Internal wave-driven mixing: governing processes and consequences for climate

Abstract

Turbulent mixing from breaking oceanic internal waves drives a vertical transport of water, heat and other climatically important tracers in the ocean, thereby playing an important role in shaping the circulation and distributions of heat and carbon within the climate system. However, linking internal wave-driven mixing to its impacts on climate poses a formidable challenge, since it requires understanding of the complex life cycle of internal waves — including generation, propagation and breaking into turbulence — and knowledge of the spatio-temporal variability of these processes in the diverse, rapidly evolving oceanic environment. In this Review, we trace the energy pathways from tides, winds and geostrophic currents to internal wave mixing, connecting this mixing with the global climate system. Additionally, we discuss avenues for future work, including understanding energy transfer processes within the internal wave field, how internal waves can be modified by background currents and how internal wave mixing is integrated within the global climate system.

Key points

  • Tides, winds and geographic currents can generate oceanic internal waves and, as a result, are major sources of energy for the internal wave field.

  • Interactions between internal waves and topography, currents or other internal waves can transfer energy to smaller spatio-temporal scales. How these processes combine to yield the observed internal wave environment, however, is not well understood.

  • Internal waves can eventually become unstable, causing them to turbulently dissipate energy and mix water across density classes, thereby altering ocean dynamics.

  • The location and timing of internal wave generation, energy transfer to smaller scales and subsequent turbulent dissipation conspire to form the continually evolving global distribution of mixing from internal waves.

  • The global climate is shaped by the magnitude and geography of internal wave mixing, including the global oceanic overturning circulation, water property distribution and air–sea interactions.

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Fig. 1: The primary internal wave mechanisms leading to ocean mixing.
Fig. 2: Turbulent mixing in two different internal wave environments.
Fig. 3: A simplified global energy budget of internal waves.
Fig. 4: The life cycle of internal tides.
Fig. 5: The seasonal cycle in wind activity can track the seasonal cycle in near-inertial wave energy and dissipation rate.
Fig. 6: Two mechanisms of internal wave generation from geostrophic currents.
Fig. 7: Global diapycnal mixing from internal waves and implications for climate.

References

  1. 1.

    Fer, I., Voet, G., Seim, K. S., Rudels, B. & Latarius, K. Intense mixing of the Faroe Bank Channel overflow. Geophys. Res. Lett. 37, L02604 (2010).

    Article  Google Scholar 

  2. 2.

    D’Asaro, E. A. Turbulence in the upper-ocean mixed layer. Annu. Rev. Mar. Sci. 6, 101–115 (2014).

    Article  Google Scholar 

  3. 3.

    Munk, W. & Wunsch, C. Abyssal recipes II: energetics of tidal and wind mixing. Deep Sea Res. Part I Oceanogr. Res. Pap. 45, 1977–2010 (1998).

    Article  Google Scholar 

  4. 4.

    Talley, L. D. Closure of the global overturning circulation through the Indian, Pacific, and Southern Oceans: schematics and transports. Oceanography 26, 80–97 (2013).

    Article  Google Scholar 

  5. 5.

    de Lavergne, C., Madec, G., Le Sommer, J., Nurser, A. G. & Naveira Garabato, A. C. On the consumption of Antarctic Bottom Water in the abyssal ocean. J. Phys. Oceanogr. 46, 635–661 (2016).

    Article  Google Scholar 

  6. 6.

    Kunze, E. The internal-wave-driven meridional overturning circulation. J. Phys. Oceanogr. 47, 2673–2689 (2017).

    Article  Google Scholar 

  7. 7.

    Wunsch, C. & Ferrari, R. Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech. 36, 281–314 (2004).

    Article  Google Scholar 

  8. 8.

    Ferrari, R. & Wunsch, C. Ocean circulation kinetic energy: reservoirs, sources, and sinks. Annu. Rev. Fluid Mech. 41, 253–282 (2009).

    Article  Google Scholar 

  9. 9.

    Kunze, E. Internal-wave-driven mixing: global geography and budgets. J. Phys. Oceanogr. 47, 1325–1345 (2017).

    Article  Google Scholar 

  10. 10.

    Anderson, L. A. & Sarmiento, J. L. Redfield ratios of remineralization determined by nutrient data analysis. Glob. Biogeochem. Cycles 8, 65–80 (1994).

    Article  Google Scholar 

  11. 11.

    Sarmiento, J. L., Gruber, N., Brzezinski, M. & Dunne, J. High-latitude controls of thermocline nutrients and low latitude biological productivity. Nature 427, 56–60 (2004).

    Article  Google Scholar 

  12. 12.

    Friedrich, T., Timmermann, A., Decloedt, T., Luther, D. & Mouchet, A. The effect of topography-enhanced diapycnal mixing on ocean and atmospheric circulation and marine biogeochemistry. Ocean Model. 39, 262–274 (2011).

    Article  Google Scholar 

  13. 13.

    Deutsch, C. & Weber, T. Nutrient ratios as a tracer and driver of ocean biogeochemistry. Annu. Rev. Mar. Sci. 4, 113–141 (2012).

    Article  Google Scholar 

  14. 14.

    Tuerena, R. E. et al. Internal tides drive nutrient fluxes into the deep chlorophyll maximum over mid-ocean ridges. Global Biogeochem. Cycles 33, 995–1009 (2019).

    Article  Google Scholar 

  15. 15.

    Phillips, O. M. The Dynamics of the Upper Ocean (CUP Archive, 1966).

  16. 16.

    Woods, J. Wave-induced shear instability in the summer thermocline. J. Fluid Mech. 32, 791–800 (1968).

    Article  Google Scholar 

  17. 17.

    Garrett, C. & Munk, W. Internal waves in the ocean. Annu. Rev. Fluid Mech. 11, 339–369 (1979).

    Article  Google Scholar 

  18. 18.

    Bell, T. Topographically generated internal waves in the open ocean. J. Geophys. Res. 80, 320–327 (1975).

    Article  Google Scholar 

  19. 19.

    Munk, W. H. Abyssal recipes. Deep Sea Res. Oceanogr. Abstr. 13, 707–730 (1966).

    Article  Google Scholar 

  20. 20.

    MacKinnon, J. A. et al. Climate process team on internal wave-driven ocean mixing. Bull. Am. Meteorol. Soc. 98, 2429–2454 (2017).

    Article  Google Scholar 

  21. 21.

    Alford, M. H., MacKinnon, J. A., Simmons, H. L. & Nash, J. D. Near-inertial internal gravity waves in the ocean. Annu. Rev. Mar. Sci. 8, 95–123 (2016).

    Article  Google Scholar 

  22. 22.

    Gill, A. E. Atmosphere—Ocean Dynamics (Elsevier, 2016).

  23. 23.

    Olbers, D. J. Nonlinear energy transfer and the energy balance of the internal wave field in the deep ocean. J. Fluid Mech. 74, 375–399 (1976).

    Article  Google Scholar 

  24. 24.

    Lvov, Y. V., Polzin, K. L. & Yokoyama, N. Resonant and near-resonant internal wave interactions. J. Phys. Oceanogr. 42, 669–691 (2012).

    Article  Google Scholar 

  25. 25.

    Eden, C., Pollmann, F. & Olbers, D. Numerical evaluation of energy transfers in internal gravity wave spectra of the ocean. J. Phys. Oceanogr. 49, 737–749 (2019).

    Article  Google Scholar 

  26. 26.

    Hibiya, T., Nagasawa, M. & Niwa, Y. Nonlinear energy transfer within the oceanic internal wave spectrum at mid and high latitudes. J. Geophys. Res. Oceans 107, 3207 (2002).

    Article  Google Scholar 

  27. 27.

    MacKinnon, J. A. et al. Parametric subharmonic instability of the internal tide at 29 N. J. Phys. Oceanogr. 43, 17–28 (2013).

    Article  Google Scholar 

  28. 28.

    Olbers, D., Pollmann, F. & Eden, C. On PSI interactions in internal gravity wave fields and the decay of baroclinic tides. J. Phys. Oceanogr. 50, 751–771 (2020).

    Article  Google Scholar 

  29. 29.

    Jones, W. L. Ray tracing for internal gravity waves. J. Geophys. Res. 74, 2028–2033 (1969).

    Article  Google Scholar 

  30. 30.

    Staquet, C. & Sommeria, J. Internal gravity waves: from instabilities to turbulence. Annu. Rev. Fluid Mech. 34, 559–593 (2002).

    Article  Google Scholar 

  31. 31.

    Bühler, O. & McIntyre, M. E. Wave capture and wave–vortex duality. J. Fluid Mech. 534, 67–95 (2005).

    Article  Google Scholar 

  32. 32.

    Müller, P. & Xu, N. Scattering of oceanic internal gravity waves off random bottom topography. J. Phys. Oceanogr. 22, 474–488 (1992).

    Article  Google Scholar 

  33. 33.

    Müller, P. & Liu, X. Scattering of internal waves at finite topography in two dimensions. Part I: Theory and case studies. J. Phys. Oceanogr. 30, 532–549 (2000).

    Article  Google Scholar 

  34. 34.

    Legg, S. & Adcroft, A. Internal wave breaking at concave and convex continental slopes. J. Phys. Oceanogr. 33, 2224–2246 (2003).

    Article  Google Scholar 

  35. 35.

    Nash, J. D., Kunze, E., Toole, J. M. & Schmitt, R. W. Internal tide reflection and turbulent mixing on the continental slope. J. Phys. Oceanogr. 34, 1117–1134 (2004).

    Article  Google Scholar 

  36. 36.

    Bühler, O. & Holmes-Cerfon, M. Decay of an internal tide due to random topography in the ocean. J. Fluid Mech. 678, 271–293 (2011).

    Article  Google Scholar 

  37. 37.

    Thorpe, S. Models of energy loss from internal waves breaking in the ocean. J. Fluid Mech. 836, 72–116 (2018).

    Article  Google Scholar 

  38. 38.

    van Haren, H. Instability observations associated with wave breaking in the stable-stratified deep-ocean. Physica D 292–293, 62–69 (2015).

    Article  Google Scholar 

  39. 39.

    Gregg, M. C., Seim, H. E. & Percival, D. B. Statistics of shear and turbulent dissipation profiles in random internal wave-fields. J. Phys. Oceanogr. 23, 1777–1799 (1993).

    Article  Google Scholar 

  40. 40.

    Alford, M. H. & Pinkel, R. Observations of overturning in the thermocline: the context of ocean mixing. J. Phys. Oceanogr. 30, 805–832 (2000).

    Article  Google Scholar 

  41. 41.

    Olbers, D. J. Models of the oceanic internal wave field. Rev. Geophys. 21, 1567–1606 (1983).

    Article  Google Scholar 

  42. 42.

    Onuki, Y. & Hibiya, T. Decay rates of internal tides estimated by an improved wave–wave interaction analysis. J. Phys. Oceanogr. 48, 2689–2701 (2018).

    Article  Google Scholar 

  43. 43.

    Osborn, T. R. Estimates of the local-rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr. 10, 83–89 (1980).

    Article  Google Scholar 

  44. 44.

    Gregg, M., D’Asaro, E., Riley, J. & Kunze, E. Mixing efficiency in the ocean. Annu. Rev. Mar. Sci. 10, 443–473 (2018).

    Article  Google Scholar 

  45. 45.

    Oakey, N. Determination of the rate of dissipation of turbulent energy from simultaneous temperature and velocity shear microstructure measurements. J. Phys. Oceanogr. 12, 256–271 (1982).

    Article  Google Scholar 

  46. 46.

    Gregg, M. Uncertainties and limitations in measuring ε and χ T. J. Atmos. Oceans Technol. 16, 1483–1490 (1999).

    Article  Google Scholar 

  47. 47.

    Henyey, F. S., Wright, J. & Flatte, S. M. Energy and action flow through the internal wave field: An eikonal approach. J. Geophys. Res. Oceans 91, 8487–8495 (1986).

    Article  Google Scholar 

  48. 48.

    Gregg, M. C. Scaling turbulent dissipation in the thermocline. J. Geophys. Res. Oceans 94, 9686–9698 (1989).

    Article  Google Scholar 

  49. 49.

    Polzin, K. L., Toole, J. M. & Schmitt, R. W. Finescale parameterizations of turbulent dissipation. J. Phys. Oceanogr. 25, 306–328 (1995).

    Article  Google Scholar 

  50. 50.

    Polzin, K. L., Naveira Garabato, A. C., Huussen, T. N., Sloyan, B. M. & Waterman, S. N. Finescale parameterizations of turbulent dissipation. J. Geophys. Res. Oceans 119, 1383–1419 (2014).

    Article  Google Scholar 

  51. 51.

    Waterman, S., Polzin, K. L., Naveira Garabato, A. C., Sheen, K. L. & Forryan, A. Suppression of internal wave breaking in the Antarctic Circumpolar Current near topography. J. Phys. Oceanogr. 44, 1466–1492 (2014).

    Article  Google Scholar 

  52. 52.

    Whalen, C. B., MacKinnon, J. A., Talley, L. D. & Waterhouse, A. F. Estimating the mean diapycnal mixing using a finescale strain parameterization. J. Phys. Oceanogr. 45, 1174–1188 (2015).

    Article  Google Scholar 

  53. 53.

    Egbert, G. D. & Ray, R. D. Significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data. Nature 405, 775–778 (2000).

    Article  Google Scholar 

  54. 54.

    Nycander, J. Generation of internal waves in the deep ocean by tides. J. Geophys. Res. Oceans 110, C10028 (2005).

    Article  Google Scholar 

  55. 55.

    Alford, M. H. Improved global maps and 54-year history of wind-work on ocean inertial motions. Geophys. Res. Lett. 30, 1424 (2003).

    Google Scholar 

  56. 56.

    Jiang, J., Lu, Y. & Perrie, W. Estimating the energy flux from the wind to ocean inertial motions: The sensitivity to surface wind fields. Geophys. Res. Lett. 32, L15610 (2005).

    Article  Google Scholar 

  57. 57.

    Watanabe, M. & Hibiya, T. Global estimates of the wind-induced energy flux to inertial motions in the surface mixed layer. Geophys. Res. Lett. 29, 1239 (2002).

    Google Scholar 

  58. 58.

    Simmons, H. L. & Alford, M. H. Simulating the long-range swell of internal waves generated by ocean storms. Oceanography 25, 30–41 (2012).

    Article  Google Scholar 

  59. 59.

    Rimac, A., Storch, J.-S., Eden, C. & Haak, H. The influence of high-resolution wind stress field on the power input to near-inertial motions in the ocean. Geophys. Res. Lett. 40, 4882–4886 (2013).

    Article  Google Scholar 

  60. 60.

    Nikurashin, M. & Ferrari, R. Global energy conversion rate from geostrophic flows into internal lee waves in the deep ocean. Geophys. Res. Lett. 38, L08610 (2011).

    Article  Google Scholar 

  61. 61.

    Scott, R. B., Goff, J. A., Naveira Garabato, A. C. & Nurser, A. J. G. Global rate and spectral characteristics of internal gravity wave generation by geostrophic flow over topography. J. Geophys. Res. Oceans 116, C09029 (2011).

    Article  Google Scholar 

  62. 62.

    Wright, C. J., Scott, R. B., Ailliot, P. & Furnival, D. Lee wave generation rates in the deep ocean. Geophys. Res. Lett. 41, 2434–2440 (2014).

    Article  Google Scholar 

  63. 63.

    Nikurashin, M., Ferrari, R., Grisouard, N. & Polzin, K. The impact of finite-amplitude bottom topography on internal wave generation in the Southern Ocean. J. Phys. Oceanogr. 44, 2938–2950 (2014).

    Article  Google Scholar 

  64. 64.

    Yang, L., Nikurashin, M., Hogg, A. M. & Sloyan, B. M. Energy loss from transient eddies due to lee wave generation in the Southern Ocean. J. Phys. Oceanogr. 48, 2867–2885 (2018).

    Article  Google Scholar 

  65. 65.

    Thomas, L. N. On the effects of frontogenetic strain on symmetric instability and inertia–gravity waves. J. Fluid Mech. 711, 620–640 (2012).

    Article  Google Scholar 

  66. 66.

    Nagai, T., Tandon, A., Kunze, E. & Mahadevan, A. Spontaneous generation of near-inertial waves by the Kuroshio Front. J. Phys. Oceanogr. 45, 2381–2406 (2015).

    Article  Google Scholar 

  67. 67.

    McComas, C. H. & Müller, P. The dynamic balance of internal waves. J. Phys. Oceanogr. 11, 970–986 (1981).

    Article  Google Scholar 

  68. 68.

    Garrett, C. & Munk, W. Space-time scales of internal waves: A progress report. J. Geophys. Res. 80, 291–297 (1975).

    Article  Google Scholar 

  69. 69.

    Munk, W. in Evolution of Physical Oceanography (eds Warren, B.A. & Wunsch, C.) 264–291 (MIT Press, 1981).

  70. 70.

    Polzin, K. L. & Lvov, Y. V. Toward regional characterizations of the oceanic internal wavefield. Rev. Geophys. 49, RG4003 (2011).

    Article  Google Scholar 

  71. 71.

    Lien, R.-C., Tang, T. Y., Chang, M. H. & D’Asaro, E. A. Energy of nonlinear internal waves in the South China Sea. Geophys. Res. Lett. 32, L05615 (2005).

    Article  Google Scholar 

  72. 72.

    Levine, M. D. A modification of the Garrett–Munk internal wave spectrum. J. Phys. Oceanogr. 32, 3166–3181 (2002).

    Article  Google Scholar 

  73. 73.

    MacKinnon, J. & Gregg, M. Shear and baroclinic energy flux on the summer New England shelf. J. Phys. Oceanogr. 33, 1462–1475 (2003).

    Article  Google Scholar 

  74. 74.

    Garrett, C. & Kunze, E. Internal tide generation in the deep ocean. Annu. Rev. Fluid Mech. 39, 57–87 (2007).

    Article  Google Scholar 

  75. 75.

    Kunze, E., Firing, E., Hummon, J. M., Chereskin, T. K. & Thurnherr, A. M. Global abyssal mixing inferred from lowered ADCP shear and CTD strain profiles. J. Phys. Oceanogr. 36, 1553–1576 (2006).

    Article  Google Scholar 

  76. 76.

    Whalen, C. B., Talley, L. D. & MacKinnon, J. A. Spatial and temporal variability of global ocean mixing inferred from Argo profiles. Geophys. Res. Lett. 39, L18612 (2012).

    Article  Google Scholar 

  77. 77.

    Waterhouse, A. F. et al. Global patterns of diapycnal mixing from measurements of the turbulent dissipation rate. J. Phys. Oceanogr. 44, 1854–1872 (2014).

    Article  Google Scholar 

  78. 78.

    de Lavergne, C. et al. Toward global maps of internal tide energy sinks. Ocean Model. 137, 52–75 (2019).

    Article  Google Scholar 

  79. 79.

    Egbert, G. D. & Ray, R. D. Estimates of M2 tidal energy dissipation from TOPEX/Poseidon altimeter data. J. Geophys. Res. Oceans 106, 22475–22502 (2001).

    Article  Google Scholar 

  80. 80.

    Nakamura, T., Isoda, Y., Mitsudera, H., Takagi, S. & Nagasawa, M. Breaking of unsteady lee waves generated by diurnal tides. Geophys. Res. Lett. 37, L04602 (2010).

    Google Scholar 

  81. 81.

    Nash, J. D. & Moum, J. N. Internal hydraulic flows on the continental shelf: High drag states over a small bank. J. Geophys. Res. Oceans 106, 4593–4611 (2001).

    Article  Google Scholar 

  82. 82.

    St. Laurent, L. & Garrett, C. The role of internal tides in mixing the deep ocean. J. Phys. Oceanogr. 32, 2882–2899 (2002).

    Article  Google Scholar 

  83. 83.

    Vic, C. et al. Deep-ocean mixing driven by small-scale internal tides. Nat. Commun. 10, 2099 (2019).

    Article  Google Scholar 

  84. 84.

    Falahat, S., Nycander, J., Roquet, F. & Zarroug, M. Global calculation of tidal energy conversion into vertical normal modes. J. Phys. Oceanogr. 44, 3225–3244 (2014).

    Article  Google Scholar 

  85. 85.

    Zhao, Z., Alford, M. H., Girton, J. B., Rainville, L. & Simmons, H. L. Global observations of open-ocean mode-1 M2 internal tides. J. Phys. Oceanogr. 46, 1657–1684 (2016).

    Article  Google Scholar 

  86. 86.

    Polzin, K. Idealized solutions for the energy balance of the finescale internal wave field. J. Phys. Oceanogr. 34, 231–246 (2004).

    Article  Google Scholar 

  87. 87.

    Melet, A. et al. Internal tide generation by abyssal hills using analytical theory. J. Geophys. Res. Oceans 118, 6303–6318 (2013).

    Article  Google Scholar 

  88. 88.

    Goff, J. A. & Arbic, B. K. Global prediction of abyssal hill roughness statistics for use in ocean models from digital maps of paleo-spreading rate, paleo-ridge orientation, and sediment thickness. Ocean Model. 32, 36–43 (2010).

    Article  Google Scholar 

  89. 89.

    Lefauve, A., Muller, C. & Melet, A. A three-dimensional map of tidal dissipation over abyssal hills. J. Geophys. Res. Oceans 120, 4760–4777 (2015).

    Article  Google Scholar 

  90. 90.

    Polzin, K. L., Toole, J. M., Ledwell, J. R. & Schmitt, R. W. Spatial variability of turbulent mixing in the abyssal ocean. Science 276, 93–96 (1997).

    Article  Google Scholar 

  91. 91.

    Ledwell, J. R. et al. Evidence for enhanced mixing over rough topography in the abyssal ocean. Nature 403, 179–182 (2000).

    Article  Google Scholar 

  92. 92.

    Muller, C. J. & Bühler, O. Saturation of the internal tides and induced mixing in the abyssal ocean. J. Phys. Oceanogr. 39, 2077–2096 (2009).

    Article  Google Scholar 

  93. 93.

    Polzin, K. L. An abyssal recipe. Ocean Model. 30, 298–309 (2009).

    Article  Google Scholar 

  94. 94.

    Klymak, J. M., Legg, S. & Pinkel, R. A simple parameterization of turbulent tidal mixing near supercritical topography. J. Phys. Oceanogr. 40, 2059–2074 (2010).

    Article  Google Scholar 

  95. 95.

    Nikurashin, M. & Legg, S. A mechanism for local dissipation of internal tides generated at rough topography. J. Phys. Oceanogr. 41, 378–395 (2011).

    Article  Google Scholar 

  96. 96.

    St. Laurent, L. C. & Nash, J. D. in Proceedings of the 13th ‘Aha Huliko’a Hawaiian Winter Workshop 45–58 (University of Hawaii at Manoa, 2004).

  97. 97.

    Klymak, J. M. et al. An estimate of tidal energy lost to turbulence at the Hawaiian Ridge. J. Phys. Oceanogr. 36, 1148–1164 (2006).

    Article  Google Scholar 

  98. 98.

    Richet, O., Muller, C. & Chomaz, J.-M. Impact of a mean current on the internal tide energy dissipation at the critical latitude. J. Phys. Oceanogr. 47, 1457–1472 (2017).

    Article  Google Scholar 

  99. 99.

    Dushaw, B. D., Howe, B. M., Cornuelle, B. D., Worcester, P. F. & Luther, D. S. Barotropic and baroclinic tides in the central North Pacific Ocean determined from long-range reciprocal acoustic transmissions. J. Phys. Oceanogr. 25, 631–647 (1995).

    Article  Google Scholar 

  100. 100.

    Ray, R. D. & Mitchum, G. T. Surface manifestation of internal tides generated near Hawaii. Geophys. Res. Lett. 23, 2101–2104 (1996).

    Article  Google Scholar 

  101. 101.

    Zhao, Z. Mapping internal tides from satellite altimetry without blind directions. J. Geophys. Res. Oceans 124, 8605–8625 (2019).

    Article  Google Scholar 

  102. 102.

    Zhao, Z. The global mode-2 M2 internal tide. J. Geophys. Res. Oceans 123, 7725–7746 (2018).

    Article  Google Scholar 

  103. 103.

    Alford, M. H. & Zhao, Z. Global patterns of low-mode internal-wave propagation. Part I: Energy and energy flux. J. Phys. Oceanogr. 37, 1829–1848 (2007).

    Article  Google Scholar 

  104. 104.

    Zhao, Z., Alford, M. H., MacKinnon, J. A. & Pinkel, R. Long-range propagation of the semidiurnal internal tide from the Hawaiian Ridge. J. Phys. Oceanogr. 40, 713–736 (2010).

    Article  Google Scholar 

  105. 105.

    Vic, C. et al. The lifecycle of semidiurnal internal tides over the northern Mid-Atlantic Ridge. J. Phys. Oceanogr. 48, 61–80 (2018).

    Article  Google Scholar 

  106. 106.

    Kelly, S., Jones, N., Nash, J. & Waterhouse, A. The geography of semidiurnal mode-1 internal-tide energy loss. Geophys. Res. Lett. 40, 4689–4693 (2013).

    Article  Google Scholar 

  107. 107.

    Waterhouse, A. F. et al. Observations of the Tasman Sea internal tide beam. J. Phys. Oceanogr. 48, 1283–1297 (2018).

    Article  Google Scholar 

  108. 108.

    Johnston, T. S. & Merrifield, M. A. Internal tide scattering at seamounts, ridges, and islands. J. Geophys. Res. Oceans 108, 3180 (2003).

    Article  Google Scholar 

  109. 109.

    Mathur, M., Carter, G. S. & Peacock, T. Topographic scattering of the low-mode internal tide in the deep ocean. J. Geophys. Res. Oceans 119, 2165–2182 (2014).

    Article  Google Scholar 

  110. 110.

    Klymak, J. M., Buijsman, M., Legg, S. & Pinkel, R. Parameterizing surface and internal tide scattering and breaking on supercritical topography: the one- and two-ridge cases. J. Phys. Oceanogr. 43, 1380–1397 (2013).

    Article  Google Scholar 

  111. 111.

    Johnston, T. S., Rudnick, D. L. & Kelly, S. M. Standing internal tides in the Tasman Sea observed by gliders. J. Phys. Oceanogr. 45, 2715–2737 (2015).

    Article  Google Scholar 

  112. 112.

    Martini, K. I., Alford, M. H., Kunze, E., Kelly, S. M. & Nash, J. D. Internal bores and breaking internal tides on the Oregon continental slope. J. Phys. Oceanogr. 43, 120–139 (2013).

    Article  Google Scholar 

  113. 113.

    Legg, S. Scattering of low-mode internal waves at finite isolated topography. J. Phys. Oceanogr. 44, 359–383 (2014).

    Article  Google Scholar 

  114. 114.

    Ansong, J. K. et al. Geographical distribution of diurnal and semidiurnal parametric subharmonic instability in a global ocean circulation model. J. Phys. Oceanogr. 48, 1409–1431 (2018).

    Article  Google Scholar 

  115. 115.

    Hibiya, T. & Nagasawa, M. Latitudinal dependence of diapycnal diffusivity in the thermocline estimated using a finescale parameterization. Geophys. Res. Lett. 31, L01301 (2004).

    Article  Google Scholar 

  116. 116.

    Hazewinkel, J. & Winters, K. PSI of the internal tide on a β plane: flux divergence and near-inertial wave propagation. J. Phys. Oceanogr. 41, 1673–1682 (2011).

    Article  Google Scholar 

  117. 117.

    Eden, C. & Olbers, D. An energy compartment model for propagation, nonlinear interaction, and dissipation of internal gravity waves. J. Phys. Oceanogr. 44, 2093–2106 (2014).

    Article  Google Scholar 

  118. 118.

    Rainville, L. & Pinkel, R. Propagation of low-mode internal waves through the ocean. J. Phys. Oceanogr. 36, 1220–1236 (2006).

    Article  Google Scholar 

  119. 119.

    Polzin, K. L. Mesoscale eddy–internal wave coupling. Part I: Symmetry, wave capture, and results from the mid-ocean dynamics experiment. J. Phys. Oceanogr. 38, 2556–2574 (2008).

    Article  Google Scholar 

  120. 120.

    Polzin, K. L. Mesoscale eddy–internal wave coupling. Part II: Energetics and results from PolyMode. J. Phys. Oceanogr. 40, 789–801 (2010).

    Article  Google Scholar 

  121. 121.

    Kelly, S. M., Lermusiaux, P. F., Duda, T. F. & Haley, P. J. Jr A coupled-mode shallow-water model for tidal analysis: internal tide reflection and refraction by the Gulf Stream. J. Phys. Oceanogr. 46, 3661–3679 (2016).

    Article  Google Scholar 

  122. 122.

    Buijsman, M. C. et al. Semidiurnal internal tide incoherence in the equatorial Pacific. J. Geophys. Res. Oceans 122, 5286–5305 (2017).

    Article  Google Scholar 

  123. 123.

    Dunphy, M., Ponte, A. L., Klein, P. & Le Gentil, S. Low-mode internal tide propagation in a turbulent eddy field. J. Phys. Oceanogr. 47, 649–665 (2017).

    Article  Google Scholar 

  124. 124.

    Pollard, R. T. & Millard, R. C. Comparison between observed and simulated wind-generated inertial oscillations. Deep Sea Res. Oceanogr. Abstr. 17, 813–821 (1970).

    Article  Google Scholar 

  125. 125.

    Alford, M. H. & Whitmont, M. Seasonal and spatial variability of near-inertial kinetic energy from historical moored velocity records. J. Phys. Oceanogr. 37, 2022–2037 (2007).

    Article  Google Scholar 

  126. 126.

    Whalen, C. B., MacKinnon, J. A. & Talley, L. D. Large-scale impacts of the mesoscale environment on mixing from wind-driven internal waves. Nat. Geosci. 11, 842–847 (2018).

    Article  Google Scholar 

  127. 127.

    D’Asaro, E. A. et al. Upper-ocean inertial currents forced by a strong storm. Part I: Data and comparisons with linear theory. J. Phys. Oceanogr. 25, 2909–2936 (1995).

    Article  Google Scholar 

  128. 128.

    Price, J. F. Internal wave wake of a moving storm. Part I. Scales, energy budget and observations. J. Phys. Oceanogr. 13, 949–965 (1983).

    Article  Google Scholar 

  129. 129.

    Church, J. A., Joyce, T. & Price, J. F. Current and density observations across the wake of Hurricane Gay. J. Phys. Oceanogr. 19, 259–265 (1989).

    Article  Google Scholar 

  130. 130.

    Sanford, T. B., Price, J. F. & Girton, J. B. Upper-ocean response to Hurricane Frances (2004) observed by profiling EM-APEX floats. J. Phys. Oceanogr. 41, 1041–1056 (2011).

    Article  Google Scholar 

  131. 131.

    Dohan, K. & Davis, R. E. Mixing in the transition layer during two storm events. J. Phys. Oceanogr. 41, 42–66 (2011).

    Article  Google Scholar 

  132. 132.

    Johnston, T. S. et al. Decay mechanisms of near-inertial mixed layer oscillations in the Bay of Bengal. Oceanography 29, 180–191 (2016).

    Article  Google Scholar 

  133. 133.

    Gill, A. E. On the behavior of internal waves in the wakes of storms. J. Phys. Oceanogr. 14, 1129–1151 (1984).

    Article  Google Scholar 

  134. 134.

    Alford, M. H. Redistribution of energy available for ocean mixing by long-range propagation of internal waves. Nature 423, 159–162 (2003).

    Article  Google Scholar 

  135. 135.

    Alford, M., Cronin, M. & Klymak, J. Annual cycle and depth penetration of wind-generated near-inertial internal waves at Ocean Station Papa in the Northeast Pacific. J. Phys. Oceanogr. 42, 889–909 (2012).

    Article  Google Scholar 

  136. 136.

    Chaigneau, A., Pizarro, O. & Rojas, W. Global climatology of near-inertial current characteristics from Lagrangian observations. Geophys. Res. Lett. 35, L13603 (2008).

    Article  Google Scholar 

  137. 137.

    Furuichi, N., Hibiya, T. & Niwa, Y. Model-predicted distribution of wind-induced internal wave energy in the world’s oceans. J. Geophys. Res. Oceans 113, C09034 (2008).

    Article  Google Scholar 

  138. 138.

    Zhai, X., Greatbatch, R. J., Eden, C. & Hibiya, T. On the loss of wind-induced near-inertial energy to turbulent mixing in the upper ocean. J. Phys. Oceanogr. 39, 3040–3045 (2009).

    Article  Google Scholar 

  139. 139.

    Rimac, A., Storch, J.-S. V. & Eden, C. The total energy flux leaving the ocean’s mixed layer. J. Phys. Oceanogr. 46, 1885–1900 (2016).

    Article  Google Scholar 

  140. 140.

    Jouanno, J., Capet, X., Madec, G., Roullet, G. & Klein, P. Dissipation of the energy imparted by mid-latitude storms in the Southern Ocean. Ocean Sci. 12, 743–769 (2016).

    Article  Google Scholar 

  141. 141.

    Weller, R. A. The relation of near-inertial motions observed in the mixed layer during the JASIN (1978) experiment to the local wind stress and to the quasi-geostrophic flow field. J. Phys. Oceanogr. 12, 1122–1136 (1982).

    Article  Google Scholar 

  142. 142.

    Jing, Z., Wu, L. & Ma, X. Energy exchange between the mesoscale oceanic eddies and wind-forced near-inertial oscillations. J. Phys. Oceanogr. 47, 721–733 (2017).

    Article  Google Scholar 

  143. 143.

    Whitt, D. B. & Thomas, L. N. Resonant generation and energetics of wind-forced near-inertial motions in a geostrophic flow. J. Phys. Oceanogr. 45, 181–208 (2015).

    Article  Google Scholar 

  144. 144.

    Van Meurs, P. Interactions between near-inertial mixed layer currents and the mesoscale: The importance of spatial variabilities in the vorticity field. J. Phys. Oceanogr. 28, 1363–1388 (1998).

    Article  Google Scholar 

  145. 145.

    D’Asaro, E. A. Upper-ocean inertial currents forced by a strong storm. Part III: Interaction of inertial currents and mesoscale eddies. J. Phys. Oceanogr. 25, 2953–2958 (1995).

    Article  Google Scholar 

  146. 146.

    Elipot, S., Lumpkin, R. & Prieto, G. Modification of inertial oscillations by the mesoscale eddy field. J. Geophys. Res. Oceans 115, C09010 (2010).

    Article  Google Scholar 

  147. 147.

    Alford, M. H. & Gregg, M. C. Near-inertial mixing: modulation of shear, strain and microstructure at low latitude. J. Geophys. Res. Oceans 106, 16947–16968 (2001).

    Article  Google Scholar 

  148. 148.

    Plueddemann, A. & Farrar, J. Observations and models of the energy flux from the wind to mixed-layer inertial currents. Deep Sea Res. Part II Top. Stud. Oceanogr. 53, 5–30 (2006).

    Article  Google Scholar 

  149. 149.

    Liu, G., Perrie, W. & Hughes, C. Surface wave effects on the wind-power input to mixed layer near-inertial motions. J. Phys. Oceanogr. 47, 1077–1093 (2017).

    Article  Google Scholar 

  150. 150.

    Liu, Y., Jing, Z. & Wu, L. Wind power on oceanic near-inertial oscillations in the global ocean estimated from surface drifters. Geophys. Res. Lett. 46, 2647–2653 (2019).

    Article  Google Scholar 

  151. 151.

    Alford, M. H., MacKinnon, J. A., Pinkel, R. & Klymak, J. M. Space–time scales of shear in the North Pacific. J. Phys. Oceanogr. 47, 2455–2478 (2017).

    Article  Google Scholar 

  152. 152.

    Cuypers, Y., Le Vaillant, X., Bouruet-Aubertot, P., Vialard, J. & Mcphaden, M. J. Tropical storm-induced near-inertial internal waves during the Cirene experiment: Energy fluxes and impact on vertical mixing. J. Geophys. Res. Oceans 118, 358–380 (2013).

    Article  Google Scholar 

  153. 153.

    Garrett, C. What is the “near-inertial” band and why is it different from the rest of the internal wave spectrum? J. Phys. Oceanogr. 31, 962–971 (2001).

    Article  Google Scholar 

  154. 154.

    Jeon, C. et al. Poleward-propagating near-inertial waves enabled by the western boundary current. Sci. Rep. 9, 9955 (2019).

    Article  Google Scholar 

  155. 155.

    Nagasawa, M., Niwa, Y. & Hibiya, T. Spatial and temporal distribution of the wind-induced internal wave energy available for deep water mixing in the North Pacific. J. Geophys. Res. Oceans 105, 13933–13943 (2000).

    Article  Google Scholar 

  156. 156.

    Komori, N., Ohfuchi, W., Taguchi, B., Sasaki, H. & Klein, P. Deep ocean inertia-gravity waves simulated in a high-resolution global coupled atmosphere–ocean GCM. Geophys. Res. Lett. 35, L04610 (2008).

    Article  Google Scholar 

  157. 157.

    Silverthorne, K. E. & Toole, J. M. Seasonal kinetic energy variability of near-inertial motions. J. Phys. Oceanogr. 39, 1035–1049 (2009).

    Article  Google Scholar 

  158. 158.

    Inoue, R., Watanabe, M. & Osafune, S. Wind-induced mixing in the North Pacific. J. Phys. Oceanogr. 47, 1587–1603 (2017).

    Article  Google Scholar 

  159. 159.

    Kunze, E. Near-inertial wave-propagation in geostrophic shear. J. Phys. Oceanogr. 15, 544–565 (1985).

    Article  Google Scholar 

  160. 160.

    Young, W. & Jelloul, M. B. Propagation of near-inertial oscillations through a geostrophic flow. J. Mar. Res. 55, 735–766 (1997).

    Article  Google Scholar 

  161. 161.

    Klein, P., Smith, S. L. & Lapeyre, G. Organization of near-inertial energy by an eddy field. Q. J. R. Meteorol. Soc. 130, 1153–1166 (2004).

    Article  Google Scholar 

  162. 162.

    Danioux, E., Klein, P. & Rivière, P. Propagation of wind energy into the deep ocean through a fully turbulent mesoscale eddy field. J. Phys. Oceanogr. 38, 2224–2241 (2008).

    Article  Google Scholar 

  163. 163.

    Mooers, C. N. Several effects of a baroclinic current on the cross-stream propagation of inertial-internal waves. Geophys. Astrophys. Fluid Dyn. 6, 245–275 (1975).

    Article  Google Scholar 

  164. 164.

    Whitt, D. & Thomas, L. Near-inertial waves in strongly baroclinic currents. J. Phys. Oceanogr. 43, 706–725 (2013).

    Article  Google Scholar 

  165. 165.

    Whitt, D. B., Thomas, L. N., Klymak, J. M., Lee, C. M. & D’Asaro, E. A. Interaction of superinertial waves with submesoscale cyclonic filaments in the north wall of the Gulf Stream. J. Phys. Oceanogr. 48, 81–99 (2018).

    Article  Google Scholar 

  166. 166.

    Padman, L., Levine, M., Dillon, T., Morison, J. & Pinkel, R. Hydrography and microstructure of an Arctic cyclonic eddy. J. Geophys. Res. Oceans 95, 9411–9420 (1990).

    Article  Google Scholar 

  167. 167.

    Kunze, E. The energy balance in a warm-core ring’s near-inertial critical layer. J. Phys. Oceanogr. 25, 942–957 (1995).

    Article  Google Scholar 

  168. 168.

    Joyce, T., Toole, J., Klein, P. & Thomas, L. A near-inertial mode observed within a Gulf Stream warm-core ring. J. Geophys. Res. Oceans 118, 1797–1806 (2013).

    Article  Google Scholar 

  169. 169.

    Sheen, K. et al. Modification of turbulent dissipation rates by a deep Southern Ocean eddy. Geophys. Res. Lett. 42, 3450–3457 (2015).

    Article  Google Scholar 

  170. 170.

    Fer, I., Bosse, A., Ferron, B. & Bouruet-Aubertot, P. The dissipation of kinetic energy in the Lofoten Basin Eddy. J. Phys. Oceanogr. 48, 1299–1316 (2018).

    Article  Google Scholar 

  171. 171.

    Wunsch, C. The work done by the wind on the oceanic general circulation. J. Phys. Oceanogr. 28, 2332–2340 (1998).

    Article  Google Scholar 

  172. 172.

    von Storch, J.-S., Sasaki, H. & Marotzke, J. Wind-generated power input to the deep ocean: An estimate using a 1/10 general circulation model. J. Phys. Oceanogr. 37, 657–672 (2007).

    Article  Google Scholar 

  173. 173.

    Arbic, B. K. & Flierl, G. R. Baroclinically unstable geostrophic turbulence in the limits of strong and weak bottom Ekman friction: Application to midocean eddies. J. Phys. Oceanogr. 34, 2257–2273 (2004).

    Article  Google Scholar 

  174. 174.

    Sen, A., Scott, R. B. & Arbic, B. K. 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 (2008).

    Article  Google Scholar 

  175. 175.

    Klymak, J. M. Nonpropagating form drag and turbulence due to stratified flow over large-scale abyssal hill topography. J. Phys. Oceanogr. 48, 2383–2395 (2018).

    Article  Google Scholar 

  176. 176.

    Renault, L. et al. Modulation of wind work by oceanic current interaction with the atmosphere. J. Phys. Oceanogr. 46, 1685–1704 (2016).

    Article  Google Scholar 

  177. 177.

    Melet, A., Hallberg, R., Adcroft, A., Nikurashin, M. & Legg, S. Energy flux into internal lee waves: sensitivity to future climate changes using linear theory and a climate model. J. Clim. 28, 2365–2384 (2015).

    Article  Google Scholar 

  178. 178.

    Zheng, K. & Nikurashin, M. Downstream propagation and remote dissipation of internal waves in the Southern Ocean. J. Phys. Oceanogr. 49, 1873–1887 (2019).

    Article  Google Scholar 

  179. 179.

    Waterman, S., Garabato, A. C. N. & Polzin, K. L. Internal waves and turbulence in the Antarctic Circumpolar Current. J. Phys. Oceanogr. 43, 259–282 (2013).

    Article  Google Scholar 

  180. 180.

    Sheen, K. L. et al. Rates and mechanisms of turbulent dissipation and mixing in the Southern Ocean: Results from the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean (DIMES). J. Geophys. Res. Oceans 118, 2774–2792 (2013).

    Article  Google Scholar 

  181. 181.

    Meyer, A., Sloyan, B. M., Polzin, K. L., Phillips, H. E. & Bindoff, N. L. Mixing variability in the Southern Ocean. J. Phys. Oceanogr. 45, 966–987 (2015).

    Article  Google Scholar 

  182. 182.

    Cusack, J. M., Naveira Garabato, A. C., Smeed, D. A. & Girton, J. B. Observation of a large lee wave in the Drake Passage. J. Phys. Oceanogr. 47, 793–810 (2017).

    Article  Google Scholar 

  183. 183.

    Clement, L., Frajka-Williams, E., Sheen, K., Brearley, J. & Garabato, A. N. Generation of internal waves by eddies impinging on the western boundary of the North Atlantic. J. Phys. Oceanogr. 46, 1067–1079 (2016).

    Article  Google Scholar 

  184. 184.

    Brearley, J. A., Sheen, K. L., Naveira Garabato, A. C., Smeed, D. A. & Waterman, S. Eddy-induced modulation of turbulent dissipation over rough topography in the Southern Ocean. J. Phys. Oceanogr. 43, 2288–2308 (2013).

    Article  Google Scholar 

  185. 185.

    Köhler, J. et al. Variability in the internal wave field induced by the Atlantic Deep Western Boundary Current at 16°N. J. Phys. Oceanogr. 44, 492–516 (2014).

    Article  Google Scholar 

  186. 186.

    Sheen, K. et al. Eddy-induced variability in Southern Ocean abyssal mixing on climatic timescales. Nat. Geosci. 7, 577–582 (2014).

    Article  Google Scholar 

  187. 187.

    Kunze, E. & Lien, R.-C. Energy sinks for lee waves in shear flow. J. Phys. Oceanogr. 49, 2851–2865 (2019).

    Article  Google Scholar 

  188. 188.

    Naveira Garabato, A. C., Polzin, K. L., King, B. A., Heywood, K. J. & Visbeck, M. Widespread intense turbulent mixing in the Southern Ocean. Science 303, 210–213 (2004).

    Article  Google Scholar 

  189. 189.

    St. Laurent, L. et al. Turbulence and diapycnal mixing in Drake Passage. J. Phys. Oceanogr. 42, 2143–2152 (2012).

    Article  Google Scholar 

  190. 190.

    Alford, M. H. et al. Turbulent mixing and hydraulic control of abyssal water in the Samoan Passage. Geophys. Res. Lett. 40, 4668–4674 (2013).

    Article  Google Scholar 

  191. 191.

    Thurnherr, A. Diapycnal mixing associated with an overflow in a deep submarine canyon. Deep Sea Res. Part II Top. Stud. Oceanogr. 53, 194–206 (2006).

    Article  Google Scholar 

  192. 192.

    Nikurashin, M. & Ferrari, R. Radiation and dissipation of internal waves generated by geostrophic motions impinging on small-scale topography: Theory. J. Phys. Oceanogr. 40, 1055–1074 (2010).

    Article  Google Scholar 

  193. 193.

    Trossman, D. S. et al. Internal lee wave closures: Parameter sensitivity and comparison to observations. J. Geophys. Res. Oceans 120, 7997–8019 (2015).

    Article  Google Scholar 

  194. 194.

    Griffiths, M. & Reeder, M. J. Stratospheric inertia–gravity waves generated in a numerical model of frontogenesis. I: Model solutions. Q. J. R. Meteorol. Soc. 122, 1153–1174 (1996).

    Google Scholar 

  195. 195.

    Reeder, M. J. & Griffiths, M. Stratospheric inertia–gravity waves generated in a numerical model of frontogenesis. II: Wave sources, generation mechanisms and momentum fluxes. Q. J. R. Meteorol. Soc. 122, 1175–1195 (1996).

    Google Scholar 

  196. 196.

    Danioux, E., Vanneste, J., Klein, P. & Sasaki, H. Spontaneous inertia-gravity-wave generation by surface-intensified turbulence. J. Fluid Mech. 699, 153–173 (2012).

    Article  Google Scholar 

  197. 197.

    Vanneste, J. Balance and spontaneous wave generation in geophysical flows. Annu. Rev. Fluid Mech. 45, 147–172 (2013).

    Article  Google Scholar 

  198. 198.

    Snyder, C., Skamarock, W. C. & Rotunno, R. Frontal dynamics near and following frontal collapse. J. Atmos. Sci. 50, 3194–3212 (1993).

    Article  Google Scholar 

  199. 199.

    Shakespeare, C. J. & Hogg, A. M. Spontaneous surface generation and interior amplification of internal waves in a regional-scale ocean model. J. Phys. Oceanogr. 47, 811–826 (2017).

    Article  Google Scholar 

  200. 200.

    Rossby, C. G. On the mutual adjustment of pressure and velocity distributions in certain simple current systems. J. Mar. Res. 1, 15–28 (1937).

    Google Scholar 

  201. 201.

    Ford, R. Gravity wave radiation from vortex trains in rotating shallow water. J. Fluid Mech. 281, 81–118 (1994).

    Article  Google Scholar 

  202. 202.

    Xie, J.-H. & Vanneste, J. A generalised-Lagrangian-mean model of the interactions between near-inertial waves and mean flow. J. Fluid Mech. 774, 143–169 (2015).

    Article  Google Scholar 

  203. 203.

    Wagner, G. & Young, W. 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, 806–837 (2016).

    Article  Google Scholar 

  204. 204.

    Alford, M. H., Shcherbina, A. Y. & Gregg, M. C. Observations of near-inertial internal gravity waves radiating from a frontal jet. J. Phys. Oceanogr. 43, 1225–1239 (2013).

    Article  Google Scholar 

  205. 205.

    Ferrari, R. & Wunsch, C. The distribution of eddy kinetic and potential energies in the global ocean. Tellus 62, 92–108 (2010).

    Article  Google Scholar 

  206. 206.

    Shakespeare, C. J. & Hogg, A. The life cycle of spontaneously generated internal waves. J. Phys. Oceanogr. 48, 343–359 (2018).

    Article  Google Scholar 

  207. 207.

    Toggweiler, J. & Samuels, B. On the ocean’s large-scale circulation near the limit of no vertical mixing. J. Phys. Oceanogr. 28, 1832–1852 (1998).

    Article  Google Scholar 

  208. 208.

    Oka, A. & Niwa, Y. Pacific deep circulation and ventilation controlled by tidal mixing away from the sea bottom. Nat. Commun. 4, 2419 (2013).

    Article  Google Scholar 

  209. 209.

    Melet, A., Legg, S. & Hallberg, R. Climatic impacts of parameterized local and remote tidal mixing. J. Clim. 29, 3473–3500 (2016).

    Article  Google Scholar 

  210. 210.

    Hieronymus, M., Nycander, J., Nilsson, J., Döös, K. & Hallberg, R. Oceanic overturning and heat transport: The role of background diffusivity. J. Clim. 32, 701–716 (2019).

    Article  Google Scholar 

  211. 211.

    Adcroft, A., Scott, J. R. & Marotzke, J. Impact of geothermal heating on the global ocean circulation. Geophys. Res. Lett. 28, 1735–1738 (2001).

    Article  Google Scholar 

  212. 212.

    Emile-Geay, J. & Madec, G. Geothermal heating, diapycnal mixing and the abyssal circulation. Ocean Sci. Discuss. 5, 203–217 (2009).

    Article  Google Scholar 

  213. 213.

    Naveira Garabato, A. C. et al. Rapid mixing and exchange of deep-ocean waters in an abyssal boundary current. Proc. Natl Acad. Sci. USA 116, 13233–13238 (2019).

    Article  Google Scholar 

  214. 214.

    Bryden, H. L. & Nurser, A. G. Effects of strait mixing on ocean stratification. J. Phys. Oceanogr. 33, 1870–1872 (2003).

    Article  Google Scholar 

  215. 215.

    Ganachaud, A. Large-scale mass transports, water mass formation, and diffusivities estimated from World Ocean Circulation Experiment (WOCE) hydrographic data. J. Geophys. Res. Oceans 108, 3213 (2003).

    Article  Google Scholar 

  216. 216.

    Lumpkin, R. & Speer, K. Global ocean meridional overturning. J. Phys. Oceanogr. 37, 2550–2562 (2007).

    Article  Google Scholar 

  217. 217.

    Jayne, S. R. The impact of abyssal mixing parameterizations in an ocean general circulation model. J. Phys. Oceanogr. 39, 1756–1775 (2009).

    Article  Google Scholar 

  218. 218.

    De Lavergne, C., Madec, G., Le Sommer, J., Nurser, A. G. & Naveira Garabato, A. C. The impact of a variable mixing efficiency on the abyssal overturning. J. Phys. Oceanogr. 46, 663–681 (2016).

    Article  Google Scholar 

  219. 219.

    Melet, A., Hallberg, R., Legg, S. & Nikurashin, M. Sensitivity of the ocean state to lee wave–driven mixing. J. Phys. Oceanogr. 44, 900–921 (2014).

    Article  Google Scholar 

  220. 220.

    Saenko, O. & Merryfield, W. On the effect of topographically enhanced mixing on the global ocean circulation. J. Phys. Oceanogr. 35, 826–834 (2005).

    Article  Google Scholar 

  221. 221.

    Simmons, H. L., Jayne, S. R., Laurent, L. C. S. & Weaver, A. J. Tidally driven mixing in a numerical model of the ocean general circulation. Ocean Model. 6, 245–263 (2004).

    Article  Google Scholar 

  222. 222.

    Melet, A., Hallberg, R., Legg, S. & Polzin, K. Sensitivity of the ocean state to the vertical distribution of internal-tide-driven mixing. J. Phys. Oceanogr. 43, 602–615 (2013).

    Article  Google Scholar 

  223. 223.

    Tatebe, H., Tanaka, Y., Komuro, Y. & Hasumi, H. Impact of deep ocean mixing on the climatic mean state in the Southern Ocean. Sci. Rep. 8, 14479 (2018).

    Article  Google Scholar 

  224. 224.

    Zhu, Y. & Zhang, R.-H. A modified vertical mixing parameterization for its improved ocean and coupled simulations in the tropical Pacific. J. Phys. Oceanogr. 49, 21–37 (2019).

    Article  Google Scholar 

  225. 225.

    Jochum, M. et al. The impact of oceanic near-inertial waves on climate. J. Clim. 26, 2833–2844 (2013).

    Article  Google Scholar 

  226. 226.

    Stanley, G. J. & Saenko, O. A. Bottom-enhanced diapycnal mixing driven by mesoscale eddies: Sensitivity to wind energy supply. J. Phys. Oceanogr. 44, 68–85 (2014).

    Article  Google Scholar 

  227. 227.

    Koch-Larrouy, A., Lengaigne, M., Terray, P., Madec, G. & Masson, S. Tidal mixing in the Indonesian Seas and its effect on the tropical climate system. Clim. Dyn. 34, 891–904 (2010).

    Article  Google Scholar 

  228. 228.

    Kida, S. & Wijffels, S. The impact of the Indonesian Throughflow and tidal mixing on the summertime sea surface temperature in the western Indonesian Seas. J. Geophys. Res. Oceans 117, C09007 (2012).

    Article  Google Scholar 

  229. 229.

    Sasaki, H., Kida, S., Furue, R., Nonaka, M. & Masumoto, Y. An increase of the Indonesian Throughflow by internal tidal mixing in a high-resolution quasi-global ocean simulation. Geophys. Res. Lett. 45, 8416–8424 (2018).

    Article  Google Scholar 

  230. 230.

    Saenko, O. A., Zhai, X., Merryfield, W. J. & Lee, W. G. The combined effect of tidally and eddy-driven diapycnal mixing on the large-scale ocean circulation. J. Phys. Oceanogr. 42, 526–538 (2012).

    Article  Google Scholar 

  231. 231.

    Munday, D., Allison, L., Johnson, H. & Marshall, D. Remote forcing of the Antarctic Circumpolar Current by diapycnal mixing. Geophys. Res. Lett. 38, L08609 (2011).

    Article  Google Scholar 

  232. 232.

    Savva, M. A. & Vanneste, J. Scattering of internal tides by barotropic quasigeostrophic flows. J. Fluid Mech. 856, 504–530 (2018).

    Article  Google Scholar 

  233. 233.

    Alford, M. H., Simmons, H. L., Marques, O. B. & Girton, J. B. Internal tide attenuation in the North Pacific. Geophys. Res. Lett. 46, 8205–8213 (2019).

    Article  Google Scholar 

  234. 234.

    Zaron, E. D. Topographic and frictional controls on tides in the Sea of Okhotsk. Ocean Model. 117, 1–11 (2017).

    Article  Google Scholar 

  235. 235.

    Naveira Garabato, A. C., Nurser, A. G., Scott, R. B. & Goff, J. A. The impact of small-scale topography on the dynamical balance of the ocean. J. Phys. Oceanogr. 43, 647–668 (2013).

    Article  Google Scholar 

  236. 236.

    Klymak, J. M., Pinkel, R. & Rainville, L. Direct breaking of the internal tide near topography: Kaena Ridge, Hawaii. J. Phys. Oceanogr. 38, 380–399 (2008).

    Article  Google Scholar 

  237. 237.

    Zhao, Z. et al. Decomposition of the multimodal multidirectional M2 internal tide field. J. Atmos. Oceans Technol. 36, 1157–1173 (2019).

    Article  Google Scholar 

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Acknowledgements

C.B.W. acknowledges the support of the National Aeronautics and Space Administration award 80NSSC19K1116, the National Science Foundation award OCE-1923558 and Office of Naval Research grant N00014-18-1-2598. A.C.N.G. acknowledges the support of the Royal Society and the Wolfson Foundation.

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C.B.W. led the design and writing of the Review. C.deL., A.C.N.G., J.M.K., J.A.M. and K.L.S. all contributed to the writing.

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Correspondence to Caitlin B. Whalen.

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Nature Reviews Earth and Environment thanks Yohei Onuki and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Glossary

Orthogonal modes

In the context of internal waves, orthogonal modes are a theoretical framework used to describe the vertical structure of internal waves, where low-mode internal waves have larger vertical scales and high-mode internal waves have smaller vertical scales.

Buoyancy frequency

(N).The oscillation frequency of a vertically displaced water parcel, which scales with the local vertical stratification gradient.

Coriolis frequency

(f). Alternatively referred to as the interial frequency. The oscillation frequency of a horizontally displaced water parcel influenced solely by the Earth’s rotation and defined by 2Ω sinϕ, where Ω is the angular velocity of the Earth and ϕ is the latitude.

Diapycnal diffusivity

(K). Diffusivity across density surfaces, with unit m2 s−1.

Turbulent kinetic enregy dissipation rate ε

Rate of energy dissipation due to viscosity, with units W kg−1.

Barotropic tides

Nearly full-depth periodic rise and fall of ocean water due to the gravitational attraction of the Moon and the Sun.

Lee waves

Internal waves often generated by deep geostrophic flow encountering topographic features.

Baroclinic tides

Depth-varying oscillations at tidal frequencies arising from barotropic tides impinging on topographic features. Also referred to as internal tides.

Near-inertial waves

Internal waves at or near the Coriolis/inertial frequency, often, but not always, generated by the wind.

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Whalen, C.B., de Lavergne, C., Naveira Garabato, A.C. et al. Internal wave-driven mixing: governing processes and consequences for climate. Nat Rev Earth Environ (2020). https://doi.org/10.1038/s43017-020-0097-z

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