Skip to main content

Mixing Mechanisms in Lakes

  • Chapter
Physics and Chemistry of Lakes

Abstract

Transport phenomena are among the most important processes in natural systems. Chemical compounds, the constituents of biogeochemical systems, are in continual motion in all parts of the earth. The thermal motion of atoms and molecules is perceived on the macroscopic level as molecular diffusion i.e., as the slow but persistent movement “down along the concentration gradient.” Although the average speed of the atoms is on the order of tens to hundreds of meters per second, the net transport is small, because the molecules do not maintain the same direction long enough. Thus, typical molecular diffusion coefficients of solutes in water are approximately 10-9 m2s - 1 corresponding to characteristic annual transport distances of approximately 20 cm. In solids the diffusion coefficients even drop to values as low as 10-14m2s-1 or less.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Amorocho J, deVries JJ (1980) A new evaluation of the wind stress coefficient over water surfaces. J Geophys Res 85:433–442

    Google Scholar 

  • Anati DA, Stiller M, Shasha S, Gat JR (1987) Changes in the thermohaline structure of the Dead Sea: 1979–1984. Earth Planet Sci Lett 84:109–121

    Google Scholar 

  • Armi L (1978) Some evidence for boundary mixing in the deep ocean. J Geophys Res 83:1971–1979

    Google Scholar 

  • Armi L (1979) Effects of variation in eddy diffusivity on property distributions in the ocean. J Mar Res 37:515–530

    Google Scholar 

  • Barry RG, Chorley RJ (1976) Atmosphere, weather and climate. Methnen, London

    Google Scholar 

  • Batchelor GK (1950) The application of the similarity theory of turbulence to atmospheric diffusion. Q J R Meteorol Soc 76:133–146

    Google Scholar 

  • Batchelor GK (1959) Small-scale variation of convected quantities like temperature in turbulent fluid. J Fluid Mech 5:113–139

    Google Scholar 

  • Boudreau BP, Imboden DM (1987) Mathematics of tracer mixing in sediments: III. The theory of non-local mixing within sediments. Am J Sci 287: 693–719

    Google Scholar 

  • Brutsaert W (1975) On a derivable formula for longwave radiation from clear skies. Water Resour Res 11:742–744

    Google Scholar 

  • Bührer H, Ambuhl H (1975) Die Einleitung von gereinigtem Abwasser in Seen. Schweiz Z Hydrol 37:347–369

    Google Scholar 

  • Bünti JL (1914) Chronicle. Neujahrsbl Uri, Altdorf 20:8–9

    Google Scholar 

  • Caldwell DR, Chriss TM (1979) The viscous sublayer at the sea floor. Science 205:1131–1132

    CAS  Google Scholar 

  • Carter HH, Okubo A (1965) A study of the physical processes of the movement and dispersion in the Cape Kennedy area. Final Rep under US Atomic Energy Comm, Chesapeake Bay Inst, John Hopkins Univ, Rep No NYO-2973–1, 164 pp

    Google Scholar 

  • Chen CTA, Millero FJ (1986) Precise thermodynamic properties for natural waters covering only the limnological range. Limnol Oceanogr 31:657–662

    CAS  Google Scholar 

  • Chriss TM, Caldwell DR (1982) Evidence for the influence of form drag on bottom boundary layer flow. J Geophys Res 87:4148–4154

    Google Scholar 

  • Chriss TM, Caldwell DR (1984) Universal similarity and the thickness of the viscous sub layer at the ocean floor. J Geophys Res 89:6403–6414

    Google Scholar 

  • Chung Y, Kim K (1980) Excess 222Rn and the benthic layer in the western and southern Indian ocean. Earth Planet Sci Lett 49:351–359

    CAS  Google Scholar 

  • Colman JA, Armstrong DE (1987) Vertical eddy diffusivity determined with Radon-222 in the benthic boundary layer of ice covered lakes. Limnol Oceanogr 32:577–590

    CAS  Google Scholar 

  • Corrsin S (1961) The reactant concentration spectrum in turbulent mixing with a first-order reaction. J Fluid Mech 11:407–416

    Google Scholar 

  • Csanady GT (1974) Spring thermocline behavior in Lake Ontario during IFYGL. J Phys Oceanogr 4:425–445

    Google Scholar 

  • Deardorff JW (1970) Convective velocity and temperature scales for unstable planetary boundary layer and for Rayleigh convection. J Atmos Sci 27:1211–1213

    Google Scholar 

  • Deardorff JW, Willis CE, Lilly DK (1969) Laboratory investigation of non-steady penetrative convection. J Fluid Mech 28:675–704

    Google Scholar 

  • Denman KL, Miyake M (1973) Upper layer modification at Ocean Station Papa: observations and simulations. J Phys Oceanogr 3:185–196

    Google Scholar 

  • Denman KL, Okubo A, Platt T (1977) The chlorophyll fluctuation spectrum in the sea. Limnol Oceanogr 22:1033–1038

    CAS  Google Scholar 

  • Dewey RK, Crawford WR (1988) Bottom stress estimates from vertical dissipation rate profiles on the continental shelf. J Phys Oceanogr 87:1167–1177

    Google Scholar 

  • Dewey RK, Crawford WR, Gargett AE, Oakey NS (1987) A microstructure instrument for profiling oceanic turbulence in coastal bottom boundary layers. J Atmos Oceanic Technol 4:288–297

    Google Scholar 

  • Dillon TM (1982) Vertical overturns: a comparison of Thorpe and Ozmidov length scales. J Geophys Res 87:9601–9613

    Google Scholar 

  • Dillon TM, Caldwell DR (1980) The Batchelor spectrum and dissipation in the upper ocean. J Geophys Res 85:1910–1916

    Google Scholar 

  • Dillon TM, Powell TM (1979) Observations of a surface mixed layer. Deep-Sea Res 26(A):915–932

    Google Scholar 

  • Dillon TM, Richman JG, Hansen CG, Pearson MD (1981) Near-surface turbulence measurements in a lake. Nature 290:390–392

    Google Scholar 

  • Dimai A, Gloor M, Wuest A (1994) Bestimmung der Intensitat von Turbulenz in der Bodengrenzschicht von Seen. Limnologica 24:339–350

    Google Scholar 

  • Dubois DM (1975) A model of patchiness for preypredator plankton populations. Ecol Modelling 1:67–80

    Google Scholar 

  • Eckart C (1948) An analysis of the stirring and mixing processes in incompressible fluids. J Mar Res 7: 265–275

    Google Scholar 

  • Elliott AJ (1984) Measurements of the turbulence in an abyssal boundary layer. J Phys Oceanogr 14:1778–1786

    Google Scholar 

  • Ewart TE, Bendiner WP (1981) An observation of the horizontal and vertical diffusion of a passive tracer in the deep ocean. J Geophys Res 86:10974–10982

    Google Scholar 

  • Forel FA (1876) La formule des seiches. C R Acad Sci Paris 83:712–714

    Google Scholar 

  • Fozdar FM, Parker GJ, Imberger J (1985) Matching temperature and conductivity sensor response characteristics. J Phys Oceanogr 15:1557–1569

    Google Scholar 

  • Gallegos CL, Platt T (1982) Phytoplankton production and water motion in surface mixed layers. Deep-Sea Res 29:65–76

    Google Scholar 

  • Gargett AE, Sanford TS, Osborn TR (1979) Surface mixing layers in the Sargasso Sea. J Phys Oceanogr 9:1090–1111

    Google Scholar 

  • Gargett AE, Osborn TR, Nasmyth PW (1984) Local isotropy and the decay of turbulence in a stratified fluid. J Fluid Mech 144:231–280

    Google Scholar 

  • Garrett C (1990) The role of secondary circulation in boundary mixing. J Geophys Res 95:3181–3188

    Google Scholar 

  • Garrett C (1991) Marginal mixing theories. Atmos Ocean 29:313–331

    Google Scholar 

  • Gill AE (1982) Ocean atmosphere dynamics. Academic Press, New York

    Google Scholar 

  • Gloor M, Wüest A, Münnich M (1994) Benthic boundary mixing and resuspension induced by internal seiches. Hydrobiologia 284:59–68

    Google Scholar 

  • Grant WD, Williams III AJ, Glenn SM (1984) Bottom stress estimates and their prediction on the northern California continental shelf during CODE-I: the importance of wave-current interaction. J Phys Oceanogr 14:506–527

    Google Scholar 

  • Gregg MC (1987) Diapycnal mixing in the thermocline: a review. J Geophys Res 92:5249–5286

    Google Scholar 

  • Gregg MC, Sanford TB (1988) The dependence of.turbulent dissipation on stratification in a diffusively stable thermocline. J Geophys Res 93:12381–12392

    Google Scholar 

  • Gust G (1982) Tools for oceanic small-scale, highfrequency flows: metal-clad hot wires. J Geophys Res 87:447–455

    Google Scholar 

  • Gust G, Weatherly GL (1985) Velocities, turbulence and skin friction in a deep-sea logarithmic layer. J Geophys Res 90:4779–4792

    Google Scholar 

  • Herdendorf CE (1990) Distribution of the world’s large lakes. In: Tilzer M, Serruya C (eds) Large lakes: ecological structure and function. Springer, Berlin, Heidelberg, New York, pp 3–38

    Google Scholar 

  • Hinze JO (1975) Turbulence, 2nd edn. McGraw-Hill, New York, 618 pp

    Google Scholar 

  • Horn W, Mortimer CH, Schwab DJ (1986) Windinduced internal seiches in Lake Zurich observed and modeled. Limnol Oceanogr 31:1232–1254

    Google Scholar 

  • Horsch GM, Stefan HG (1988) Convective circulation in littoral water due to surface cooling. Limnol Oceanogr 33: 1068–1083

    Google Scholar 

  • Huppert HE, Turner JS (1972) Double-diffusive convection and its implications for the temperature and salinity structure of the ocean and Lake Yanda. J Phys Oceanogr 2:456–461

    Google Scholar 

  • Hutchinson GE (1957) A treatise on limnology. Wiley, New York

    Google Scholar 

  • Hutter K (1983) Hydrodynamics of lakes. Springer, Berlin, Heidelberg, New York

    Google Scholar 

  • Imberger J (1985) The diurnal mixed layer. Limnol Oceanogr 30:737–770

    Google Scholar 

  • Imberger J, Patterson JC (1990) Physical Limnology. Advances in applied mechanics. Academic Press, Cambridge, pp 303–475

    Google Scholar 

  • Imboden DM (1981) Tracer and mixing in the aquatic environment. Swiss Federal Institute of Technology, Ziirich

    Google Scholar 

  • Imboden DM (1990) Mixing and transport in lakes: mechanisms and ecological relevance. In: Tilzer M, Serruya C (eds) Large lakes: ecological structure and function. Springer, Berlin, Heidelberg, New York, pp 47–80

    Google Scholar 

  • Imboden DM, Lerman A (1978) Chemical models of lakes. In: Lerman A, (ed) Lakes - chemistry, geology, physics. Springer, Berlin, Heidelberg, New York, pp 341–356

    Google Scholar 

  • Imboden DM, Joller T (1984) Turbulent mixing in the hypolimnion of Baldeggersee (Switzerland) traced by natural radon-222. Limnol Oceanogr 29:831–844

    Google Scholar 

  • Imboden DM, Stotz B, Wiiest A (1988) Hypolimnic mixing in a deep alpine lake and the role of a storm event. Verh Int Verein Limnol 23:67–73

    Google Scholar 

  • Ivey CN, Imberger J (1991) On the nature ofturbulence in a stratified fluid. Part I. The energetics of mixing. J Phys Oceanogr 21:650–659

    Google Scholar 

  • Joseph J, Sendner H (1958) Uber die horizontale Diffusion im Meer. Dtsch Hydrogr Z 11:49–77

    Google Scholar 

  • Kelvin L, Thomson SW (1875) On an alleged error in Laplace’s theory of the tides. Philes Mag 4:227–242

    Google Scholar 

  • Kierstead H, Slobodkin LB (1953) The size of water masses containing plankton blooms. J Mar Res 12:141–147

    Google Scholar 

  • Kolmogorov AN (1941) The local structure of turbulence in an incompressible viscous fluid for very large Reynolds numbers. Dokl Akad Nauk USSR 30:299–303

    Google Scholar 

  • Kuhn W (1979) Aus Wärmehaushalt und Klimadaten berechnete Verdunstung des Zürichsees. Vierteljahresschr Naturforsch Ges Zür 123:261–283

    Google Scholar 

  • Kullenberg G (1972) Apparent horizontal diffusion in stratified vertical shear flow. Tellus 24:17–28

    Google Scholar 

  • Kullenberg G, Murthy CR, Westerberg H (1973) An experimental study of diffusion characteristics in the thermocline and hypolimnion regions of Lake Ontario. Proc 16th Conf Great Lakes Res, pp 774–790

    Google Scholar 

  • Kunze E (1987) Limits on growing, finite length salt fingers: a Richardson number constraint. J Mar Res 45:533–556

    Google Scholar 

  • Lambert A (1988) Records of riverborne turbidity currents and indications of slope failure in the Rhone delta of Lake Geneva. Limnol Oceanogr 33: 458–468

    Google Scholar 

  • Langmuir I (1938) Surface motion of water induced by wind. Science 87:119–123

    CAS  Google Scholar 

  • LeBlond PH, Mysak LA (1978) Waves in the ocean. Elsevier, Amsterdam

    Google Scholar 

  • Ledwell JR, Watson AJ, Law CS (1993) Evidence for slow mixing across the pycnocline from an openocean tracer-release experiment. Nature 364: 701–703

    CAS  Google Scholar 

  • Leeder MR (1983) On the dynamics of sediment suspension by residual Reynolds stresses – confirmation of Bagnold’s theory. Sedimentology 30:485–491

    Google Scholar 

  • Leibovich S (1983) The form and dynamics of Langmuir circulations. Annu Rev Fluid Mech 15 :391–427

    Google Scholar 

  • Lemmin U (1987) The structure and dynamics of internal waves in Baldeggersee. Limnol Oceanogr 32:43–61

    Google Scholar 

  • Lemmin U, Mortimer CH (1986) Tests of an extension to internal seiches of Defant’s procedure for determination of seiche characteristics in real lakes. Limnol Oceanogr 31:1207–1231

    Google Scholar 

  • Lewis MR, Horue EPW, Cullen JJ, Oakey NS, Platt T (1984a) Turbulent motions may control phytoplankton photosynthesis in the upper ocean. Nature 311:49–50

    CAS  Google Scholar 

  • Lewis MR, Cullen JJ, Platt T (1984b) Relationship between vertical mixing and photo adaptation of phytoplankton: similarity criteria. Mar Ecol Prog Ser 15:141–149

    Google Scholar 

  • Lighthill J (1978) Waves in fluids. Cambridge Univ Press, Cambridge

    Google Scholar 

  • Lombardo CP, Gregg MC (1989) Similarity scaling of ε and X in a convecting surface boundary layer. J Geophys Res 94:6273–6284

    Google Scholar 

  • Marti DE, Imboden DM (1986) Thermische Energieflüsse an der Wasseroberfläche: Beispiel Sempachersee. Schweiz Z Hydrol 48:196–229

    Google Scholar 

  • McDougall TJ (1987a) Thermobaricity, cabbeling and water mass conversion. J Geophys Res 92: 5448–5464

    Google Scholar 

  • McDougall TJ (1987b) Neutral surfaces. J Phys Oceanogr 17: 1950–1964

    Google Scholar 

  • McDougall TJ, Taylor JR (1984) Flux measurements across a finger interface at low values of the stability ratio. J Mar Res 42:1–14

    Google Scholar 

  • Miller MC, McCave IN, Komar PD (1977) Threshold of sediment motion under unidirectional currents. Sedimentology 24:507–527

    Google Scholar 

  • Mortimer CH (1974) Lake hydrodynamics. Verh Int Verein LimnoI20:124–197

    Google Scholar 

  • Mortimer CH (1975) Substantive corrections to SIL communications (IVL Mitteilungen) Numbers 6 and 20. Verh Int Verein Limnol 19:60–72

    Google Scholar 

  • Mortimer CH (1979) Strategies for coupling data collection and analysis with dynamic modelling of lake motion. In: Graf WH, Mortimer CH (eds) Hydrodynamics of lakes. Elsevier, Amsterdam, pp 183–222

    Google Scholar 

  • Münnich M (1993) On the influence of bottom topography on the vertical structure of internal seiches. Diss No 10434, ETH Zürich

    Google Scholar 

  • Münnich M, Wuest A, Imboden DM (1992) Observations of the second vertical mode of the internal seiche in an alpine lake. Limnol Oceanogr 37: 1705–1719

    Google Scholar 

  • Murthy CR (1976) Horizontal diffusion characteristics in Lake Ontario. J Phys Oceanogr 6:76–84

    Google Scholar 

  • Mysak LA, Salvadé G, Hutter K, Scheiwiler T (1983) Lake of Lugano and topographic waves. Nature 306:46–48

    Google Scholar 

  • Newman FC (1976) Temperature steps in Lake Kivu: a bottom heated saline lake. J Phys Oceanogr 6: 157–163

    Google Scholar 

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

    Google Scholar 

  • Oakey NS, Elliott JA (1982) Dissipation within the surface mixed layer. J Phys Oceanogr 12: 171–185

    Google Scholar 

  • Okubo A (1967) The effect of shear in an oscillatory current on horizontal diffusion from an instantaneous source. Limnol Oceanogr 1:194–204

    Google Scholar 

  • Okubo A (1971) Oceanic diffusion diagrams. Deep-Sea Res 18:789–802

    Google Scholar 

  • Okubo A, Ozmidov RV (1970) Empirical dependence of the coefficient of horizontal turbulent diffusion in the ocean on the scale of the phenomenon in question. Izv Atm Oc Phys 6:534–536

    Google Scholar 

  • Osborn TR (1974) Vertical profiling of velocity microstructure. J Phys Oceanogr 4:109–115

    Google Scholar 

  • Osborn TR (1980) Estimates of the local rate of vertical diffusion from dissipation measurements. J Phys Oceanogr 10:83–89

    Google Scholar 

  • Osborn TR, Cox CS (1972) Oceanic fine structure. Geophys Fluid Dyn 3:321–345

    Google Scholar 

  • Padman L, Dillon TM (1987) Vertical heat fluxes through the Beaufort Sea thermohaline staircase. J Geophys Res 92:10799–10806

    Google Scholar 

  • Pahl-Wostl C, Imboden D (1990) DYPHORA – A dynamic model for the rate of photosynthesis of algae. J Plankton Res 12: 1207–1221

    Google Scholar 

  • Patterson JC (1987) A model for convective motions in reservoir side arm. Proc XXII, IAHR Congr Lausanne 1987, pp 68–73

    Google Scholar 

  • Peeters F (1994) Horizontale Mischung in Seen. Diss No 10476 ETH Zürich, p 147

    Google Scholar 

  • Peeters F, Wuest A, Imboden DM (1993) Comparison of the results of tracer experiments in lakes with predictions based on horizontal mixing models. Verh Int Verein Limnol 25:67–74

    Google Scholar 

  • Peters H, Gregg MC (1987) Some dynamical and statistical properties of equatorial turbulence. In: Nihoul J, (ed) Small-scale turbulence and mixing in the ocean, Proc of the 19th Int Liege Colloq on Ocean hydrodynamics. Elsevier, Amsterdam

    Google Scholar 

  • Peters H, Gregg MC, Toole JM (1988) On the parametrization of equatorial turbulence. J Geophys Res 93:1199–1218

    Google Scholar 

  • Platt T, Denman KL (1975) Spectral analysis in ecology. Annu Rev Ecol Syst 6:189–210

    Google Scholar 

  • Powell T, Jassby A (1974) The estimation of vertical eddy diffusivities below the thermocline in lakes. Water Resour Res 10:191–198

    Google Scholar 

  • Powell TM, Richerson PJ, Dillon TM, Agee BA, Dozier BJ, Godden DA, Myrup LO (1975) Spatial scales of current speed and phytoplankton biomass fluctuations in Lake Tahoe. Science 189: 1088–1090

    CAS  Google Scholar 

  • Quay PD, Broecker WS, Hesslein RH, Schindler DW (1980) Vertical diffusion rates determined by tritium tracer experiments in the thermocline and hypolimnion of two lakes. Limnol Oceanogr 25:201–218

    CAS  Google Scholar 

  • Richardson LF (1926) Atmospheric diffusion on a distance-neighbour graph. Proc R Soc A 110: 709–737

    Google Scholar 

  • Sanderson B, Perry K, Pederson T (1986) Vertical diffusion in meromictic Powell Lake, British Columbia. J Geophys Res 91:7647–7655

    CAS  Google Scholar 

  • Saylor JH, Huang JCK, Reid RO (1980) Vortex modes in southern Lake Michigan. J Phys Oceanogr 10: 1814–1823

    Google Scholar 

  • Schlatter JW (1991) Schwefelhexafluorid als Tracer zum Studium von Mischungsprozessen in Seen. Diss No 9596, ETH Zürich

    Google Scholar 

  • Schmitt RW (1979) Flux measurements on salt fingers at an interface. J Mar Res 37:419–436

    Google Scholar 

  • Schmitt RW, Perkins H, Boyd JD, Stalcup MC (1987) C-salt: an investigation of the thermohaline staircase in the western tropical North Atlantic. Deep-Sea Res 34:1655–1665

    Google Scholar 

  • Shay TJ, Gregg MC (1986) Convectively driven turbulent mixing in the upper ocean. J Phys Oceanogr 16: 1777–1798

    Google Scholar 

  • Shields A (1936) Anwendung der Aehnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung. Mitt Preuss Versuchsanst Wasserbau Schiffbau 26, Berlin. pp 1–26

    Google Scholar 

  • Siegenthaler C, Sturm M (1991) Slump induced surges and sediment transport in Lake Uri, Switzerland. Verh Int Verein Limnol 24:955–958

    Google Scholar 

  • Soloviev A V (1990) Coherent structures at the ocean surface in convectively unstable conditions. Nature 346:157–160

    Google Scholar 

  • Soulsby RL (1983) The bottom boundary layer of shelf seas. In: Johns B, (ed) Physical oceanography of coastal and shelf seas. Elsevier, Amsterdam, pp 189–266

    Google Scholar 

  • Spigel RH, Imberger J (1980) The classification of mixed-layer dynamics in lakes of small to medium size. J Phys Oceanogr 10:1104–1121

    Google Scholar 

  • Steele JH (1974) Spatial heterogeneity and population stability. Nature 248:83

    Google Scholar 

  • Steele JH (1978) Some comments on plankton patches. In: Steele JH, (ed) Spatial pattern in plankton communities. Nato Conf Ser IV. Plenum, New York, pp 1–20

    Google Scholar 

  • Stein horn I (1985) The disappearance of the long term meromictic stratification of the Dead Sea. Limnol Oceanogr 30:451–462

    CAS  Google Scholar 

  • Stern ME (1976) Maximum buoyancy flux across a salt finger interface. J Mar Res 34:95–110

    Google Scholar 

  • Stern ME, Turner JS (1969) Salt fingers and convecting layers. Deep-Sea Res 16:497–511

    Google Scholar 

  • Stocker T, Hutter K (1987) Topographic waves in channels and lakes on the f-plane. Springer, Berlin, Heidelberg, New York

    Google Scholar 

  • Stull RB (1984) Transilient turbulence theory. Part l. The concept of eddy mixing across finite distances. J Atmos Sci 41:3351–3367

    Google Scholar 

  • Stull RB (1986) Transilient turbulence theory. Part 3. Bulk dispersion rate and numerical stability. J Atmos Sci 43:50–57

    Google Scholar 

  • Stull RB (1988) An introduction to boundary layer meteorology. Kluwer, Dordrecht

    Google Scholar 

  • Swinbank WC (1963) Long-wave radiation from clear skies. Q J R Meteorol Soc 89:339–348

    Google Scholar 

  • Taylor GI (1953) Dispersion of soluble matter in solyent‘ flowing slowly through a tube. Proc R Soc Lond A 219:186–203

    CAS  Google Scholar 

  • Thorpe SA (1969) Experiments on the stability of stratified shear flows. Radio Sci 4: 1327–1332

    Google Scholar 

  • Thorpe SA (1977) Turbulence and mixing in a Scottish loch. Philos Trans R Soc Lond Ser A 286: 125–181

    Google Scholar 

  • Thorpe SA (1988) The dynamics of the boundary layers of the deep ocean. Sci Prog 72:189–206

    Google Scholar 

  • Toole JM, Polzin KL, Schmitt RW (1994) Estimates of diapycnal mixing in the abyssal ocean. Science 264:1120–1123

    CAS  Google Scholar 

  • Turner JS (1965) The coupled turbulent transports of salt and heat across a sharp density interface. Int J Heat Mass Transfer 8:759–767

    CAS  Google Scholar 

  • Turner JS (1967) Salt fingers across a density interface. Deep-Sea Res 14:599–611

    Google Scholar 

  • Turner JS (1968) The behavior of a stable salinity gradient heated from below. J Fluid Mech 33: 183–200

    Google Scholar 

  • Turner JS (1973) Buoyancy effects in fluids. Cambridge Univ Press, Cambridge

    Google Scholar 

  • Van der Hoven I (1957) Power spectrum of horizontal wind speed in the frequency range from 0.0007 to 900 cycles per hour. J Meteorol 14:160

    Google Scholar 

  • Van Senden DC, Imboden OM (1989) Internal seiche pumping between sill-separated basins. Geophys Astrophys Fluid Dyn 48: 135–150

    Google Scholar 

  • Weatherly GL (1972) A study of the bottom boundary layer of the Florida current. J Phys Oceanogr 2: 54–72

    Google Scholar 

  • Wehrli B (1993) Chemie am Seegrund. Vierteljahresschr Naturforsch Ges Zürich 138:1–11

    Google Scholar 

  • Welander P (1968) Theoretical forms for the vertical exchange coefficients in a stratified fluid with application to lakes and seas. Geophys Gothenburg 1:1–27

    Google Scholar 

  • Wiegand RC, Chamberlain V (1987) Internal waves of the second vertical mode in a stratified lake. Limnol Oceanogr 32:29–42

    Google Scholar 

  • Wimbush M, Munk W (1970) The benthic boundary layer. In: Maxwell AE, (ed) The sea, vol 4. Interscience, New York, pp 731–758

    Google Scholar 

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

    Google Scholar 

  • Woods AW (1991) Boundary-driven mixing. J Fluid Mech 226:625–654

    Google Scholar 

  • Wroblewski JS, O’Brien JJ (1976) A spatial model of phytoplankton patchiness. Mar BioI 35:161–175

    Google Scholar 

  • Wüest A (1987) Ursprung und Grösse von Mischungsprozessen im Hypolimnion natürlicher Seen. Diss No 8350, ETH Zürich

    Google Scholar 

  • Wüest A (1994) Interaktionen in Seen: Die Biologie als Quelle dominanter physik ali scher Kräfte. Limnologica 24:93–104

    Google Scholar 

  • Wüest A, Imboden OM, Schurter M (1988) Origin and size of hypolimnic mixing in Urnersee, the southern basin of Vierwaldstattersee (Lake Lucerne). Schweiz Z Hydrol 50:40–70

    Google Scholar 

  • Wüest A, Aeschbach-Hertig W, Baur H, Hofer M, Kipfer R, Schurter M (1992) Density structure and tritium-helium age of deep hypolimnetic water in the northern basin of Lake Lugano. Aquat Sci 54:205–218

    Google Scholar 

  • Wüest A, van Senden DC, Imberger J, Piepke G, Gloor M (1994) Diapycnal diffusivity measured by microstructure and tracer techniques: a comparison. Symp on Turbulent flow, Grenoble, 8 pp

    Google Scholar 

  • Wunsch C (1972) The spectrum from two years to two minutes of temperature fluctuations in the main thermocline at Bermuda. Deep-Sea Res 19:577–593

    Google Scholar 

  • Wyngaard JC, Cote OR (1971) The budget of turbulent kinetic energy and temperature variance in the atmosphere surface layer. J Atmos Sci 28:190–201

    Google Scholar 

  • Young WR, Rhines PB, Garrett CJR (1982) Shear-flow dispersion, internal waves and horizontal mixing in the ocean. J Phys Oceanogr 12:515–527

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg New York

About this chapter

Cite this chapter

Imboden, D.M., Wüest, A. (1995). Mixing Mechanisms in Lakes. In: Lerman, A., Imboden, D.M., Gat, J.R. (eds) Physics and Chemistry of Lakes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85132-2_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-85132-2_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-85134-6

  • Online ISBN: 978-3-642-85132-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics