1932

Abstract

Lakes and other confined water bodies are not exposed to tides, and their wind forcing is usually much weaker compared to ocean basins and estuaries. Hence, convective processes are often the dominant drivers for shaping mixing and stratification structures in inland waters. Due to the diverse environments of lakes—defined by local morphological, geochemical, and meteorological conditions, among others—a fascinating variety of convective processes can develop with remarkably unique signatures. Whereas the classical cooling-induced and shear-induced convections are well-known phenomena due to their dominant roles in ocean basins, other convective processes are specific to lakes and often overlooked, for example, sidearm, under-ice, and double-diffusive convection or thermobaric instability and bioconvection. Additionally, the peculiar properties of the density function at low salinities/temperatures leave distinctive traces. In this review, we present these various processes and connect observations with theories and model results.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-fluid-010518-040506
2019-01-05
2024-12-04
Loading full text...

Full text loading...

/deliver/fulltext/fluid/51/1/annurev-fluid-010518-040506.html?itemId=/content/journals/10.1146/annurev-fluid-010518-040506&mimeType=html&fmt=ahah

Literature Cited

  1. Adrian R, O'Reilly CM, Zagarese H, Baines SB, Hessen DO et al. 2009. Lakes as sentinels of climate change. Limnol. Oceanogr. 54:62283–97
    [Google Scholar]
  2. Alavian V, Jirka GH, Denton RA, Johnson MC, Stefan HG 1992. Density currents entering lakes and reservoirs. J. Hydraul. Eng. 118:1464–89
    [Google Scholar]
  3. Anati DA, Stiller M 1991. The post-1979 thermohaline structure of the Dead Sea and the role of double-diffusive mixing. Limnol. Oceanogr. 36:342–53
    [Google Scholar]
  4. Anati DA, Stiller M, Shasha S, Gat JR 1987. Changes in the thermo-haline structure of the Dead Sea: 1979–1984. Earth Planet. Sci. Lett. 84:109–21
    [Google Scholar]
  5. Baines PG 2001. Mixing in flows down gentle slopes into stratified environments. J. Fluid Mech. 443:237–70
    [Google Scholar]
  6. Bearon RN, Grünbaum D 2006. Bioconvection in a stratified environment: experiments and theory. Phys. Fluids 18:127102
    [Google Scholar]
  7. Becherer JK, Umlauf L 2011. Boundary mixing in lakes: 1. Modeling the effect of shear-induced convection. J. Geophys. Res. 116:C10017
    [Google Scholar]
  8. Boehrer B, Dietz S, von Rohden C, Kiwel U, Jöhnk KD et al. 2009.a Double-diffusive deep water circulation in an iron-meromictic lake. Geochem. Geophys. Geosyst. 10:Q06006
    [Google Scholar]
  9. Boehrer B, Fukuyama R, Chikita K, Kikukawa H 2009.b Deep water stratification in deep caldera lakes Ikeda, Towada, Tazawa, Kuttara, Toya and Shikotsu. Limnology 10:17–24
    [Google Scholar]
  10. Boehrer B, Golmen L, Løvik JE, Rahn K, Klaveness D 2013. Thermobaric stratification in very deep Norwegian freshwater lakes. J. Gt. Lakes Res. 39:690–95
    [Google Scholar]
  11. Boehrer B, Schultze M 2008. Stratification of lakes. Rev. Geophys. 46:RG2005
    [Google Scholar]
  12. Bouffard D, Perga M-E 2016. Are flood-driven turbidity currents hot spots for priming effect in lakes. ? Biogeosciences 13:3573–84
    [Google Scholar]
  13. Bouffard D, Zdorovennov RE, Zdorovennova GE, Pasche N, Wüest A, Terzhevik AY 2016. Ice-covered Lake Onega: effects of radiation on convection and internal waves. Hydrobiologia 780:21–36
    [Google Scholar]
  14. Carmack EC, Gray CBJ, Pharo CH, Daley RJ 1979. Importance of lake-river interaction on seasonal patterns in the general circulation of Kamloops Lake, British Columbia. Limnol. Oceanogr. 24:634–44
    [Google Scholar]
  15. Carmack EC, Weiss RF 1991. Convection in Lake Baikal: an example of thermobaric instability. Deep Convection and Deep Water Formation in the Oceans PC Chu, JC Gascard 215–28 Amsterdam: Elsevier
    [Google Scholar]
  16. Carpenter JR, Sommer T, Wüest A 2012.a Simulations of a double-diffusive interface in the diffusive convection regime. J. Fluid Mech. 711:411–36
    [Google Scholar]
  17. Carpenter JR, Sommer T, Wüest A 2012.b Stability of a double-diffusive interface in the diffusive convection regime. J. Phys. Oceanogr. 42:840–54
    [Google Scholar]
  18. Cenedese C, Adduce C 2010. A new parameterization for entrainment in overflows. J. Phys. Oceanogr. 40:1835–50
    [Google Scholar]
  19. Chen C-TA, Millero FJ 1986. Thermodynamic properties for natural waters covering only the limnological range. Limnol. Oceanogr. 31:657–62
    [Google Scholar]
  20. Chowdhury MR, Wells MG, Howell T 2016. Movements of the thermocline lead to high variability in benthic mixing in the nearshore of a large lake. Water Resour. Res. 52:3019–39
    [Google Scholar]
  21. Cole JJ, Prairie YT, Caraco NF, McDowell WH, Tranvik LJ et al. 2007. Plumbing the global carbon cycle: integrating inland waters into the terrestrial carbon budget. Ecosystems 10:172–85
    [Google Scholar]
  22. Cortés A, Fleenor WE, Wells MG, de Vicente I, Rueda FJ 2014. Pathways of river water to the surface layers of stratified reservoirs. Limnol. Oceanogr. 59:233–50
    [Google Scholar]
  23. Cossu R, Wells MG 2013. The interaction of large amplitude internal seiches with a shallow sloping lakebed: observations of benthic turbulence in Lake Simcoe, Ontario, Canada. PLOS ONE 8:e57444
    [Google Scholar]
  24. Crawford GB, Collier RW 1997. Observations of a deep-mixing event in Crater Lake, Oregon. Limnol. Oceanogr. 42:299–306
    [Google Scholar]
  25. Crawford GB, Collier RW 2007. Long-term observations of deepwater renewal in Crater Lake, Oregon. Hydrobiologia 574:47–68
    [Google Scholar]
  26. Csanady GT 1975. Hydrodynamics of large lakes. Annu. Rev. Fluid Mech. 7:357–86
    [Google Scholar]
  27. Davarpanah Jazi S, Wells MG 2016. Enhanced sedimentation beneath particle-laden flows in lakes and the ocean due to double-diffusive convection. Geophys. Res. Lett. 43:10883–90
    [Google Scholar]
  28. Deardorff JW 1970. Convective velocity and temperature scales for the unstable planetary boundary layer and for Rayleigh convection. J. Atmos. Sci. 27:1211–13
    [Google Scholar]
  29. Ellison TH, Turner JS 1959. Turbulent entrainment in stratified flows. J. Fluid Mech. 6:423–48
    [Google Scholar]
  30. Emanuel KA 1994. Atmospheric Convection New York: Oxford Univ. Press
    [Google Scholar]
  31. Emery WJ, Castro S, Wick GA, Schluessel P, Donlon C 2001. Estimating sea surface temperature from infrared satellite and in situ temperature data. Bull. Am. Meteorol. Soc. 82:2773–85
    [Google Scholar]
  32. Eugster W, Kling G, Jonas T, McFadden JP, Wüest A et al. 2003. CO2 exchange between air and water in an Arctic Alaskan and midlatitude Swiss lake: importance of convective mixing. J. Geophys. Res. 108:4362
    [Google Scholar]
  33. Fang X, Stefan HG 1996. Dynamics of heat exchange between sediment and water in a lake. Water Resour. Res. 32:1719–27
    [Google Scholar]
  34. Farmer DD, Crawford GB, Osborn TR 1987. Temperature and velocity microstructure caused by swimming fish. Limnol. Oceanogr. 32:978–83
    [Google Scholar]
  35. Farmer DM 1975. Penetrative convection in the absence of mean shear. Q. J. R. Meteorol. Soc. 101:869–91
    [Google Scholar]
  36. Farrow DE, Patterson JC 1993. On the response of a reservoir sidearm to diurnal heating and cooling. J. Fluid Mech. 246:143–61
    [Google Scholar]
  37. Fer I, Lemmin U, Thorpe SA 2002. Winter cascading of cold water in Lake Geneva. J. Geophys. Res. Oceans 107:C613–113-16
    [Google Scholar]
  38. Finckh P 1981. Heat-flow measurements in 17 perialpine lakes. Geol. Soc. Am. Bull. 92:452–514
    [Google Scholar]
  39. Fink G, Wessels M, Wüest A 2016. Flood frequency matters: why climate change degrades deep-water quality of peri-alpine lakes. J. Hydrol. 540:457–68
    [Google Scholar]
  40. Forrest AL, Laval BE, Pieters R, Lim DSS 2013. A cyclonic gyre in an ice-covered lake. Limnol. Oceanogr. 58:363–75
    [Google Scholar]
  41. Garaud P 2018. Double-diffusive convection at low Prandtl number. Annu. Rev. Fluid Mech. 50:275–98
    [Google Scholar]
  42. Golosov SD, Ignatieva NV 1999. Hydrothermodynamic features of mass exchange across the sediment–water interface in shallow lakes. Hydrobiologia 408/409:153–57
    [Google Scholar]
  43. Gregg MC, D'Asaro EA, Riley JJ, Kunze E 2018. Mixing efficiency in the ocean. Annu. Rev. Mar. Sci. 10:443–73
    [Google Scholar]
  44. Guasto JS, Rusconi R, Stocker R 2012. Fluid mechanics of planktonic microorganisms. Annu. Rev. Fluid Mech. 44:373–400
    [Google Scholar]
  45. Gulati RD, Zadereev ES, Degermendzhi AG 2017. Ecology of Meromictic Lakes Cham, Switz.: Springer
    [Google Scholar]
  46. Henderson SM 2016. Upslope internal-wave Stokes drift, and compensating downslope Eulerian mean currents, observed above a lakebed. J. Phys. Oceanogr. 46:1947–61
    [Google Scholar]
  47. Hoare RA 1966. Problems of heat transfer in Lake Vanda, a density stratified Antarctic lake. Nature 210:787–89
    [Google Scholar]
  48. Hogg CAR, Marti CL, Huppert HE, Imberger J 2013. Mixing of an interflow into the ambient water of Lake Iseo. Limnol. Oceanogr. 58:579–92
    [Google Scholar]
  49. Hughes GO, Gayen B, Griffiths RW 2013. Available potential energy in Rayleigh–Bénard convection. J. Fluid Mech. 729:R3
    [Google Scholar]
  50. Huppert HE, Linden PF 1979. On heating a stable salinity gradient from below. J. Fluid Mech. 95:3431–464
    [Google Scholar]
  51. Huppert HE, Turner JS 1972. Double-diffusive convection and its implications for the temperature and salinity structure of the ocean and Lake Vanda. J. Phys. Oceanogr. 2:456–61
    [Google Scholar]
  52. Imberger J 1985. The diurnal mixed layer. Limnol. Ocean 30:737–70
    [Google Scholar]
  53. Imberger J 1998. Flux paths in a stratified lake: a review. Physical Processes in Lakes and Oceans J Imberger 1–17 Washington, DC: Am. Geophys. Union
    [Google Scholar]
  54. Imberger J, Hamblin PF 1982. Dynamics of lakes, reservoirs, and cooling ponds. Annu. Rev. Fluid Mech. 14:153–87
    [Google Scholar]
  55. Ivey GN, Winters KB, Koseff JR 2008. Density stratification, turbulence, but how much mixing. ? Annu. Rev. Fluid Mech. 40:169–84
    [Google Scholar]
  56. Jonas T, Terzhevik AY, Mironov DV, Wüest A 2003.a Radiatively driven convection in an ice-covered lake investigated by using temperature microstructure technique. J. Geophys. Res. 108:3183
    [Google Scholar]
  57. Jonas T, Wüest A, Eugster W, Stips A 2003.b Observations of a quasi shear-free lacustrine convective boundary layer: stratification and its implications on turbulence. J. Geophys. Res. 108:3328
    [Google Scholar]
  58. Katija K 2012. Biogenic inputs to ocean mixing. J. Exp. Biol. 215:1040–49
    [Google Scholar]
  59. Kelley DE 1997. Convection in ice-covered lakes: effects on algal suspension. J. Plankton Res. 19:1859–80
    [Google Scholar]
  60. Kirillin G, Engelhardt C, Golosov S 2009. Transient convection in upper lake sediments produced by internal seiching. Geophys. Res. Lett. 36:L18601
    [Google Scholar]
  61. Kirillin G, Forrest AL, Graves KE, Fischer A, Engelhardt C, Laval BE 2015. Axisymmetric circulation driven by marginal heating in ice-covered lakes. Geophys. Res. Lett. 42:2893–900
    [Google Scholar]
  62. Kirillin G, Leppäranta M, Terzhevik A, Granin N, Bernhardt J et al. 2012. Physics of seasonally ice-covered lakes: a review. Aquat. Sci. 74:659–82
    [Google Scholar]
  63. Kouraev AV, Zakharova EA, Rémy F, Kostianoy AG, Shimaraev MN et al. 2016. Giant ice rings on lakes Baikal and Hovsgol: inventory, associated water structure and potential formation mechanism. Limnol. Oceanogr. 61:1001–14
    [Google Scholar]
  64. Kunze E, Dower JF, Beveridge I, Dewey R, Bartlett KP 2006. Observations of biologically generated turbulence in a coastal inlet. Science 313:1768–70
    [Google Scholar]
  65. Laval BE, Morrison J, Potts DJ, Carmack EC, Vagle S et al. 2008. Wind-driven summertime upwelling in a fjord-type lake and its impact on downstream river conditions: Quesnel Lake and River, British Columbia, Canada. J. Gt. Lakes Res. 34:189–203
    [Google Scholar]
  66. Laval BE, Vagle S, Potts D, Morrison J, Sentlinger G et al. 2012. The joint effects of riverine, thermal, and wind forcing on a temperate fjord lake: Quesnel Lake, Canada. J. Gt. Lakes Res. 38:540–49
    [Google Scholar]
  67. Legg S 2012. Overflows and convectively driven flows. Buoyancy-Driven Flows EP Chassignet, C Cenedese, J Verron 203–39 New York: Cambridge Univ. Press
    [Google Scholar]
  68. Lei C, Patterson JC 2005. Unsteady natural convection in a triangular enclosure induced by surface cooling. Int. J. Heat Fluid Flow 26:307–21
    [Google Scholar]
  69. Leshansky AM, Pismen LM 2010. Do small swimmers mix the ocean. ? Phys. Rev. E 82:025301
    [Google Scholar]
  70. Linden PF 1973. The interaction of a vortex ring with a sharp density interface: a model for turbulent entrainment. J. Fluid Mech. 60:467–80
    [Google Scholar]
  71. Linden PF 1975. The deepening of a mixed layer in a stratified fluid. J. Fluid Mech. 71:385–405
    [Google Scholar]
  72. Lorke A, Peeters F, Wüest A 2005. Shear-induced convective mixing in bottom boundary layers on slopes. Limnol. Oceanogr. 50:1612–19
    [Google Scholar]
  73. Lorke A, Umlauf L, Mohrholz V 2008. Stratification and mixing on sloping boundaries. Geophys. Res. Lett. 35:L14610
    [Google Scholar]
  74. Lorrai C, Umlauf L, Becherer JK, Lorke A, Wüest A 2011. Boundary mixing in lakes: 2. Combined effects of shear- and convectively induced turbulence on basin-scale mixing. J. Geophys. Res. 116:C10018
    [Google Scholar]
  75. Mao Y, Lei C, Patterson JC 2010. Unsteady near-shore natural convection induced by surface cooling. J. Fluid Mech. 642:213–33
    [Google Scholar]
  76. Matthews PC, Heaney SI 1987. Solar heating and its influence on mixing in ice-covered lakes. Freshw. Biol. 18:135–49
    [Google Scholar]
  77. Mellado JP 2017. Cloud-top entrainment in stratocumulus clouds. Annu. Rev. Fluid Mech. 49:145–69
    [Google Scholar]
  78. Miesch MS, Toomre J 2009. Turbulence, magnetism, and shear in stellar interiors. Annu. Rev. Fluid Mech. 41:317–45
    [Google Scholar]
  79. Mironov D, Terzhevik A, Kirillin G, Jonas T, Malm J, Farmer D 2002. Radiatively driven convection in ice-covered lakes: observations, scaling, and a mixed layer model. J. Geophys. Res. 107:7–17-16
    [Google Scholar]
  80. Monismith SG, Imberger J, Morison ML 1990. Convective motions in the sidearm of a small reservoir. Limnol. Oceanogr. 35:1676–702
    [Google Scholar]
  81. Mortimer CH, Mackereth FJH 1958. Convection and its consequences in ice-covered lakes. SIL Proc.1922–2010 13:923–32
    [Google Scholar]
  82. Moum JN, Perlin A, Klymak JM, Levine MD, Boyd T, Kosro PM 2004. Convectively driven mixing in the bottom boundary layer. J. Phys. Oceanogr. 34:2189–202
    [Google Scholar]
  83. Newman FC 1976. Temperature steps in Lake Kivu: a bottom heated saline lake. J. Phys. Oceanogr. 6:157–63
    [Google Scholar]
  84. Noss C, Lorke A 2012. Zooplankton induced currents and fluxes in stratified waters. Water Qual. Res. J. 47:276–86
    [Google Scholar]
  85. Parker G, Garcia M, Fukushima Y, Yu W 1987. Experiments on turbidity currents over an erodible bed. J. Hydraul. Res. 25:123–47
    [Google Scholar]
  86. Pedley TJ, Kessler JO 1992. Hydrodynamic phenomena in suspensions of swimming microorganisms. Annu. Rev. Fluid Mech. 24:313–58
    [Google Scholar]
  87. Peeters F, Finger D, Hofer M, Brennwald M, Livingstone DM, Kipfer R 2003. Deep-water renewal in Lake Issyk-Kul driven by differential cooling. Limnol. Oceanogr. 48:1419–31
    [Google Scholar]
  88. Peeters F, Straile D, Lorke A, Ollinger D 2007. Turbulent mixing and phytoplankton spring bloom development in a deep lake. Limnol. Oceanogr. 52:286–98
    [Google Scholar]
  89. Peltier WR, Caulfield CP 2003. Mixing efficiency in stratified shear flows. Annu. Rev. Fluid Mech. 35:135–167
    [Google Scholar]
  90. Pieters R, Lawrence GA 2009. Effect of salt exclusion from lake ice on seasonal circulation. Limnol. Oceanogr. 54:401–12
    [Google Scholar]
  91. Powers SM, Hampton SE 2016. Winter limnology as a new frontier. Limnol. Oceanogr. Bull. 25:103–8
    [Google Scholar]
  92. Råman Vinnå L, Wüest A, Zappa M, Fink G, Bouffard D 2018. Tributaries affect the thermal response of lakes to climate change. Hydrol. Earth Syst. Sci. 22:31–51
    [Google Scholar]
  93. Rippeth TP, Fisher NR, Simpson JH 2001. The cycle of turbulent dissipation in the presence of tidal straining. J. Phys. Oceanogr. 31:2458–71
    [Google Scholar]
  94. Rodgers GK 1965. The thermal bar in the Laurentian Great Lakes. Proceedings of the 8th Conference on Great Lakes Research358–63 Ann Arbor, MI: Inst. Sci. Technol., Univ. Michigan
    [Google Scholar]
  95. Rutgersson A, Smedman A, Sahlée E 2011. Oceanic convective mixing and the impact on air-sea gas transfer velocity. Geophys. Res. Lett. 38:L02602
    [Google Scholar]
  96. Sánchez X, Roget E 2007. Microstructure measurements and heat flux calculations of a triple-diffusive process in a lake within the diffusive layer convection regime. J. Geophys. Res. Oceans 112:C02012
    [Google Scholar]
  97. Scheifele B, Pawlowicz R, Sommer T, Wüest A 2014. Double diffusion in saline Powell Lake, British Columbia. J. Phys. Oceanogr. 44:2893–908
    [Google Scholar]
  98. Schmid M, Budnev NM, Granin NG, Sturm M, Schurter M, Wüest A 2008. Lake Baikal deepwater renewal mystery solved. Geophys. Res. Lett. 35:L09605
    [Google Scholar]
  99. Schmid M, Busbridge M, Wüest A 2010. Double-diffusive convection in Lake Kivu. Limnol. Oceanogr. 55:225–38
    [Google Scholar]
  100. Schmid M, Lorke A, Dinkel C, Tanyileke G, Wüest A 2004.a Double-diffusive convection in Lake Nyos, Cameroon. Deep Sea Res. Part I 51:1097–111
    [Google Scholar]
  101. Schmid M, Tietze K, Halbwachs M, Lorke A, McGinnis DF, Wüest A 2004.b How hazardous is the gas accumulation in Lake Kivu? Arguments for a risk assessment in light of the Nyiragongo Volcano eruption of 2002. Acta Vulcanol 14–15:115–22
    [Google Scholar]
  102. Schmitt RW 1994. Double diffusion in oceanography. Annu. Rev. Fluid Mech. 26:255–85
    [Google Scholar]
  103. Schwefel R, Gaudard A, Wüest A, Bouffard D 2016. Effects of climate change on deep-water oxygen and winter mixing in a deep lake (Lake Geneva): comparing observational findings and modeling. Water Resour. Res. 52:8811–26
    [Google Scholar]
  104. Shay TJ, Gregg MC 1986. Convectively driven turbulent mixing in the upper ocean. J. Phys. Oceanogr. 16:1777–98
    [Google Scholar]
  105. Shibley NC, Timmermans ML, Carpenter JR, Toole JM 2017. Spatial variability of the Arctic Ocean's double-diffusive staircase. J. Geophys. Res. Oceans 122:980–94
    [Google Scholar]
  106. Simoncelli S, Thackeray SJ, Wain DJ 2017. Can small zooplankton mix lakes. ? Limnol. Oceanogr. Lett. 2:167–76
    [Google Scholar]
  107. Simpson JH, Brown J, Matthews J, Allen G 1990. Tidal straining, density currents, and stirring in the control of estuarine stratification. Estuaries Coasts 13:125–32
    [Google Scholar]
  108. Soloviev A, Lukas R 2014. The Near-Surface Layer of the Ocean: Structure, Dynamics and Applications Dordrecht, Neth.: Springer
    [Google Scholar]
  109. Sommer T, Carpenter JR, Schmid M, Lueck RG, Schurter M, Wüest A 2013. Interface structure and flux laws in a natural double-diffusive layering. J. Geophys. Res. Oceans 118:6092–106
    [Google Scholar]
  110. Sommer T, Carpenter JR, Wüest A 2014. Double-diffusive interfaces in Lake Kivu reproduced by direct numerical simulations. Geophys. Res. . Lett 41:5114–21
    [Google Scholar]
  111. Sommer T, Danza F, Berg J, Sengupta A, Constantinescu G et al. 2017. Bacteria-induced mixing in natural waters. Geophys. Res. Lett. 44:9424–32
    [Google Scholar]
  112. Steinhorn I 1985. The disappearance of the long term meromictic stratification of the Dead Sea. Limnol. Oceanogr. 30:451472
    [Google Scholar]
  113. Stern ME 1960. The “salt-fountain” and thermohaline convection. Tellus 12:172–75
    [Google Scholar]
  114. Stommel H, Arons AB, Blanchard D 1956. An oceanographical curiosity—the perpetual salt fountain. Deep Sea Res 3:152–53
    [Google Scholar]
  115. Strøm K 1962. Trapped sea water. New Sci 274:384–86
    [Google Scholar]
  116. Sturman JJ, Oldham CE, Ivey GN 1999. Steady convective exchange flows down slopes. Aquat. Sci. 61:260–78
    [Google Scholar]
  117. Sutherland BR, Gingras MK, Knudson C, Steverango L, Surma C 2018. Particle-bearing currents in uniform density and two-layer fluids. Phys. Rev. Fluids 3:2023801
    [Google Scholar]
  118. Tanaka M, Girard G, Davis R, Peuto A, Bignell N 2001. Recommended table for the density of water between 0 °C and 40 °C based on recent experimental reports. Metrologia 38:301–9
    [Google Scholar]
  119. Tedford EW, MacIntyre S, Miller SD, Czikowsky MJ 2014. Similarity scaling of turbulence in a temperate lake during fall cooling. J. Geophys. Res. Oceans 119:4689–713
    [Google Scholar]
  120. Timmermans M-L, Toole J, Krishfield R, Winsor P 2008. Ice-tethered profiler observations of the double-diffusive staircase in the Canada Basin thermocline. J. Geophys. Res. Oceans 113:C00A02
    [Google Scholar]
  121. Tivey MA, de Ronde CEJ, Tontini FC, Walker SL, Fornari DJ 2016. A novel heat flux study of a geothermally active lake—Lake Rotomahana, New Zealand. J. Volcanol. Geotherm. Res. 314:95–109
    [Google Scholar]
  122. Toffolon M, Wüest A, Sommer T 2015. Minimal model for double diffusion and its application to Kivu, Nyos, and Powell Lake. J. Geophys. Res. Oceans 120:6202–24
    [Google Scholar]
  123. Townsend AA 1964. Natural convection in water over an ice surface. Q. J. R. Meteorol. Soc. 90:248–59
    [Google Scholar]
  124. Turner JS 1974. Double-diffusive phenomena. Annu. Rev. Fluid Mech. 6:37–54
    [Google Scholar]
  125. Turner JS 1986. Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J. Fluid Mech. 173:431–71
    [Google Scholar]
  126. Ulloa H, Wüest A, Bouffard D 2018. Mechanical energy budget and mixing efficiency for a radiatively heated ice-covered waterbody. J. Fluid Mech. 852:R1
    [Google Scholar]
  127. Vehmaa A, Salonen K 2009. Development of phytoplankton in Lake Pääjärvi (Finland) during under-ice convective mixing period. Aquat. Ecol. 43:693–705
    [Google Scholar]
  128. Velmurugan V, Srithar K 2008. Prospects and scopes of solar pond: a detailed review. Renew. Sustain. Energy Rev. 12:2253–63
    [Google Scholar]
  129. Verburg P, Antenucci JP, Hecky RE 2011. Differential cooling drives large-scale convective circulation in Lake Tanganyika. Limnol. Oceanogr. 56:910–26
    [Google Scholar]
  130. Verburg P, Hecky RE, Kling H 2003. Ecological consequences of a century of warming in Lake Tanganyika. Science 301:505–7
    [Google Scholar]
  131. Visser AW 2007. Biomixing of the oceans. ? Science 316:838–39
    [Google Scholar]
  132. von Rohden C, Boehrer B, Ilmberger J 2010. Evidence for double diffusion in temperate meromictic lakes. Hydrol. Earth Syst. Sci. 14:667–74
    [Google Scholar]
  133. Wang S, Ardekani AM 2015. Biogenic mixing induced by intermediate Reynolds number swimming in stratified fluids. Sci. Rep. 5:17448
    [Google Scholar]
  134. Weinberger H 1964. The physics of the solar pond. Sol. Energy 8:45–56
    [Google Scholar]
  135. Wells M, Cenedese C, Caulfield CP 2010. The relationship between flux coefficient and entrainment ratio in density currents. J. Phys. Oceanogr. 40:2713–27
    [Google Scholar]
  136. Wells M, Nadarajah P 2009. The intrusion depth of density currents flowing into stratified water bodies. J. Phys. Oceanogr. 39:1935–47
    [Google Scholar]
  137. Wilson AT, Wellman HW 1962. Lake Vanda: an Antarctic lake. Nature 196:1171–73
    [Google Scholar]
  138. Wilson RC, Hook SJ, Schneider P, Schladow SG 2013. Skin and bulk temperature difference at Lake Tahoe: a case study on lake skin effect. J. Geophys. Res. Atmos. 118:10332–46
    [Google Scholar]
  139. Woods AW 2010. Turbulent plumes in nature. Annu. Rev. Fluid Mech. 42:391–412
    [Google Scholar]
  140. Wüest A, Carmack EC 2000. A priori estimates of mixing and circulation in the hard-to reach water body of Lake Vostok. Ocean Model 2:29–43
    [Google Scholar]
  141. Wüest A, Lorke A 2003. Small-scale hydrodynamics in lakes. Annu. Rev. Fluid Mech. 35:373–412
    [Google Scholar]
  142. Wüest A, Piepke G, Halfman JD 1996. Combined effects of dissolved solids and temperature on the density stratification of Lake Malawi (East Africa). The Limnology, Climatology and Paleoclimatology of the East African Lakes TC Johnson, EO Odada 183–202 New York: Gordon Breach
    [Google Scholar]
  143. Wüest A, Ravens TM, Granin NG, Kocsis O, Schurter M, Sturm M 2005. Cold intrusions in Lake Baikal—direct observational evidence for deep water renewal. Limnol. Oceanogr. 50:184–96
    [Google Scholar]
  144. Wüest A, Sommer T, Schmid M, Carpenter JR 2012. Diffusive-type of double diffusion in lakes—a review. Environmental Fluid Mechanics: Memorial Volume in Honour of Prof. Gerhard H. Jirka W Rodi, M Uhlmann 271–84 Boca Raton, FL: CRC
    [Google Scholar]
  145. Zilitinkevic SS 1991. Turbulent Penetrative Convection Adelshot, UK: Avebury
    [Google Scholar]
/content/journals/10.1146/annurev-fluid-010518-040506
Loading
/content/journals/10.1146/annurev-fluid-010518-040506
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error