    • Search Google Scholar
    • Export Citation
  • Eyink, G. L., 2005: Locality of turbulent cascades. Physica D, 207, 91116, https://doi.org/10.1016/j.physd.2005.05.018.

  • 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.

    • Search Google Scholar
    • Export Citation
  • Fratantoni, D. M., 2001: North Atlantic surface circulation during the 1990’s observed with satellite-tracked drifters. J. Geophys. Res., 106, 22 06722 093, https://doi.org/10.1029/2000JC000730.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Garrett, C., and W. Munk, 1972: Space-time scales of internal waves. Geophys. Fluid Dyn., 3, 225264, https://doi.org/10.1080/03091927208236082.

    • Search Google Scholar
    • Export Citation
  • Germano, M., 1992: Turbulence: The filtering approach. J. Fluid Mech., 238, 325336, https://doi.org/10.1017/S0022112092001733.

  • Hua, B. L., J. C. McWilliams, and P. Klein, 1998: Lagrangian accelerations in geostrophic turbulence. J. Fluid Mech., 366, 87108, https://doi.org/10.1017/S0022112098001001.

    • Search Google Scholar
    • Export Citation
  • Jakobsen, P. K., M. H. Ribergaard, D. Quadfasel, T. Schmith, and C. W. Hughes, 2003: Near-surface circulation in the northern North Atlantic as inferred from Lagrangian drifters: Variability from the mesoscale to interannual. J. Geophys. Res., 108, 3251, https://doi.org/10.1029/2002JC001554.

    • Search Google Scholar
    • Export Citation
  • Kafiabad, H. A., and J. Vanneste, 2023: Computing Lagrangian means. J. Fluid Mech., 960, A36, https://doi.org/10.1017/jfm.2023.228.

  • Kafiabad, H. A., M. A. C. Savva, and J. Vanneste, 2019: Diffusion of inertia-gravity waves by geostrophic turbulence. J. Fluid Mech., 869, R7, https://doi.org/10.1017/jfm.2019.300.

    • Search Google Scholar
    • Export Citation
  • Kar, S., and R. Barkan, 2023: Kinetic energy exchanges between a two-dimensional front and internal waves. J. Phys. Oceanogr., 53, 25372557, https://doi.org/10.1175/JPO-D-22-0240.1.

    • Search Google Scholar
    • Export Citation
  • Lvov, Y. V., K. L. Polzin, and N. Yokoyama, 2012: Resonant and near-resonant internal wave interactions. J. Phys. Oceanogr., 42, 669691, https://doi.org/10.1175/2011JPO4129.1.

    • Search Google Scholar
    • Export Citation
  • MacKinnon, J. A., and Coauthors, 2017: Climate process team on internal wave–driven ocean mixing. Bull. Amer. Meteor. Soc., 98, 24292454, https://doi.org/10.1175/BAMS-D-16-0030.1.

    • Search Google Scholar
    • Export Citation
  • McComas, C. H., and F. P. Bretherton, 1977: Resonant interaction of oceanic internal waves. J. Geophys. Res., 82, 13971412, https://doi.org/10.1029/JC082i009p01397.

    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., 2016: Submesoscale currents in the ocean. Proc. Roy. Soc., 472A, 20160117, 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
  • Rama, J., C. J. Shakespeare, and A. M. Hogg, 2022: Importance of background vorticity effect and Doppler shift in defining near-inertial internal waves. Geophys. Res. Lett., 49, e2022GL099498, https://doi.org/10.1029/2022GL099498.

    • Search Google Scholar
    • Export Citation
  • Rocha, C. B., G. L. Wagner, and W. R. Young, 2018: Stimulated generation: Extraction of energy from balanced flow by near-inertial waves. J. Fluid Mech., 847, 417451, https://doi.org/10.1017/jfm.2018.308.

    • Search Google Scholar
    • Export Citation
  • Saha, S., and Coauthors, 2010: NCEP Climate Forecast System Reanalysis (CFSR) selected hourly time-series products, January 1979 to December 2010. Research Data Archive at the National Center for Atmospheric Research, accessed 10 September 2018, https://doi.org/10.5065/D6513W89.

  • Saha, S., and Coauthors, 2014: The NCEP climate forecast system version 2. J. Climate, 27, 21852208, https://doi.org/10.1175/JCLI-D-12-00823.1.

    • Search Google Scholar
    • Export Citation
  • Salmon, R., 1980: Baroclinic instability and geostrophic turbulence. Geophys. Astrophys. Fluid Dyn., 15, 167211, https://doi.org/10.1080/03091928008241178.

    • Search Google Scholar
    • Export Citation
  • Savva, M. A. C., H. A. Kafiabad, and J. Vanneste, 2021: Inertia-gravity-wave scattering by three-dimensional geostrophic turbulence. J. Fluid Mech., 916, A6, https://doi.org/10.1017/jfm.2021.205.

    • Search Google Scholar
    • Export Citation
  • Schubert, R., J. Gula, R. J. Greatbatch, B. Baschek, and A. Biastoch, 2020: The submesoscale kinetic energy cascade: Mesoscale absorption of submesoscale mixed layer eddies and frontal downscale fluxes. J. Phys. Oceanogr., 50, 25732589, https://doi.org/10.1175/JPO-D-19-0311.1.

    • Search Google Scholar
    • Export Citation
  • Scott, R. B., and B. K. Arbic, 2007: Spectral energy fluxes in geostrophic turbulence: Implications for ocean energetics. J. Phys. Oceanogr., 37, 673688, https://doi.org/10.1175/JPO3027.1.

    • Search Google Scholar
    • Export Citation
  • Shakespeare, C. J., 2023: Eddy acceleration and decay driven by internal tides. J. Phys. Oceanogr., 53, 27872796, https://doi.org/10.1175/JPO-D-23-0127.1.

    • Search Google Scholar
    • Export Citation
  • Shakespeare, C. J., A. H. Gibson, A. M. Hogg, S. D. Bachman, S. R. Keating, and N. Velzeboer, 2021: A new open source implementation of Lagrangian filtering: A method to identify internal waves in high-resolution simulations. J. Adv. Model. Earth Syst., 13, e2021MS002616, https://doi.org/10.1029/2021MS002616.

    • Search Google Scholar
    • Export Citation
  • Shchepetkin, A. F., and J. C. McWilliams, 2005: The Regional Oceanic Modeling System (ROMS): A split-explicit, free-surface, topography-following-coordinate oceanic model. Ocean Modell., 9, 347404, https://doi.org/10.1016/j.ocemod.2004.08.002.

    • Search Google Scholar
    • Export Citation
  • Srinivasan, K., R. Barkan, and J. C. McWilliams, 2023: A forward energy flux at submesoscales driven by frontogenesis. J. Phys. Oceanogr., 53, 287305, https://doi.org/10.1175/JPO-D-22-0001.1.

    • Search Google Scholar
    • Export Citation
  • Taylor, S., and D. Straub, 2016: Forced near-inertial motion and dissipation of low-frequency kinetic energy in a wind-driven channel flow. J. Phys. Oceanogr., 46, 7993, https://doi.org/10.1175/JPO-D-15-0060.1.

    • Search Google Scholar
    • Export Citation
  • Taylor, S., and D. Straub, 2020: Effects of adding forced near-inertial motion to a wind-driven channel flow. J. Phys. Oceanogr., 50, 29832996, https://doi.org/10.1175/JPO-D-19-0299.1.

    • Search Google Scholar
    • Export Citation
  • Tedesco, P. F., L. E. Baker, A. C. Naveira Garabato, M. R. Mazloff, S. T. Gille, C. P. Caulfield, and A. Mashayek, 2024: Spatiotemporal characteristics of the near-surface turbulent cascade at the submesoscale in the Drake Passage. J. Phys. Oceanogr., 54, 187215, https://doi.org/10.1175/JPO-D-23-0108.1.

    • Search Google Scholar
    • Export Citation
  • Thomas, J., and D. Daniel, 2020: Turbulent exchanges between near-inertial waves and balanced flows. J. Fluid Mech., 902, A7, https://doi.org/10.1017/jfm.2020.510.

    • 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, L. N., 2012: On the effects of frontogenetic strain on symmetric instability and inertia-gravity waves. J. Fluid Mech., 711, 620640, https://doi.org/10.1017/jfm.2012.416.

    • Search Google Scholar
    • Export Citation
  • Thomas, L. N., A. Tandon, and A. Mahadevan, 2008: Submesoscale processes and dynamics. Ocean Modeling in and Eddying Regime, Geophys. Monogr., Vol. 177, Amer. Geophys. Union, 17–38.

  • Thomas, L. N., L. Rainville, O. Asselin, W. R. Young, J. Girton, C. B. Whalen, L. Centurioni, and V. Hormann, 2020: Direct observations of near-inertial wave ζ-refraction in a dipole vortex. Geophys. Res. Lett., 47, e2020GL090375,https://doi.org/10.1029/2020GL090375.

    • Search Google Scholar
    • Export Citation
  • Thomas, L. N., E. D. Skyllingstad, L. Rainville, V. Hormann, L. Centurioni, J. N. Moum, O. Asselin, and C. M. Lee, 2023: Damping of inertial motions through the radiation of near-inertial waves in a dipole vortex in the Iceland basin. J. Phys. Oceanogr., 53, 18211833, https://doi.org/10.1175/JPO-D-22-0202.1.

    • Search Google Scholar
    • Export Citation
  • Torres, H. S., and Coauthors, 2022: Separating energetic internal gravity waves and small-scale frontal dynamics. Geophys. Res. Lett., 49, e2021GL096249, https://doi.org/10.1029/2021GL096249.

    • Search Google Scholar
    • Export Citation
  • Towns, J., and Coauthors, 2014: XSEDE: Accelerating scientific discovery. Comput. Sci. Eng., 16, 6274, https://doi.org/10.1109/MCSE.2014.80.

    • Search Google Scholar
    • Export Citation
  • Vanneste, J., 2013: Balance and spontaneous wave generation in geophysical flows. Annu. Rev. Fluid Mech., 45, 147172, https://doi.org/10.1146/annurev-fluid-011212-140730.

    • Search Google Scholar
    • Export Citation
  • Wagner, G. L., and W. R. Young, 2016: A three-component model for the coupled evolution of near-inertial waves, quasi-geostrophic flow and the near-inertial second harmonic. J. Fluid Mech., 802, 806837, https://doi.org/10.1017/jfm.2016.487.

    • Search Google Scholar
    • Export Citation
  • Wang, C., Z. Liu, and H. Lin, 2023: On dynamical decomposition of multiscale oceanic motions. J. Adv. Model. Earth Syst., 15, e2022MS003556, https://doi.org/10.1029/2022MS003556.

    • 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
  • Whitt, D. B., and L. N. Thomas, 2013: Near-inertial waves in strongly baroclinic currents. J. Phys. Oceanogr., 43, 706725, https://doi.org/10.1175/JPO-D-12-0132.1.

    • Search Google Scholar
    • Export Citation
  • Whitt, D. B., and L. N. Thomas, 2015: Resonant generation and energetics of wind-forced near-inertial motions in a geostrophic flow. J. Phys. Oceanogr., 45, 181208, https://doi.org/10.1175/JPO-D-14-0168.1.

    • Search Google Scholar
    • Export Citation
  • Wunsch, C., and R. Ferrari, 2004: Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech., 36, 281314, https://doi.org/10.1146/annurev.fluid.36.050802.122121.

    • Search Google Scholar
    • Export Citation
  • Xie, J.-H., 2020: Downscale transfer of quasigeostrophic energy catalyzed by near-inertial waves. J. Fluid Mech., 904, A40, https://doi.org/10.1017/jfm.2020.709.

    • Search Google Scholar
    • Export Citation
  • Xie, J.-H., and J. Vanneste, 2015: A generalised-Lagrangian-mean model of the interactions between near-inertial waves and mean flow. J. Fluid Mech., 774, 143169, https://doi.org/10.1017/jfm.2015.251.

    • Search Google Scholar
    • Export Citation
  • Yang, L., R. Barkan, K. Srinivasan, J. C. McWilliams, C. J. Shakespear, and A. H. Gibson, 2023: Oceanic eddies induce a rapid formation of an internal wave continuum. Commun. Earth Environ., 4, 484, https://doi.org/10.1038/s43247-023-01137-1.

    • Search Google Scholar
    • Export Citation
  • Zhang, L.-F., and J.-H. Xie, 2023: The catalytic effect of near-inertial waves on β-plane zonal jets. J. Fluid Mech., 962, A33, https://doi.org/10.1017/jfm.2023.310.

    • Search Google Scholar
    • Export Citation
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