1932

Abstract

Oceanic lee waves are generated in the deep stratified ocean by the flow of ocean currents over sea floor topography, and when they break, they can lead to mixing in the stably stratified ocean interior. While the theory of linear lee waves is well established, the nonlinear mechanisms leading to mixing are still under investigation. Tidally driven lee waves have long been observed in the ocean, along with associated mixing, but observations of lee waves forced by geostrophic eddies are relatively sparse and largely indirect. Parameterizations of the mixing due to ocean lee waves are now being developed and implemented in ocean climate models. This review summarizes current theory and observations of lee wave generation and mixing driven by lee wave breaking, distinguishing between steady and tidally oscillating forcing. The existing parameterizations of lee wave–driven mixing informed by theory and observations are outlined, and the impacts of the parameterized lee wave–driven mixing on simulations of large-scale ocean circulation are summarized.

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2021-01-05
2024-04-23
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Literature Cited

  1. Adcroft A, Hallberg R, Dunne JP, Samuels BL, Galt JA et al. 2010. Simulations of underwater plumes of dissolved oil in the Gulf of Mexico. Geophys. Res. Lett. 37:L18605
    [Google Scholar]
  2. Aguilar DA, Sutherland BR. 2006. Internal wave generation from rough topography. Phys. Fluids 18:066603
    [Google Scholar]
  3. Alexander MJ, Teitelbaum H. 2011. Three-dimensional properties of Andes mountain waves observed by satellite: a case study. J. Geophys. Res. Atmos. 116:D23110
    [Google Scholar]
  4. Alford MH, Klymak JM, Carter GS 2014. Breaking internal lee waves at Kaena Ridge, Hawaii. Geophys. Res. Lett. 41:906–12
    [Google Scholar]
  5. Alford MH, Peacock T, MacKinnon JA, Nash JD, Buijsman MC et al. 2015. The formation and fate of internal waves in the South China Sea. Nature 521:65–69
    [Google Scholar]
  6. Bell TH. 1975a. Lee waves in stratified flows with simple harmonic time dependence. J. Fluid Mech. 67:705–22
    [Google Scholar]
  7. Bell TH. 1975b. Topographically generated internal waves in the open ocean. J. Geophys. Res. 80:320–27
    [Google Scholar]
  8. Booker JR, Bretherton FP. 1967. The critical layer for internal gravity waves in a shear flow. J. Fluid Mech. 27:513–39
    [Google Scholar]
  9. Brearley JA, Sheen KL, Naveira Garabato AC, Smeed DA, Waterman S 2013. Eddy-induced modulation of turbulent dissipation over rough topography in the Southern Ocean. J. Phys. Oceanogr. 43:2288–308
    [Google Scholar]
  10. Broad AS. 1995. Linear theory of momentum fluxes in 3-D flows with turning of the mean wind with height. Q. J. R. Meteorol. Soc. 121:1891–902
    [Google Scholar]
  11. Broadbridge MB, Naveira Garabato AC, Nurser AJG 2016. Forcing of the overturning circulation across a circumpolar channel by internal wave breaking. J. Geophys. Res. Oceans 121:5436–51
    [Google Scholar]
  12. Caulfield C. 2021. Layering, instabilities, and mixing in turbulent stratified flows. Annu. Rev. Fluid Mech. 53:113–45
    [Google Scholar]
  13. Clément L, Frajka-Williams E, Sheen KL, Brearley JA, Garabato ACN 2016. Generation of internal waves by eddies impinging on the western boundary of the North Atlantic. J. Phys. Oceanogr. 46:1067–79
    [Google Scholar]
  14. Clément L, Thurnherr AM, St. Laurent LC 2017. Turbulent mixing in a deep fracture zone on the Mid-Atlantic Ridge. J. Phys. Oceanogr. 47:1873–96
    [Google Scholar]
  15. Conover JH. 1964. The identification and significance of orographically induced clouds observed by TIROS satellites. J. Appl. Meteorol. 3:226–34
    [Google Scholar]
  16. Cusack JM, Naveira Garabato AC, Smeed DA, Girton JB 2017. Observation of a large lee wave in the Drake Passage. J. Phys. Oceanogr. 47:793–810
    [Google Scholar]
  17. da Silva J, New A, Magalhaes J 2011. On the structure and propagation of internal solitary waves generated at the Mascarene Plateau in the Indian Ocean. Deep Sea Res. I 58:229–40
    [Google Scholar]
  18. Dale AC, Inall ME. 2015. Tidal mixing processes amid small-scale, deep-ocean topography. Geophys. Res. Lett. 42:484–91
    [Google Scholar]
  19. de Lavergne C, Madec G, Le Sommer J, Nurser AJG, Naveira Garabato AC 2016. On the consumption of Antarctic Bottom Water in the abyssal ocean. J. Phys. Oceanogr. 46:635–61
    [Google Scholar]
  20. de Marez C, Lahaye N, Gula J 2020. Interaction of the Gulf Stream with small scale topography: a focus on lee waves. Sci. Rep. 10:2332
    [Google Scholar]
  21. Dossmann Y, Rosevear MG, Griffiths RW, McHogg A, Hughes GO, Copeland M 2016. Experiments with mixing in stratified flow over a topographic ridge. J. Geophys. Res. Oceans 121:6961–77
    [Google Scholar]
  22. Drazin PG. 1961. On the steady flow of a fluid of variable density past an obstacle. Tellus 13:239–51
    [Google Scholar]
  23. Eden C, Czeschel L, Olbers D 2014. Toward energetically consistent ocean models. J. Phys. Oceanogr. 44:3160–84
    [Google Scholar]
  24. Eden C, Greatbatch RJ. 2008. Diapycnal mixing by meso-scale eddies. Ocean Model 23:113–20
    [Google Scholar]
  25. Farmer D, Armi L. 1999. Stratified flow over topography: the role of small-scale entrainment and mixing in flow establishment. Proc. R. Soc. A 455:3221–58
    [Google Scholar]
  26. Ferrari R, Wunsch C. 2009. Ocean circulation kinetic energy: reservoirs, sources, and sinks. Annu. Rev. Fluid Mech. 41:253–82
    [Google Scholar]
  27. Garrett C, Kunze E. 2007. Internal tide generation in the deep ocean. Annu. Rev. Fluid Mech. 39:57–87
    [Google Scholar]
  28. Garrett C, Munk W. 1972. Space-time scales of internal waves. Geophys. Fluid Dyn. 3:225–64
    [Google Scholar]
  29. Goff JA. 2010. Global prediction of abyssal hill root-mean-square heights from small-scale altimetric gravity variability. J. Geophys. Res. Solid Earth 115:B12104
    [Google Scholar]
  30. Goff JA, Arbic BK. 2010. 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
    [Google Scholar]
  31. Goff JA, Jordan TH. 1988. Stochastic modeling of seafloor morphology: inversion of sea beam data for second-order statistics. J. Geophys. Res. Solid Earth 93:13589–608
    [Google Scholar]
  32. Gonella J. 1972. A rotary-component method for analysing meteorological and oceanographic vector time series. Deep Sea Res. Oceanogr. Abstr. 19:833–46
    [Google Scholar]
  33. Gouretski V, Koltermann K. 2004. WOCE global hydrograhic climatology Tech. Rep. 35: Bundesamt Seeschifffahrt Hydrogr Hamburg, Ger:.
  34. Gregg M. 1989. Scaling turbulent dissipation in the thermocline. J. Geophys. Res. 94:9686–98
    [Google Scholar]
  35. Gregg M, Sanford T, Winkel D 2003. Reduced mixing from the breaking of internal waves in equatorial waters. Nature 422:513–15
    [Google Scholar]
  36. Henyey FS, Wright J, Flatté SM 1986. Energy and action flow through the internal wave field: an eikonal approach. J. Geophys. Res. Oceans 91:8487–95
    [Google Scholar]
  37. Klymak JM. 2018. Nonpropagating form drag and turbulence due to stratified flow over large-scale abyssal hill topography. J. Phys. Oceanogr. 48:2383–95
    [Google Scholar]
  38. Klymak JM, Gregg MC. 2003. The role of upstream waves and a downstream density pool in the growth of lee waves: stratified flow over the Knight Inlet sill. J. Phys. Oceanogr. 33:1446–61
    [Google Scholar]
  39. Klymak JM, Legg SM. 2010. A simple mixing scheme for models that resolve breaking internal waves. Ocean Model 33:224–34
    [Google Scholar]
  40. Klymak JM, Legg S, Pinkel R 2010a. A simple parameterization of turbulent tidal mixing near supercritical topography. J. Phys. Oceanogr. 40:2059–74
    [Google Scholar]
  41. Klymak JM, Legg S, Pinkel R 2010b. High-mode stationary waves in stratified flow over large obstacles. J. Fluid Mech. 644:321–36
    [Google Scholar]
  42. Klymak JM, Pinkel R, Rainville L 2008. Direct breaking of the internal tide near topography: Kaena Ridge, Hawaii. J. Phys. Oceanogr. 38:380–99
    [Google Scholar]
  43. Köhler J, Mertens C, Walter M, Stöber U, Rhein M, Kanzow T 2014. Variability in the internal wave field induced by the Atlantic deep western boundary current at 16°N. J. Phys. Oceanogr. 44:492–516
    [Google Scholar]
  44. Konyaev K, Sabinin K, Serebryany A 1995. Large-amplitude internal waves at the Mascarene Ridge in the Indian Ocean. Deep Sea Res. I 42:2075–91
    [Google Scholar]
  45. Kunze E, Lien RC. 2019. Energy sinks for lee waves in shear flow. J. Phys. Oceanogr. 49:2851–65
    [Google Scholar]
  46. Legg S, Klymak J. 2008. Internal hydraulic jumps and overturning generated by tidal flow over a tall steep ridge. J. Phys. Oceanogr. 38:1949–64
    [Google Scholar]
  47. Liang X, Thurnherr AM. 2012. Eddy-modulated internal waves and mixing on a midocean ridge. J. Phys. Oceanogr. 42:1242–48
    [Google Scholar]
  48. Long RR. 1955. Some aspects of the flow of stratified fluids. Tellus 7:341–57
    [Google Scholar]
  49. MacKinnon JA, Zhao Z, Whalen CB, Waterhouse AF, Trossman DS et al. 2017. Climate process team on internal wave–driven ocean mixing. Bull. Am. Meteorol. Soc. 98:2429–54
    [Google Scholar]
  50. Marshall DP, Adcroft AJ. 2010. Parameterization of ocean eddies: potential vorticity mixing, energetics and Arnold's first stability theorem. Ocean Model 32:188–204
    [Google Scholar]
  51. Mayer FT, Fringer OB. 2017. An unambiguous definition of the Froude number for lee waves in the deep ocean. J. Fluid Mech. 831:R3
    [Google Scholar]
  52. Mayer FT, Fringer OB. 2020. Improving nonlinear and nonhydrostatic ocean lee wave drag parameterization. J. Phys. Oceanogr. 50:2417–35
    [Google Scholar]
  53. McFarlane NA. 1987. The effect of orographically excited gravity wave drag on the general circulation of the lower stratosphere and troposphere. J. Atmos. Sci. 44:1775–800
    [Google Scholar]
  54. Melet A, Hallberg R, Adcroft A, Nikurashin M, Legg S 2015. Energy flux into internal lee waves: sensitivity to future climate changes using linear theory and a climate model. J. Climate 28:2365–84
    [Google Scholar]
  55. Melet A, Hallberg R, Legg S, Nikurashin M 2014. Sensitivity of the ocean state to lee wave–driven mixing. J. Phys. Oceanogr. 44:900–21
    [Google Scholar]
  56. Meyer A, Polzin KL, Sloyan BM, Phillips HE 2016. Internal waves and mixing near the Kerguelen Plateau. J. Phys. Oceanogr. 46:417–37
    [Google Scholar]
  57. Meyer A, Sloyan BM, Polzin KL, Phillips HE, Bindoff NL 2015. Mixing variability in the Southern Ocean. J. Phys. Oceanogr. 45:966–87
    [Google Scholar]
  58. Musgrave RC, MacKinnon JA, Pinkel R, Waterhouse AF, Nash J 2016a. Tidally driven processes leading to near-field turbulence in a channel at the crest of the Mendocino Escarpment. J. Phys. Oceanogr. 46:1137–55
    [Google Scholar]
  59. Musgrave RC, MacKinnon JA, Pinkel R, Waterhouse AF, Nash J, Kelly SM 2017. The influence of subinertial internal tides on near-topographic turbulence at the Mendocino Ridge: observations and modeling. J. Phys. Oceanogr. 47:2139–54
    [Google Scholar]
  60. Musgrave RC, Pinkel R, MacKinnon JA, Mazloff MR, Young WR 2016b. Stratified tidal flow over a tall ridge above and below the turning latitude. J. Fluid Mech. 793:933–57
    [Google Scholar]
  61. Nakamura T, Awaji T, Hatayama T, Akitomo K, Takizawa T et al. 2000. The generation of large-amplitude unsteady lee waves by subinertial K1 tidal flow: a possible vertical mixing mechanism in the Kuril Straits. J. Phys. Oceanogr. 30:1601–21
    [Google Scholar]
  62. Nikurashin M, Ferrari R. 2010a. Radiation and dissipation of internal waves generated by geostrophic motions impinging on small-scale topography: application to the Southern Ocean. J. Phys. Oceanogr. 40:2025–42
    [Google Scholar]
  63. Nikurashin M, Ferrari R. 2010b. Radiation and dissipation of internal waves generated by geostrophic motions impinging on small-scale topography: theory. J. Phys. Oceanogr. 40:1055–74
    [Google Scholar]
  64. Nikurashin M, Ferrari R. 2011. Global energy conversion rate from geostrophic flows into internal lee waves in the deep ocean. Geophys. Res. Lett. 38:L08610
    [Google Scholar]
  65. Nikurashin M, Ferrari R. 2013. Overturning circulation driven by breaking internal waves in the deep ocean. Geophys. Res. Lett. 40:3133–37
    [Google Scholar]
  66. Nikurashin M, Ferrari R, Grisouard N, Polzin K 2014. The impact of finite-amplitude bottom topography on internal wave generation in the Southern Ocean. J. Phys. Oceanogr. 44:2938–50
    [Google Scholar]
  67. Osborn TR. 1980. Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr. 10:83–89
    [Google Scholar]
  68. Palmer TN, Shutts GJ, Swinbank R 1986. Alleviation of a systematic westerly bias in general circulation and numerical weather prediction models through an orographic gravity wave drag parametrization. Q. J. R. Meteorol. Soc. 112:1001–39
    [Google Scholar]
  69. Peltier WR, Clark TL. 1979. The evolution and stability of finite-amplitude mountain waves. Part II: surface wave drag and severe downslope windstorms. J. Atmos. Sci. 36:1498–529
    [Google Scholar]
  70. Rippeth TP, Lincoln BJ, Lenn YD, Green JAM, Sundfjord A, Bacon S 2015. Tide-mediated warming of Arctic halocline by Atlantic heat fluxes over rough topography. Nat. Geosci. 8:191–94
    [Google Scholar]
  71. Rippeth TP, Vlasenko V, Stashchuk N, Scannell BD, Green JAM et al. 2017. Tidal conversion and mixing poleward of the critical latitude (an Arctic case study). Geophys. Res. Lett. 44:12349–57
    [Google Scholar]
  72. Saenko OA, Zhai X, Merryfield WJ, Lee WG 2012. The combined effect of tidally and eddy-driven diapycnal mixing on the large-scale ocean circulation. J. Phys. Oceanogr. 42:526–38
    [Google Scholar]
  73. Scorer RS. 1949. Theory of waves in the lee of mountains. Q. J. R. Meteorol. Soc. 75:41–56
    [Google Scholar]
  74. Scott RB, Goff JA, Naveira Garabato AC, Nurser AJG 2011. Global rate and spectral characteristics of internal gravity wave generation by geostrophic flow over topography. J. Geophys. Res. Oceans 116:C09029
    [Google Scholar]
  75. Shakespeare CJ, Hogg AM. 2017. The viscous lee wave problem and its implications for ocean modelling. Ocean Model 113:22–29
    [Google Scholar]
  76. Sheen KL, Brearley JA, Naveira Garabato AC, Smeed DA, Laurent LS et al. 2015. Modification of turbulent dissipation rates by a deep Southern Ocean eddy. Geophys. Res. Lett. 42:3450–57
    [Google Scholar]
  77. Sheen KL, Brearley JA, Naveira Garabato AC, Smeed DA, Waterman S et al. 2013. 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 118:2774–92
    [Google Scholar]
  78. Sloyan BM. 2005. Spatial variability of mixing in the Southern Ocean. Geophys. Res. Lett. 32:L18603
    [Google Scholar]
  79. Smith RB. 1989. Mountain-induced stagnation points in hydrostatic flow. Tellus A 41A:270–74
    [Google Scholar]
  80. St. Laurent LC, Naveira Garabato AC, Ledwell JR, Thurnherr AM, Toole JM, Watson AJ. 2012. Turbulence and diapycnal mixing in Drake Passage. J. Phys. Oceanogr. 42:2143–52
    [Google Scholar]
  81. St. Laurent LC, Simmons HL, Jayne SR. 2002. Estimating tidally driven mixing in the deep ocean. Geophys. Res. Lett. 29:21–121-4
    [Google Scholar]
  82. Stanley GJ, Saenko OA. 2014. Bottom-enhanced diapycnal mixing driven by mesoscale eddies: sensitivity to wind energy supply. J. Phys. Oceanogr. 44:68–85
    [Google Scholar]
  83. Teixeira MAC. 2014. The physics of orographic gravity wave drag. Front. Phys. 2:43
    [Google Scholar]
  84. Thurnherr AM, St. Laurent LC 2011. Turbulence and diapycnal mixing over the East Pacific Rise crest near 10°N. Geophys. Res. Lett. 38:L15613
    [Google Scholar]
  85. Thurnherr AM, St. Laurent LC, Speer KG, Toole JM, Ledwell JR. 2005. Mixing associated with sills in a canyon on the midocean ridge flank. J. Phys. Oceanogr. 35:1370–81
    [Google Scholar]
  86. Trossman DS, Arbic BK, Garner ST, Goff JA, Jayne SR et al. 2013. Impact of parameterized lee wave drag on the energy budget of an eddying global ocean model. Ocean Model 72:119–42
    [Google Scholar]
  87. Trossman DS, Arbic BK, Richman JG, Garner ST, Jayne SR, Wallcraft AJ 2016. Impact of topographic internal lee wave drag on an eddying global ocean model. Ocean Model 97:109–28
    [Google Scholar]
  88. Waterman S, Naveira Garabato AC, Polzin KL 2013. Internal waves and turbulence in the Antarctic circumpolar current. J. Phys. Oceanogr. 43:259–82
    [Google Scholar]
  89. Waterman S, Polzin KL, Naveira Garabato AC, Sheen KL, Forryan A 2014. Suppression of internal wave breaking in the Antarctic circumpolar current near topography. J. Phys. Oceanogr. 44:1466–92
    [Google Scholar]
  90. Watson AJ, Ledwell JR, Messias MJ, King BA, Mackay N et al. 2013. Rapid cross-density ocean mixing at mid-depths in the Drake Passage measured by tracer release. Nature 501:408–11
    [Google Scholar]
  91. Welch WT, Smolarkiewicz P, Rotunno R, Boville BA 2001. The large-scale effects of flow over periodic mesoscale topography. J. Atmos. Sci. 58:1477–92
    [Google Scholar]
  92. Wijesekera H, Padman L, Dillon T, Levine M, Paulson C, Pinkel R 1993. The application of internal-wave dissipation models to a region of strong mixing. J. Phys. Oceanogr. 23:269–86
    [Google Scholar]
  93. Winters KB. 2016. The turbulent transition of a supercritical downslope flow: sensitivity to downstream conditions. J. Fluid Mech. 792:997–1012
    [Google Scholar]
  94. Winters KB, Armi L. 2012. Hydraulic control of continuously stratified flow over an obstacle. J. Fluid Mech. 700:502–13
    [Google Scholar]
  95. Winters KB, Armi L. 2013. The response of a continuously stratified fluid to an oscillating flow past an obstacle. J. Fluid Mech. 727:83–118
    [Google Scholar]
  96. Winters KB, Armi L. 2014. Topographic control of stratified flows: upstream jets, blocking and isolating layers. J. Fluid Mech. 753:80–103
    [Google Scholar]
  97. Winters KB, Lombard PN, Riley JJ, D'Asaro EA 1995. Available potential energy and mixing in density-stratified fluids. J. Fluid Mech. 289:115–28
    [Google Scholar]
  98. Winters KB, Riley JJ. 1992. Instability of internal waves near a critical level. Dyn. Atmos. Oceans 16:249–78
    [Google Scholar]
  99. Wright CJ, Scott RB, Ailliot P, Furnival D 2014. Lee wave generation rates in the deep ocean. Geophys. Res. Lett. 41:2434–40
    [Google Scholar]
  100. Wurtele MG, Sharman RD, Datta A 1996. Atmospheric lee waves. Annu. Rev. Fluid Mech. 28:429–76
    [Google Scholar]
  101. Yang L, Nikurashin M, Hogg AM, Sloyan BM 2018. Energy loss from transient eddies due to lee wave generation in the Southern Ocean. J. Phys. Oceanogr. 48:2867–85
    [Google Scholar]
  102. Zhai X, Johnson HL, Marshall DP 2010. Significant sink of ocean-eddy energy near western boundaries. Nat. Geosci. 3:608–12
    [Google Scholar]
  103. Zheng K, Nikurashin M. 2019. Downstream propagation and remote dissipation of internal waves in the Southern Ocean. J. Phys. Oceanogr. 49:1873–87
    [Google Scholar]
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