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Recent progress in modeling imbalance in the atmosphere and ocean

Bruce R. Sutherland1,2,*, Ulrich Achatz3, Colm-cille P. Caulfield4,5, and Jody M. Klymak6,7

  • 1Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
  • 2Department of Earth and Atmospheric Sciences, University of Alberta, Edmonton, Alberta T6G 2E3, Canada
  • 3Institut fuer Atmosphaere und Umwelt, Goethe-Universitaet Frankfurt, Frankfurt 60438, Germany
  • 4BP Institute, University of Cambridge, Cambridge CB3 0EZ, United Kingdom
  • 5Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
  • 6School of Earth and Ocean Sciences, University of Victoria, Victoria, British Columbia V8W 3P6, Canada
  • 7Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia V8W 3P6, Canada

  • *bruce.sutherland@ualberta.ca

Phys. Rev. Fluids 4, 010501 – Published 7 January, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.010501

Abstract

Imbalance refers to the departure from the large-scale primarily vortical flows in the atmosphere and ocean whose motion is governed by a balance of Coriolis, pressure-gradient, and buoyancy forces and can be described approximately by quasigeostrophic theory or similar balance models. Imbalanced motions are manifest either as fully nonlinear turbulence or as internal gravity waves which can extract energy from these geophysical flows but which can also feed energy back into the flows. Capturing the physics underlying these mechanisms is essential to understanding how energy is transported from large geophysical scales ultimately to microscopic scales, where it is dissipated. In the atmosphere, it is also necessary for understanding momentum transport and its impact upon the mean wind and current speeds. During a February 2018 workshop at the Banff International Research Station (BIRS), atmospheric scientists, physical oceanographers, physicists, and mathematicians gathered to discuss recent progress in understanding these processes through interpretation of observations, numerical simulations, and mathematical modeling. The outcome of this meeting is reported upon here.

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References (156)

  1. G. K. Vallis, Atmospheric and Oceanic Fluid Dynamics (Cambridge University Press, Cambridge, UK, 2006), p. 745.
  2. R. Klein, Scale-dependent models for atmospheric flows, Annu. Rev. Fluid Mech. 42, 249 (2010).
  3. G. D. Nastrom and D. C. Fritts, Sources of mesoscale variability of gravity waves, part I: Topographic excitation, J. Atmos. Sci. 49, 101 (1992).
  4. D. C. Fritts and G. D. Nastrom, Sources of mesoscale variability of gravity waves, part II: Frontal, convective, and jet stream excitation, J. Atmos. Sci. 49, 111 (1992).
  5. R. S. Lindzen, Turbulence and stress owing to gravity wave and tidal breakdown, J. Geophys. Res. 86, 9707 (1981).
  6. G. Bölöni, B. Ribstein, J. Muraschko, C. Sgoff, J. Wei, and U. Achatz, The interaction between atmospheric gravity waves and large-scale flows: An efficient description beyond the nonacceleration paradigm, J. Atmos. Sci. 73, 4833 (2016).
  7. W. H. Munk and C. Wunsch, Abyssal recipes II: Energetics of tidal and wind mixing, Deep-Sea Res. 45, 1977 (1998).
  8. J. A. MacKinnon, Z. Zhao, C. B. Whalen, A. F. Waterhouse, D. S. Trossman, O. M. Sun, L. C. St. Laurent, H. L. Simmons, K. Polzin, R. Pinkel et al., Climate process team on internal wave-driven ocean mixing, Bull. Am. Meteorol. Soc. 98, 2429 (2017).
  9. L. Mahrt, Stably stratified atmospheric boundary layers, Annu. Rev. Fluid Mech. 46, 23 (2014).
  10. R. Ferrari and C. Wunsch, Ocean circulation kinetic energy: Reservoirs, sources, and sinks, Ann. Rev. Fluid Mech. 41, 253 (2009).
  11. Information and videos of several talks given during the workshop can be viewed online [https://www.birs.ca/events/2018/5-day-workshops/18w5119].
  12. R. S. Lindzen and J. R. Holton, A theory of the quasi-biennial oscillation, J. Atmos. Sci. 25, 1095 (1968).
  13. J. R. Holton and R. S. Lindzen, An updated theory for the quasi-biennial cycle of the tropical stratosphere, J. Atmos. Sci. 29, 1076 (1972).
  14. J. H. Richter, A. Solomon, and J. T. Bacmeister, On the simulation of the quasi-bienniel oscillation in the Community Atmosphere Model, version 5, J. Geophys. Res. 119, 3045 (2014).
  15. S. Schirber, E. Manzini, T. Krismer, and M. Giorgetta, The quasi-bienniel oscillation in a warmer climate: Sensitivity to different gravity wave parameterizations, Clim. Dyn. 45, 825 (2015).
  16. A. de la Camara, F. Lott, V. Jewtoukoff, R. Plougonven, and A. Hertzog, On the gravity wave forcing during the southern stratospheric final warming in LMDZ, J. Atmos. Sci. 73, 3213 (2016).
  17. J. Kidston, A. A. Scaife, S. C. Hardiman, D. M. Mitchell, N. Butchart, M. P. Baldwin, and L. J. Gray, Stratospheric influence on tropospheric jet streams, storm tracks, and surface weather, Nat. Geosci. 8, 433 (2015).
  18. A. A. Scaife, J. R. Knight, G. K. Vallis, and C. K. Folland, A stratospheric influence on the winter NAO and North Atlantic surface climate, Geophys. Res. Lett. 32, L18715 (2005).
  19. A. A. Scaife, T. Spangehl, D. R. Fereday, U. Cubasch, U. Langematz, H. Akiyoshi, S. Bekki, P. Braesicke, N. Butchart, M. P. Chipperfield et al., Climate change projections and stratosphere-troposphere interaction, Climate Dyn. 38, 2089 (2012).
  20. The OSCAR product can be viewed online [https://www.esr.org/research/oscar/].
  21. E. Lindborg, Horizontal wavenumber spectra of vertical velocity and horizontal divergence in the upper troposphere and lower stratosphere, J. Atmos. Sci. 64, 1017 (2007).
  22. O. Bühler, J. Callies, and R. Ferrari, Wave-vortex decomposition of one-dimensional ship-track data, J. Fluid Mech. 756, 1007 (2014).
  23. J. Callies, R. Ferrari, and O. Buhler, Transition from geostrophic turbulence to inertia-gravity waves in the atmospheric energy spectrum, PNAS 111, 17033 (2014).
  24. O. Bühler, M. Kuang, and E. G. Tabak, Anisotropic Helmholtz and wave-vortex decomposition of one-dimensional spectra, J. Fluid Mech. 815, 361 (2017).
  25. J. G. Charney, Geostrophic turbulence, J. Atmos. Sci. 28, 1087 (1971).
  26. R. H. Kraichnan, Inertial ranges in two-dimensional turbulence, Phys. Fluids 10, 1417 (1967).
  27. K. S. Gage, Evidence for a k5/3 law inertial range in mesoscale two-dimensional turbulence, J. Atmos. Sci. 36, 1950 (1979).
  28. D. K. Lilly, Stratified turbulence and the mesoscale variability of the atmosphere, J. Atmos. Sci. 40, 749 (1983).
  29. W. R. Young and M. Ben Jelloul, Propagation of near-inertial oscillations through a geostrophic flow, J. Mar. Res. 55, 735 (1997).
  30. J. Vanneste, Balance and spontaneous generation in geophysical flows, Annu. Rev. Fluid Mech. 45, 147 (2013).
  31. J.-H. Xie and J. Vanneste, A generalised-Lagrangian-mean model of the interactions between near-inertial waves and mean flow, J. Fluid Mech. 774, 143 (2015).
  32. H. A. Kafiabad and P. Bartello, Balance dynamics in rotating stratified turbulence, J. Fluid Mech. 795, 914 (2016).
  33. J. B. Marston, G. P. Chini, and S. M. Tobias, Generalized Quasilinear Approximation: Application to Zonal Jets, Phys. Rev. Lett. 116, 214501 (2016).
  34. G. L. Wagner and W. R. Young, 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 (2016).
  35. Different groups have used other letters to represent vortical modes and waves, for example, using “G” for geostrophic to represent the rotational, slow timescale flows and “A” for ageostrophic to represent horizontally divergent, relatively fast timescale flows.
  36. T. Nagai, A. Tandon, E. Kunze, and A. Mahadevan, Spontaneous generation of near-inertial waves by the Kuroshio front, J. Phys. Oceanogr. 45, 2381 (2015).
  37. O. Bühler and M. E. McIntyre, Wave capture and wave-vortex duality, J. Fluid Mech. 534, 67 (2005).
  38. E. Kunze and T. B. Sanford, Observations of near-inertial waves in a front, J. Phys. Oceanogr. 14, 566 (1984).
  39. P. Klein, S. Llewellyn Smith, and G. Lapeyre, Organization of near-inertial energy by and eddy field, Q. J. R. Meteorol. Soc. 130, 1153 (2004).
  40. E. Danioux, J. Vanneste, and O. Bühler, On the concentration of near-inertial waves in anticyclones, J. Fluid Mech. 773, R2 (2015).
  41. F. P. Bretherton, Momentum transport by gravity waves, Quart. J. Roy. Meteorol. Soc. 95, 213 (1969).
  42. A. Tabaei and T. R. Akylas, Resonant long-short wave interactions in an unbounded rotating stratified fluid, Stud. Appl. Math. 119, 271 (2007).
  43. O. Bühler, Waves and Mean Flows, 2nd ed. (Cambridge University Press, Cambridge, UK, 2014), p. 341.
  44. T. S. van den Bremer and B. R. Sutherland, The wave-induced flow of internal gravity wave packets with arbitrary aspect ratio, J. Fluid Mech. 834, 385 (2018).
  45. O. Bühler and M. E. McIntyre, Remote recoil: A new wave-mean interaction effect, J. Fluid Mech. 492, 207 (2003).
  46. J. C. Vanderhoff, K. K. Nomura, J. W. Rottman, and C. Macaskill, Doppler spreading of internal gravity waves by an inertia-wave packet, J. Geophys. Res. 113, C05018 (2008).
  47. F. P. Bretherton, On the mean motion induced by gravity waves, J. Fluid Mech. 36, 785 (1969).
  48. T. R. Akylas and A. Tabaei, Resonant self-acceleration and instability of nonlinear internal gravity wave trains, in Frontiers of Nonlinear Physics, edited by A. Litvak (Institute of Applied Physics, Nizhny Novgorod, 2005), pp. 129–135.
  49. T. S. van den Bremer and B. R. Sutherland, The mean flow and long waves induced by two-dimensional internal gravity wavepackets, Phys. Fluids 26, 106601 (2014).
  50. D. Benielli and J. Sommeria, Excitation and breaking of internal gravity waves by parametric instability, J. Fluid Mech. 374, 117 (1998).
  51. W. R. Young, Y.-K. Tsang, and N. J. Balmforth, Near-inertial parametric subharmonic instability, J. Fluid Mech. 607, 25 (2008).
  52. T. Dauxois, S. Joubaud, P. Odier, and A. Venaille, Instabilities of internal gravity wave beams, Annu. Rev. Fluid Mech. 50, 131 (2018).
  53. T. Hibiya and M. Nagasawa, Latitudinal dependence of diapycnal diffusivity in the thermocline estimate using a finescale parameterization, Geophys. Res. Lett. 31, L01301 (2004).
  54. J. A. MacKinnon and K. B. Winters, Subtropical catastrophe: Significant loss of low-mode tidal energy at 28.9, Geophys. Res. Lett. 32, L15605 (2005).
  55. J. Hazewinkel and K. B. Winters, PSI of the internal tide on a β plane: Flux divergence and near-inertial wave propagation, J. Phys. Oceanogr. 41, 1673 (2011).
  56. J. A. MacKinnon, M. H. Alford, O. Sun, R. Pinkel, Z. Zhao, and J. Klymak, Parametric subharmonic instability of the internal tide at 29 N, J. Phys. Oceanogr. 43, 17 (2013).
  57. C. H. McComas and F. P. Bretherton, Resonant interactions of oceanic internal waves, J. Geophys. Res. 82, 1397 (1977).
  58. P. Müller, G. Holloway, F. Henyey, and N. Pomphrey, Nonlinear-interactions among internal gravity-waves, Rev. Geophys. 24, 493 (1986).
  59. Y. V. Lvov, K. L. Polzin, and N. Yokoyama, Resonant and near-resonant internal wave interactions, J. Phys. Oceanogr. 42, 669 (2012).
  60. D. R. Durran and J. A. Weyn, Thunderstorms do not get butterflies, Bull. Amer. Soc. 97, 237 (2016).
  61. K. Bossert, C. G. Kruse, C. J. Heale, D. C. Fritts, B. P. Williams, J. B. Snively, P.-D. Pautet, and M. J. Taylor, Secondary gravity wave generation over New Zealand during the DEEPWAVE campaign, J. Geophys. Res. 122, 7834 (2017).
  62. M. H. Alford and R. Pinkel, Observations of overturning in the thermocline: The context of ocean mixing, J. Phys. Oceanogr. 30, 805 (2000).
  63. B. R. Sutherland, Internal Gravity Waves (Cambridge University Press, Cambridge, UK, 2010), p. 378.
  64. P. Billant and J.-M. Chomaz, Theoretical analysis of the zigzag instability of a vertical columnar vortex pair in a strongly stratified fluid, J. Fluid Mech. 419, 29 (2000).
  65. E. Lindborg, The energy cascade in a strongly stratified fluid, J. Fluid Mech. 550, 207 (2006).
  66. G. Brethouwer, P. Billant, E. Lindborg, and J.-M. Chomaz, Scaling analysis and simulation of strongly stratified turbulent flows, J. Fluid Mech. 585, 343 (2007).
  67. H. A. Kafiabad and P. Bartello, Rotating stratified turbulence and the slow manifold, Comp. Fluids 151, 23 (2017).
  68. P. Billant and J.-M. Chomaz, Self-similarity of strongly stratified inviscid flows, Phys. Fluids 13, 1645 (2001).
  69. M. Falder, N. J. White, and C. P. Caulfield, Seismic imaging of rapid onset of stratified turbulence in the South Atlantic Ocean, J. Phys. Oceanogr. 46, 1023 (2016).
  70. The buoyancy Reynolds numbers has also been called the “activity parameter” or the “Gibson number.”
  71. C. H. Gibson, Fossil turbulence, salinity, and vorticity turbulence in the ocean, in Marine Turbulence, edited by J. C. J. Nihous (Elsevier, Amsterdam, 1980), p. 221.
  72. A. E. Gargett, T. R. Osborn, and P. W. Nasmyth, Local isotropy and the decay of turbulence in a stratified fluid, J. Fluid Mech. 144, 231 (1984).
  73. Q. Zhou, J. R. Taylor, and C. P. Caulfield, Self-similar mixing in stratified plane Couette flow for varying Prandtl number, J. Fluid Mech. 820, 86 (2017).
  74. D. C. Fritts, R. B. Smith, M. J. Taylor, J. D. Doyle, S. D. Eckermann, A. Dörnbrack, M. Rapp, B. P. Williams, P.-D. Pautet, K. Bossert et al., The Deep Propagating Gravity Wave Experiment (DEEPWAVE): An airbourne and ground-based exploration of gravity wave propagation and effects from their sources throughout the lower and middle atmosphere, Bull. Amer. Meteor. Soc. 97, 425 (2016).
  75. C. Wunsch and R. Ferrari, Vertical mixing, energy, and the general circulation of the oceans, Annu. Rev. Fluid Mech. 36, 281 (2004).
  76. M. Nikurashin and R. Ferrari, Radiation and dissipation of internal waves generated by geostrophic motions impinging on small-scale topography: Theory, J. Phys. Oceanogr. 40, 1055 (2010).
  77. C. B. Whalen, L. D. Talley, and J. A. MacKinnon, Spatial and temporal variability of global ocean mixing inferred from argo profiles, Geophys. Res. Lett. 39, L18612 (2012).
  78. S. Waterman, K. L. Polzin, and A. C. Naveira Garabato, Internal waves and turbulence in the Antactic Circumpolar Current, J. Phys. Oceanogr. 43, 259 (2013).
  79. D. S. Trossman, S. Waterman, K. L. Polzin, B. K. Arbic, S. T. Garner, A. C. Naveira-Garabato, and K. L. Sheen, Internal lee wave closures: Parameter sensitivity and comparison to observations, J. Geophys. Res. 120, 7997 (2015).
  80. D. S. Trossman, B. K. Arbic, D. N. Straub, J. G. Richman, E. P. Chassignet, A. J. Wallcraft, and X. Xu, The role of rough topography in mediating impacts of bottom drag in eddying ocean circulation models, J. Phys. Oceanogr. 47, 1941 (2017).
  81. S. Legg and A. Adcroft, Internal wave breaking at concave and convex continental slopes, J. Phys. Oceanogr. 33, 2224 (2003).
  82. K. L. Polzin, J. M. Toole, J. R. Ledwell, and R. W. Schmitt, Spatial variability of turbulent mixing in the abyssal ocean, Science 276, 93 (1997).
  83. D. L. Rudnick, T. J. Boyd, R. E. Brainard, G. S. Carter, G. D. Egbert, M. C. Gregg, P. E. Holloway, J. M. Klymak, E. Kunze, C. M. Lee et al., From tides to mixing along the Hawaiian ridge, Science 301, 355 (2003).
  84. M. D. Levine and T. J. Boyd, Tidally forced internal waves and overturns observed on a slope: Results from the HOME survey component, J. Phys. Oceanogr. 36, 1184 (2006).
  85. M. H. Alford, J. A. MacKinnon, J. D. Nash, H. L. Simmons, A. Pickering, J. M. Klymak, R. Pinkel, O. Sun, L. Rainville, R. Musgrave et al., Energy flux and dissipation in Luzon Strait: Two tales of two ridges, J. Phys. Oceanogr. 41, 2211 (2011).
  86. Q. Li and D. M. Farmer, The generation and evolution of nonlinear internal waves in the deep basin of the South China Sea, J. Phys. Oceanogr. 41, 1345 (2011).
  87. J. D. Nash, M. H. Alford, E. Kunze, K. Martini, and S. Kelly, Hotspots of deep ocean mixing on the Oregon continental slope, Geophys. Res. Lett. 34, L01605 (2007).
  88. J. M. Klymak, H. L. Simmons, D. Braznikov, S. Kelly, J. A. MacKinnon, M. H. Alford, R. Pinkel, and J. D. Nash, Reflection of linear internal tides from realistic topography: The Tasman continental slope, J. Phys. Oceanogr. 46, 3321 (2016).
  89. S. M. Kelly, N. L. Jones, J. D. Nash, and A. F. Waterhouse, The geography of semidiurnal mode-1 internal-tide energy loss, Geophys. Res. Lett. 40, 4689 (2013).
  90. R. B. Scott, J. A. Goff, A. C. Naveira Garabato, and A. J. G. Nurser, Global rate and spectral characteristics of internal gravity wave generation by geostrophic flow over topography, J. Geophys. Res. 116, C09029 (2011).
  91. J. A. Brearley, K. L. Sheen, A. C. Naveira Garabato, D. A. Smeed, and S. Waterman, Eddy-induced modulation of turbulent dissipation over rough topography in the Southern Ocean, J. Phys. Oceanogr. 43, 2288 (2013).
  92. W. R. Peltier and T. L. Clark, The evolution and stability of finite-amplitude mountain waves. Part II: Surface wave drag and severe downslope windstorms, J. Atmos. Sci. 36, 1498 (1979).
  93. J. T. Bacmeister and R. T. Pierrehumbert, On high-drag states of nonlinear stratified flow over an obstacle, J. Atmos. Sci. 45, 63 (1988).
  94. L. St. Laurent, S. Stringer, C. Garrett, and D. Perrault-Joncas, The generation of internal tides at abrupt topography, Deep Sea Res. I 50, 987 (2003).
  95. F. Pétrélis, S. Llewellyn Smith, and W. R. Young, Tidal conversion at a submarine ridge, J. Phys. Oceanogr. 36, 1053 (2006).
  96. J. M. Klymak, S. Legg, and R. Pinkel, A simple parameterization of turbulent tidal mixing near supercritical topography, J. Phys. Oceanogr. 40, 2059 (2010).
  97. D. S. Trossman, B. K. Arbic, S. T. Garner, J. A. Goff, S. R. Jayne, E. J. Metzger, and A. J. Wallcraft, Impact of parameterized lee wave drag on the energy budget of an eddying global ocean model, Ocean Model. 72, 119 (2013).
  98. F. T. Mayer and O. B. Fringer, An unambiguous definition of the Froude number for lee waves in the deep ocean, J. Fluid Mech. 831, R3 (2017).
  99. Y.-H. Kim, A. C. Bushell, D. R. Jackson, and H.-Y. Chun, Impacts of introducing a convective gravity-wave parametrization upon the QBO in the Met Office unified model, Geophys. Res. Lett. 40, 1873 (2013).
  100. L. A. Holt, M. J. Alexander, L. Coy, A. Molod, W. Putman, and S. Pawson, An evaluation of gravity waves and gravity wave sources in the Southern Hemisphere in a 7-km global climate simulation, Q. J. R. Meteorol. Soc. 143, 2481 (2017).
  101. D. C. Fritts and M. J. Alexander, Gravity wave dynamics and effects in the middle atmosphere, Rev. Geophys. 41, 1003 (2003).
  102. Y. Q. Sun, R. Rotunno, and F. Zhang, Contributions of moist convection and internal gravity waves to building the atmospheric 5/3 kinetic energy spectra, J. Atmos. Sci. 74, 185 (2017).
  103. D. S. Nolan and J. A. Zhang, Spiral gravity waves radiating from tropical cyclones, Geophys. Res. Lett. 44, 3924 (2017).
  104. R. A. Plumb, The interaction of two internal waves with the mean flow: Implications for the theory of the quasi-biennial oscillation, J. Atmos. Sci. 34, 1847 (1977).
  105. L. A. Holt, M. J. Alexander, L. Coy, A. Molod, W. Putman, and S. Pawson, Tropical waves and the quasi-bienniel oscillation in a 7-km global climate simulation, J. Atmos. Sci. 73, 3771 (2016).
  106. M. H. Alford, Redistribution of energy available for ocean mixing by long-range propagation of internal waves, Nature (London) 423, 159 (2003).
  107. J. A. Polton, J. A. Smith, J. A. MacKinnon, and A. E. Tejada-Martinez, Rapid generation of high-frequency internal waves beneath a wind and wave forced oceanic surface mixed layer, Geophys. Res. Lett. 35, L13602 (2008).
  108. K. Dohan and B. R. Sutherland, Numerical and laboratory generation of internal waves from turbulence, Dyn. Atmos. Oceans 40, 43 (2005).
  109. D. A. Aguilar and B. R. Sutherland, Internal wave generation from rough topography, Phys. Fluids 18, 066603 (2006).
  110. J. H. Beres, M. J. Alexander, and J. R. Holton, Effects of tropospheric wind shear on the spectrum of convectively generated gravity waves, J. Atmos. Sci. 59, 1805 (2002).
  111. S. L. Vadas, M. J. Alexander, and D. C. Fritts, Mechanism for the generation of secondary waves in wave breaking regions, J. Atmos. Sci. 60, 194 (2003).
  112. M. J. Alexander, M. Geller, C. McLandress, S. Polavarapu, P. Preusse, F. Sassi, K. Sato, S. Eckermann, M. Ern, A. Hertzog, Y. Kawatani, M. Pulido, T. A. Shaw, M. Sigmond, R. Vincent, and S. Watanabe, Recent developments in gravity-wave effects in climate models and the global distribution of gravity-wave momentum flux from observations and models, Q. J. R. Meteorol. Soc. 136, 1103 (2010).
  113. C. Stephan, M. J. Alexander, and J. H. Richter, Characteristics of gravity waves from convection and implications for their parametrization in global circulation models, J. Atmos. Sci. 73, 2729 (2016).
  114. R. B. Smith and C. G. Kruse, Broad-spectrum mountain waves, J. Atmos. Sci. 74, 1381 (2017).
  115. T. N. Palmer, G. J. Shutts, and R. Swinbank, Alleviation of a systematic westerly bias in general circulation and numerical weather prediction models through an orographic gravity drag parametrization, Quart. J. Roy. Meteor. Soc. 112, 1001 (1986).
  116. N. A. McFarlane, The effect of orographically excited gravity wave drag on the general circulation of the lower stratosphere and troposphere, J. Atmos. Sci. 44, 1775 (1987).
  117. C. McLandress, On the importance of gravity waves in the middle atmosphere and their parameterization in general circulation models, J. Atmos. Sol. Terr. Phys. 60, 1357 (1998).
  118. T. Moffat-Griffin, C. J. Wright, A. C. Moss, J. C. King, S. R. Colwell, J. K. Hughes, and N. J. Mitchell, The South Georgia Wave Experiment (SG-WEX): Radiosonde observations of gravity waves in the lower stratosphere. Part I: Energy density, momentum flux, and wave propagation direction, Q. J. R. Meteorol. Soc. 143, 3279 (2017).
  119. C. I. Garfinkel and L. D. Oman, Effect of gravity waves from small islands in the Southern Ocean on the Southern Hemisphere atmospheric circulation, J. Geophys. Res. Atmos. 123, 1552 (2018).
  120. R. Plougonven, V. Jewtoukoff, A. de la Cámara, F. Lott, and A. Hertzog, On the relation between gravity waves and wind speed in the lower stratosphere over the Southern Ocean, J. Atmos. Sci. 74, 1075 (2017).
  121. V. Joutoukoff, A. Hertzogg, R. Plougonven, A. de la Cámara, and F. Lott, Comparison of gravity waves in the Southern Hemisphere derived from observations and the ECMWF analyses, J. Atmos. Sci. 72, 3449 (2015).
  122. F. Rieper, U. Achatz, and R. Klein, Range of validity of an extended WKB theory for atmospheric gravity waves: One-dimensional and two-dimensional case, J. Fluid Mech. 729, 330 (2013).
  123. J. Muraschko, M. D. Fruman, U. Achatz, S. Hickel, and Y. Toledo, On the application of Wentzel-Kramer-Brillouin theory for the simulation of the weakly nonlinear dynamics of gravity waves, Q. J. R. Meteorol. Soc. 141, 676 (2015).
  124. U. Achatz, B. Ribstein, F. Senf, and R. Klein, The interaction between synoptic-scale balanced flow and a finite-amplitude mesoscale wave field throughout all atmospheric layers: Weak and moderately strong stratification, Q. J. R. Meteorol. Soc. 143, 342 (2017).
  125. A. Gervais, G. E. Swaters, T. S. van den Bremer, and B. R. Sutherland, Evolution and stability of two-dimensional anelastic internal gravity wave packets, J. Atmos. Sci. 75, 3703 (2018).
  126. D. C. Fritts, S. L. Vadas, K. Wan, and J. A. Werne, Mean and variable forcing of the middle atmosphere by gravity waves, J. Atmos. Sol. Terr. Phys. 68, 247 (2006).
  127. U. Achatz, The primary nonlinear dynamics of modal and nonmodal perturbations of monochromatic inertia-gravity waves, J. Atmos. Sci. 64, 74 (2007).
  128. U. Achatz, Gravity-wave breaking: Linear and primary nonlinear dynamics, Adv. Space Res. 40, 719 (2007).
  129. D. P. Marshall, M. H. P. Ambaum, J. R. Maddison, D. R. Munday, and L. Novak, Eddy saturation and frictional control of the Antarctic Circumpolar Current, Geophys. Res. Lett. 44, 286 (2017).
  130. J. M. Klymak, Nonpropagating form drag and turbulence due to stratified flow over large-scale abyssal hill topography, J. Phys. Oceanogr. 48, 2383 (2018).
  131. B. K. Arbic, J. F. Shriver, P. J. Hogan, H. E. Hurlburt, J. L. McClean, E. J. Metzger, R. B. Scott, A. Sen, O. M. Smedstad, and A. J. Wallcraft, Estimates of bottom flows and bottom boundary layer dissipation of the oceanic general circulation from global high-resolution models, J. Geophys. Res. 114, C02024 (2009).
  132. B. K. Arbic, K. L. Polzin, R. B. Scott, J. G. Richman, and J. F. Shriver, On eddy viscosity, energy cascades, and the horizontal resolution of gridded satellite altimeter products, J. Phys. Oceanogr. 43, 283 (2013).
  133. E. Kunze, Internal-wave-driven mixing: Global geography and budgets, J. Phys. Oceanogr. 47, 1325 (2017).
  134. A. F. Waterhouse, J. A. MacKinnon, J. D. Nash, M. H. Alford, E. Kunze, H. L. Simmons, K. L. Polzin, L. C. St. Laurent, O. M. Sun, R. Pinkel et al., Global patterns of diapycnal mixing from measurements of the turbulent dissipation rate, J. Phys. Oceanogr. 44, 1854 (2014).
  135. T. R. Osborn, Estimates of the local rate of vertical diffusion from dissipation measurements, J. Phys. Oceanogr. 10, 83 (1980).
  136. W. D. Smyth, J. N. Moum, and D. R. Caldwell, The efficiency of mixing in turbulent patches: Inferences from direct simulations and microstructure observations, J. Phys. Oceangr. 31, 1969 (2001).
  137. M. S. Davies Wykes and S. B. Dalziel, Efficient mixing in stratified flows: Experimental study of a Rayleigh-Taylor unstable interface within an otherwise stable stratification, J. Fluid Mech. 756, 1027 (2014).
  138. L. H. Shih, J. R. Koseff, G. N. Ivey, and J. H. Ferziger, Parameterization of turbulent fluxes and scales using homogeneous sheared stably stratified turbulence simulations, J. Fluid Mech. 525, 193 (2005).
  139. G. N. Ivey, K. B. Winters, and J. R. Koseff, Density stratification, turbulence but how much mixing? Annu. Rev. Fluid Mech. 40, 169 (2008).
  140. G. N. Ivey, C. E. Bluteau, and N. L. Jones, Quantifying diapycnal mixing in an energetic ocean, J. Geophys. Res.: Oceans 123, 346 (2018).
  141. H. Salehipour, W. R. Peltier, C. B. Whalen, and J. A. MacKinnon, A new characterization of the turbulent diapycnal diffusivities of mass and momentum in the ocean, Geophys. Res. Lett. 43, 3370 (2016).
  142. A. Mashayek, H. Salehipour, D. Bouffard, C. P. Caulfield, R. Ferrari, M. Nikurashin, W. R. Peltier, and W. D. Smyth, Efficiency of turbulent mixing in the abyssal ocean circulation, Geophys. Res. Lett. 44, 6296 (2017).
  143. J. R. Taylor and Q. Zhou, A multi-parameter criterion for layer formation in a stratified shear flow using sorted buoyancy coordinates, J. Fluid Mech. 823, R5 (2017).
  144. M. C. Gregg., E. A. D'Asaro, J. J. Riley, and E. Kunze, Mixing efficiency in the ocean, Ann. Rev. Marine Sci. 10, 443 (2018).
  145. A. Melet, R. Hallberg, S. Legg, and K. Polzin, Sensitivity of the ocean state to the vertical distribution of internal-tide-driven mixing, J. Phys. Oceanogr. 43, 602 (2013).
  146. L. C. St. Laurent, H. L. Simmons, and S. R. Jayne, Estimating tidally driven mixing in the deep ocean, Geophys. Res. Lett. 29, 21 (2002).
  147. M. Nikurashin, R. Ferrari, N. Grisouard, and K. Polzin, The impact of finite-amplitude bottom topography on internal wave generation in the Southern Ocean, J. Phys. Oceanogr. 44, 2938 (2014).
  148. K. L. Polzin, An abyssal recipe, Ocean Model. 30, 298 (2009).
  149. C. J. Muller and O. Bühler, Saturation of the internal tides and induced mixing in the abyssal ocean, J. Phys. Oceonogr. 39, 2077 (2009).
  150. S. R. Jayne, The impact of abyssal mixing parameterizations in an ocean general circulation model, J. Phys. Oceanogr. 39, 1756 (2009).
  151. C. de Lavergne, G. Madec, J. Le Sommer, A. J. G. Nurser, and A. C. Naveira Garabato, On the consumption of Antarctic bottom water in the abyssal ocean, J. Phys. Oceanogr. 46, 635 (2016).
  152. J. M. Klymak, M. Buijsman, S. M. Legg, and R. Pinkel, Parameterizing baroclinic internal tide scattering and breaking on supercritical topography: The one- and two-ridge cases, J. Phys. Oceanogr. 43, 1380 (2013).
  153. D. Olbers and C. Eden, A closure for internal wave-mean flow interaction. Part I: Energy conversion, J. Phys. Oceanogr. 47, 1389 (2017).
  154. C. Eden and D. Olbers, A closure for internal wave-mean flow interaction. Part II: Wave drag, J. Phys. Oceanogr. 47, 1403 (2017).
  155. O. Asselin, P. Bartello, and D. N. Straub, On quasigeostrophic dynamics near the tropopause, Phys. Fluids 28, 026601 (2016).
  156. R. Ferrari, A. Mashayek, T. J. McDougall, M. Nikurashin, and J.-M. Campin, Turning ocean mixing upside down, J. Phys. Oceanogr. 46, 2239 (2016).

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