1932

Abstract

Mixing efficiency is the ratio of the net change in potential energy to the energy expended in producing the mixing. Parameterizations of efficiency and of related mixing coefficients are needed to estimate diapycnal diffusivity from measurements of the turbulent dissipation rate. Comparing diffusivities from microstructure profiling with those inferred from the thickening rate of four simultaneous tracer releases has verified, within observational accuracy, 0.2 as the mixing coefficient over a 30-fold range of diapycnal diffusivities. Although some mixing coefficients can be estimated from pycnocline measurements, at present mixing efficiency must be obtained from channel flows, laboratory experiments, and numerical simulations. Reviewing the different approaches demonstrates that estimates and parameterizations for mixing efficiency and coefficients are not converging beyond the at-sea comparisons with tracer releases, leading to recommendations for a community approach to address this important issue.

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2018-01-03
2024-06-19
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Literature Cited

  1. Alford MH, Gregg MC, D'Asaro EA. 2005. Mixing, 3-D mapping and Lagrangian evolution of a thermohaline intrusion. J. Phys. Oceanogr. 35:1689–711 [Google Scholar]
  2. Alford MH, Pinkel R. 2000. Observations of overturning in the thermocline: the context of ocean mixing. J. Phys. Oceanogr. 30:805–32 [Google Scholar]
  3. Arneborg L. 2002. Mixing efficiencies in patchy turbulence. J. Phys. Oceanogr. 31:1496–506 [Google Scholar]
  4. Barry M, Ivey G, Winters K, Imberger J. 2001. Measurements of diapycnal diffusivities in stratified fluids. J. Fluid Mech. 442:267–91 [Google Scholar]
  5. Batchelor GK. 1959. Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5:113–39 [Google Scholar]
  6. Billant P, Chomaz J-M. 2001. Self-similarity of strongly stratified inviscid flows. Phys. Fluids 13:1645 [Google Scholar]
  7. Bouruet-Aubertot P, Koudella C, Staquet C, Winters K. 2001. Particle dispersion and mixing by breaking internal gravity waves. Dyn. Atmos. Ocean 33:95–134 [Google Scholar]
  8. Brucker K, Sarkar S. 2007. Evolution of an initially turbulent stratified shear layer. Phys. Fluids 10:105105 [Google Scholar]
  9. Carpenter J, Lawrence G, Smyth W. 2007. Evolution and mixing of asymmetric Holmboe instabilities. J. Fluid Mech. 582:103–32 [Google Scholar]
  10. Caulfield C, Peltier W. 2000. The anatomy of the mixing transition in homogenous and stratified free shear layers. J. Fluid Mech. 413:1–47 [Google Scholar]
  11. de Bruyn Kops S. 2015. Classical scaling and intermittency in strongly stratified Boussinesq turbulence. J. Fluid Mech. 775:436–63 [Google Scholar]
  12. Desaubies Y, Gregg MC. 1981. Reversible and irreversible finestructure. J. Phys. Oceanogr. 11:541–56 [Google Scholar]
  13. Desaubies Y, Smith W. 1982. Statistics of Richardson number and instability in oceanic internal waves. J. Phys. Oceanogr. 12:1245–59 [Google Scholar]
  14. Dillon TM. 1982. Vertical overturns: a comparison of Thorpe and Ozmidov length scales. J. Geophys. Res. 87:9601–13 [Google Scholar]
  15. Drazin P. 1977. On the instability of an internal gravity wave. Proc. R. Soc. Lond. A 356:411–32 [Google Scholar]
  16. Dunkerton T. 1997. Shear instability of internal inertial-gravity waves. J. Atmos. Sci. 54:1628–41 [Google Scholar]
  17. Ellison T. 1957. Turbulent transport of heat and momentum from an infinite rough plane. J. Fluid Mech. 2:456–66 [Google Scholar]
  18. Ferrari R, Polzin K. 2005. Finescale structure of the T-S relation in the eastern North Atlantic. J. Phys. Oceanogr. 35:1437–54 [Google Scholar]
  19. Fleury M, Lueck R. 1994. Direct heat flux estimates using a towed vehicle. J. Phys. Oceanogr. 24:801–18 [Google Scholar]
  20. Fringer O, Street R. 2003. The dynamics of breaking progressive interfacial waves. J. Fluid Mech. 494:319–53 [Google Scholar]
  21. Gargett A. 2003. Differential diffusion: an oceanographic primer. Prog. Oceanogr. 56:559–70 [Google Scholar]
  22. Gargett A, Moum J. 1995. Mixing efficiencies in turbulent tidal fronts: results from direct and indirect measurements of density flux. J. Phys. Oceanogr. 25:2583–608 [Google Scholar]
  23. Gargett A, Merryfield W, Holloway G. 2003. Direct numerical simulation of differential scalar diffusion in three-dimensional stratified turbulence. J. Phys. Oceanogr. 33:1758–82 [Google Scholar]
  24. Gargett AE, Osborn TR, Nasmyth PW. 1984. Local isotropy and the decay of turbulence in a stratified fluid. J. Fluid Mech. 144:231–80 [Google Scholar]
  25. Garrett CJR. 1984. Turning points in universal speculation on internal waves. A Celebration in Geophysics and Oceanography – 1982 CJR Garrett, C Wunsch 38–46 La Jolla, CA: Scripps Inst. Oceanogr. [Google Scholar]
  26. Garrett CJR, Munk WH. 1975. Space-time scales of internal waves: a progress report. J. Geophys. Res. 80:291–97 [Google Scholar]
  27. Gregg MC. 1975. Microstructure and intrusions in the California Current. J. Phys. Oceanogr. 5:253–78 [Google Scholar]
  28. Gregg MC. 1989. Small-scale mixing: a first-order process?. Parameterization of Small-Scale Processes: Proceedings, 'Aha Huliko'a Hawaiian Winter Workshop, University of Hawaii at Manoa, January 17–20, 1989 P Müller, D Henderson 117–26 Honolulu: Hawaii Inst. Geophys. [Google Scholar]
  29. Gregg MC, D'Asaro EA, Shay T, Larson N. 1986. Observations of persistent mixing and near-inertial internal waves. J. Phys. Oceanogr. 16:856–85 [Google Scholar]
  30. Gregg MC, Horne J. 2009. Turbulence, acoustic backscatter and pelagic nekton in Monterey Bay. J. Phys. Oceanogr. 39:1097–114 [Google Scholar]
  31. Gregg MC, Sanford TB. 1988. The dependence of turbulent dissipation on stratification in a diffusively stable thermocline. J. Geophys. Res. 93:12381–92 [Google Scholar]
  32. Hamilton J, Lewis M, Ruddick B. 1989. Vertical fluxes of nitrate associated with salt fingers in the world's ocean. J. Geophys. Res. 94:2137–45 [Google Scholar]
  33. Hebert D. 1988. Estimates of salt-finger fluxes. Deep-Sea Res. A 35:1887–901 [Google Scholar]
  34. Henyey FS, Wright J, Flatté SM. 1986. Energy and action flow through the internal wave field: an eikonal approach. J. Geophys. Res. 91:8487–95 [Google Scholar]
  35. Holleman R, Geyer W, Ralston D. 2016. Stratified turbulence and mixing efficiency in a salt wedge estuary. J. Phys. Oceanogr. 46:1769–83 [Google Scholar]
  36. Inoue R, Smyth W. 2009. Efficiency of mixing forced by unsteady shear flow. J. Phys. Oceanogr. 39:1150–66 [Google Scholar]
  37. Ivey G, Imberger J. 1991. On the nature of turbulence in a stratified fluid. Part I: the energetics of mixing. J. Phys. Oceanogr. 21:650–58 [Google Scholar]
  38. Jackson PR, Rehmann CR. 2003. Laboratory measurements of differential diffusion in a diffusively stable, turbulent flow. J. Phys. Oceanogr. 33:1592–603 [Google Scholar]
  39. Jacobitz F, Sarkar S, Van Atta CW. 1997. Direct numerical simulations of the turbulence evolution in a uniformly sheared and stably stratified flow. J. Fluid Mech. 342:231–61 [Google Scholar]
  40. Jayne S. 2009. The impact of abyssal mixing parameterizations in an ocean general circulation model. J. Phys. Oceanogr. 39:1756–75 [Google Scholar]
  41. Kraichnan R. 1968. Small-scale structure of a scalar field convected by turbulence. Phys. Fluids 11:945–53 [Google Scholar]
  42. Kunze E. 2011. Fluid mixing by swimming organisms in the low-Reynolds-number limit. J. Mar. Res. 69:591–601 [Google Scholar]
  43. Kunze E. 2017. Internal-wave-driven mixing: global geography and budgets. J. Phys. Oceanogr. 47:1325–45 [Google Scholar]
  44. Kunze E, MacKay C, McPhee-Shaw E, Morrice K, Girton J, Terker S. 2012. Turbulent mixing and exchange with interior waters on sloping boundaries. J. Phys. Oceanogr. 42:910–27 [Google Scholar]
  45. Lazier J. 1973. Temporal changes in some fresh water temperature structures. J. Phys. Oceanogr. 3:226–29 [Google Scholar]
  46. Ledwell J, Duda T, Sundermeyer M, Seim H. 2004. Mixing in a coastal environment: 1. A view from dye dispersion. J. Geophys. Res. 109:C10013 [Google Scholar]
  47. Ledwell J, Laurent LS, Girton J, Toole J. 2011. Diapycnal mixing in the Antarctic Circumpolar Current. J. Phys. Oceanogr. 41:241–46 [Google Scholar]
  48. Ledwell J, Montgomery E, Polzin K, Laurent LCS, Schmitt R, Toole J. 2000. Evidence for enhanced mixing over rough topography in the abyssal ocean. Nature 403:179–82 [Google Scholar]
  49. Ledwell J, Watson A, Law C. 1998. Mixing of a tracer in the pycnocline. J. Geophys. Res. 103:21499–529 [Google Scholar]
  50. Lelong M-P, Dunkerton T. 1998a. Inertia–gravity wave breaking in three dimensions. I. Convectively unstable waves. J. Atmos. Sci. 55:2489–501 [Google Scholar]
  51. Lelong M-P, Dunkerton T. 1998b. Inertia–gravity wave breaking in three dimensions. II. Convectively stable waves. J. Atmos. Sci. 55:152473–88 [Google Scholar]
  52. Lelong M-P, Sundermeyer M. 2005. Geostrophic adjustment of an isolated diapycnal mixing event and its implications for small scale lateral dispersion. J. Phys. Oceanogr. 35:2352–67 [Google Scholar]
  53. Lilly D. 1983. Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci. 40:749–61 [Google Scholar]
  54. Lombard P, Riley JJ. 1996a. Instability and breakdown of internal gravity waves. I. Linear stability analysis. Phys. Fluids 8:3271 [Google Scholar]
  55. Lombard P, Riley JJ. 1996b. On the breakdown into turbulence of propagating internal waves. Dyn. Atmos. Ocean 23:345–55 [Google Scholar]
  56. Maffioli A, Brethouwer G, Lindborg E. 2016. Mixing efficiency in stratified turbulence. J. Fluid Mech. 794:R3 [Google Scholar]
  57. Mashayek A, Caulifield C, Peltier W. 2013. Time-dependent, non-monotonic mixing in stratified turbulent shear flows: implications for oceanographic estimates of buoyancy flux. J. Fluid Mech. 736:570–93 [Google Scholar]
  58. Mashayek A, Peltier W. 2011. Three-dimensionalization of the stratified mixing layer at high Reynolds number. Phys. Fluids 23:111701 [Google Scholar]
  59. Mashayek A, Peltier W. 2013. Shear-induced mixing in geophysical flows: Does the route to turbulence matter to its efficiency?. J. Fluid Mech. 725:216–17 [Google Scholar]
  60. Mater B, Venayagamoorthy S. 2014. A unifying framework for parameterizing stably stratified shear-flow turbulence. Phys. Fluids 26:036601 [Google Scholar]
  61. McComas C, Müller P. 1981. The dynamic balance of internal waves. J. Phys. Oceanogr. 11:970–86 [Google Scholar]
  62. McEwan A. 1983a. Internal mixing in stratified fluids. J. Fluid Mech. 128:59–80 [Google Scholar]
  63. McEwan A. 1983b. The kinematics of stratified mixing through internal wavebreaking. J. Fluid Mech. 128:47–57 [Google Scholar]
  64. McPhee MG. 1992. Turbulent heat flux in the upper ocean under sea ice. J. Geophys. Res. 97:5365–79 [Google Scholar]
  65. Merryfield W. 2005. Dependence of differential mixing on n and Rp. J. Phys. Oceanogr. 35:991–1003 [Google Scholar]
  66. Mied R. 1976. The occurrence of parametric instabilities in finite-amplitude internal gravity waves. J. Fluid Mech. 78:763–84 [Google Scholar]
  67. Moum J. 1996. Efficiency of mixing in the main thermocline. J. Geophys. Res. 101:12057–69 [Google Scholar]
  68. Moum JN, Caldwell DR, Paulson CA. 1989. Mixing in the equatorial surface layer and thermocline. J. Geophys. Res. 94:2005–21 [Google Scholar]
  69. Nash J, Moum J. 2002. Microstructure estimates of turbulent salinity flux and the dissipation spectrum of salinity. J. Phys. Oceanogr. 32:2312–34 [Google Scholar]
  70. Oakey N. 1982. Determination of the rate of dissipation of turbulent energy from simultaneous temperature and velocity shear microstructure measurements. J. Phys. Oceanogr. 12:256–71 [Google Scholar]
  71. Oakey N. 1985. Statistics of mixing parameters in the upper ocean during JASIN Phase 2. J. Phys. Oceanogr. 15:1662–75 [Google Scholar]
  72. Oakey N, Greenan B. 2004. Mixing in a coastal environment: 1. A view from microstructure measurements. J. Geophys. Res. 109:C10014 [Google Scholar]
  73. Osborn TR. 1974. Vertical profiling of velocity microstructure. J. Phys. Oceanogr. 4:109–15 [Google Scholar]
  74. Osborn TR. 1980. Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr. 10:83–89 [Google Scholar]
  75. Osborn TR, Cox C. 1972. Oceanic fine structure. Geophys. Fluid Dyn. 3:321–45 [Google Scholar]
  76. Peltier W, Caulfield C. 2003. Mixing efficiency in stratified shear flows. Annu. Rev. Fluid Mech. 35:135–67 [Google Scholar]
  77. Peters H, Gregg MC. 1988. Some dynamical and statistical properties of equatorial turbulence. Small-Scale Turbulence and Mixing in the Ocean: Proceedings of the 19th International Liège Colloquium on Ocean Hydrodynamics J Nihoul, B Jamart 185–200 Amsterdam: Elsevier [Google Scholar]
  78. Peters H, Gregg MC, Sanford TB. 1995. Detail and scaling of turbulent overturns in the Pacific Equatorial Undercurrent. J. Geophys. Res. 100:18349–68 [Google Scholar]
  79. Pham H, Sarkar S. 2010. Transport and mixing of density in a continuously stratified shear layer. J. Turbul. 11:N24 [Google Scholar]
  80. Pham H, Sarkar S, Brucker K. 2009. Dynamics of a stratified shear layer above a region of uniform stratification. J. Fluid Mech. 630:191–223 [Google Scholar]
  81. Pinkel R, Anderson S. 1992. Toward a statistical description of finescale strain in the thermocline. J. Phys. Oceanogr. 22:773–95 [Google Scholar]
  82. Polzin K, Toole J, Schmidt R. 1995. Finescale parameterization of turbulent dissipation. J. Phys. Oceanogr. 25:306–28 [Google Scholar]
  83. Pope S. 2000. Turbulent Flows Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  84. Pujiana K, Moum J, Smyth W, Warner S. 2015. Distinguishing ichthyogenic turbulence from geophysical turbulence. J. Geophys. Res. 120:3792–804 [Google Scholar]
  85. Riley JJ, de Bruyn Kops SM. 2003. Dynamics of turbulence strongly influenced by buoyancy. Phys. Fluids 15:2047–59 [Google Scholar]
  86. Riley JJ, Lelong M-P. 2000. Fluid motions in the presence of strong stable stratification. Annu. Rev. Fluid Mech. 32:613–57 [Google Scholar]
  87. Rohr JJ, Itsweire EC, Van Atta CW. 1984. Mixing efficiency in stably stratified decaying turbulence. J. Fluid Mech. 29:221–336 [Google Scholar]
  88. Ruddick B, Walsh D, Oakey N. 1997. Variations in apparent mixing efficiency in the North Atlantic central water. J. Phys. Oceanogr. 27:2589–605 [Google Scholar]
  89. Salehipour H, Caulfield C, Peltier W. 2016. Turbulent mixing due to the Holmboe wave instability at high Reynolds number. J. Fluid Mech. 803:591–621 [Google Scholar]
  90. Salehipour H, Peltier W. 2015. Diapycnal diffusivity, turbulent Prandtl number and mixing efficiency in Boussinesq stratified turbulence. J. Fluid Mech. 775:464–500 [Google Scholar]
  91. Salehipour H, Peltier W, Mashayek A. 2015. Turbulent diapycnal mixing in stratified shear flows: the influence of Prandtl number on mixing efficiency and transition at high Reynolds number. J. Fluid Mech. 773:178–223 [Google Scholar]
  92. Schmitt R. 1981. Form of the temperature-salinity relationship in the central water: evidence for double-diffusive mixing. J. Phys. Oceanogr. 11:1015–26 [Google Scholar]
  93. Scotti A, White B. 2016. The mixing efficiency of stratified turbulent boundary layers. J. Phys. Oceanogr. 46:3181–91 [Google Scholar]
  94. Seim HE, Gregg MC. 1994. Detailed observations of a naturally occurring shear instability. J. Geophys. Res. 99:10049–73 [Google Scholar]
  95. Sherman J, Davis R. 1995. Observations of temperature microstructure in NATRE. J. Phys. Oceanogr. 25:1913–29 [Google Scholar]
  96. Shih L, Koseff J, Ivey G, Ferziger J. 2005. Parameterization of turbulent fluxes and scales using homogenous sheared stably stratified turbulence simulations. J. Fluid Mech. 525:193–214 [Google Scholar]
  97. Smith J. 1974. Turbulent structure of the surface boundary layer in an ice-covered ocean. Rapp. P.-V. Réun. Cons. Int. Explor. Mer 167:53–65 [Google Scholar]
  98. Smyth W, Carpenter J, Lawrence G. 2007. Mixing in symmetric Holmboe waves. J. Phys. Oceanogr. 37:1566–83 [Google Scholar]
  99. Smyth W, Moum J. 2000. Anisotropy of turbulence in stably stratified mixing layers. Phys. Fluids 12:1343–62 [Google Scholar]
  100. Smyth W, Moum J. 2012. Ocean mixing by Kelvin-Helmholtz instability. Oceanography 25:2140–49 [Google Scholar]
  101. Smyth W, Moum J, Caldwell D. 2001. The efficiency of mixing in turbulent patches: inferences from direct simulations and microstructure observations. J. Phys. Oceanogr. 31:1969–92 [Google Scholar]
  102. Smyth W, Nash J, Moum J. 2005. Differential diffusion in breaking Kelvin-Helmholtz billows. J. Phys. Oceanogr. 35:1004–22 [Google Scholar]
  103. Smyth W, Winters K. 2003. Turbulence and mixing in Holmboe waves. J. Phys. Oceanogr. 33:694–711 [Google Scholar]
  104. St. Laurent L, Schmitt R. 1999. The contribution of salt fingers to vertical mixing in the North Atlantic Tracer Release Experiment. J. Phys. Oceanogr. 29:1404–24 [Google Scholar]
  105. Staquet C. 2000. Mixing in a stably stratified shear layer: two- and three-dimensional numerical experiments. Fluid Dyn. Res. 27:367–404 [Google Scholar]
  106. Strang E, Fernando H. 2001. Entrainment and mixing in stratified shear flows. J. Fluid Mech. 428:349–86 [Google Scholar]
  107. Tailleux R. 2009a. On the energetics of stratified turbulent mixing, irreversible thermodynamics, Boussinesq models and the ocean heat engine controversy. J. Fluid Mech. 638:339–82 [Google Scholar]
  108. Tailleux R. 2009b. Understanding mixing efficiency in the ocean: Do the nonlinearities of the equation of state for seawater matter?. Ocean Sci 5:271–83 [Google Scholar]
  109. Thorpe S. 1973. Experiments on instability and turbulence in a stratified shear flow. J. Fluid Mech. 61:731–51 [Google Scholar]
  110. Toole J, Polzin K, Schmitt R. 1994. Estimates of diapycnal mixing in the abyssal ocean. Science 264:1120–23 [Google Scholar]
  111. Turner J. 1968. The influence of molecular diffusivity on turbulent entrainment across a density interface. J. Fluid Mech. 33:639–56 [Google Scholar]
  112. Whalen C, MacKinnon J, Talley L, Waterhouse A. 2015. Estimating the mean diapycnal mixing using a finescale strain parameterization. J. Phys. Oceanogr. 45:1174–88 [Google Scholar]
  113. Wijesekera H, Dillon T. 1997. Shannon entropy as an indicator of age for turbulent overturns in the oceanic thermocline. J. Geophys. Res. 102:3279–91 [Google Scholar]
  114. Winters K, D'Asaro EA. 1996. Diascalar flux and the rate of fluid mixing. J. Fluid Mech. 317:179–93 [Google Scholar]
  115. Winters K, Lombard P, Riley JJ, D'Asaro EA. 1995. Available potential energy and mixing in density-stratified fluids. J. Fluid Mech. 289:115–28 [Google Scholar]
  116. Woods J. 1968. Wave-induced shear instability in the summer thermocline. J. Fluid Mech. 32:791–800 [Google Scholar]
  117. Woods J, Wiley R. 1972. Billow turbulence and ocean microstructure. Deep-Sea Res. Oceanogr. Abstr. 19:87–121 [Google Scholar]
  118. Wunsch C, Ferrari R. 2004. Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech. 36:281–314 [Google Scholar]
  119. Yamazaki H, Osborn TR. 1990. Dissipation estimates for stratified turbulence. J. Geophys. Res. 95:9739–44 [Google Scholar]
  120. Yamazaki H, Osborn TR. 1993. Direct estimation of heat flux in a seasonal thermocline. J. Phys. Oceanogr. 23:503–16 [Google Scholar]
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