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.
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References
Amorocho J, deVries JJ (1980) A new evaluation of the wind stress coefficient over water surfaces. J Geophys Res 85:433–442
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
Armi L (1978) Some evidence for boundary mixing in the deep ocean. J Geophys Res 83:1971–1979
Armi L (1979) Effects of variation in eddy diffusivity on property distributions in the ocean. J Mar Res 37:515–530
Barry RG, Chorley RJ (1976) Atmosphere, weather and climate. Methnen, London
Batchelor GK (1950) The application of the similarity theory of turbulence to atmospheric diffusion. Q J R Meteorol Soc 76:133–146
Batchelor GK (1959) Small-scale variation of convected quantities like temperature in turbulent fluid. J Fluid Mech 5:113–139
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
Brutsaert W (1975) On a derivable formula for longwave radiation from clear skies. Water Resour Res 11:742–744
Bührer H, Ambuhl H (1975) Die Einleitung von gereinigtem Abwasser in Seen. Schweiz Z Hydrol 37:347–369
Bünti JL (1914) Chronicle. Neujahrsbl Uri, Altdorf 20:8–9
Caldwell DR, Chriss TM (1979) The viscous sublayer at the sea floor. Science 205:1131–1132
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
Chen CTA, Millero FJ (1986) Precise thermodynamic properties for natural waters covering only the limnological range. Limnol Oceanogr 31:657–662
Chriss TM, Caldwell DR (1982) Evidence for the influence of form drag on bottom boundary layer flow. J Geophys Res 87:4148–4154
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
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
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
Corrsin S (1961) The reactant concentration spectrum in turbulent mixing with a first-order reaction. J Fluid Mech 11:407–416
Csanady GT (1974) Spring thermocline behavior in Lake Ontario during IFYGL. J Phys Oceanogr 4:425–445
Deardorff JW (1970) Convective velocity and temperature scales for unstable planetary boundary layer and for Rayleigh convection. J Atmos Sci 27:1211–1213
Deardorff JW, Willis CE, Lilly DK (1969) Laboratory investigation of non-steady penetrative convection. J Fluid Mech 28:675–704
Denman KL, Miyake M (1973) Upper layer modification at Ocean Station Papa: observations and simulations. J Phys Oceanogr 3:185–196
Denman KL, Okubo A, Platt T (1977) The chlorophyll fluctuation spectrum in the sea. Limnol Oceanogr 22:1033–1038
Dewey RK, Crawford WR (1988) Bottom stress estimates from vertical dissipation rate profiles on the continental shelf. J Phys Oceanogr 87:1167–1177
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
Dillon TM (1982) Vertical overturns: a comparison of Thorpe and Ozmidov length scales. J Geophys Res 87:9601–9613
Dillon TM, Caldwell DR (1980) The Batchelor spectrum and dissipation in the upper ocean. J Geophys Res 85:1910–1916
Dillon TM, Powell TM (1979) Observations of a surface mixed layer. Deep-Sea Res 26(A):915–932
Dillon TM, Richman JG, Hansen CG, Pearson MD (1981) Near-surface turbulence measurements in a lake. Nature 290:390–392
Dimai A, Gloor M, Wuest A (1994) Bestimmung der Intensitat von Turbulenz in der Bodengrenzschicht von Seen. Limnologica 24:339–350
Dubois DM (1975) A model of patchiness for preypredator plankton populations. Ecol Modelling 1:67–80
Eckart C (1948) An analysis of the stirring and mixing processes in incompressible fluids. J Mar Res 7: 265–275
Elliott AJ (1984) Measurements of the turbulence in an abyssal boundary layer. J Phys Oceanogr 14:1778–1786
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
Forel FA (1876) La formule des seiches. C R Acad Sci Paris 83:712–714
Fozdar FM, Parker GJ, Imberger J (1985) Matching temperature and conductivity sensor response characteristics. J Phys Oceanogr 15:1557–1569
Gallegos CL, Platt T (1982) Phytoplankton production and water motion in surface mixed layers. Deep-Sea Res 29:65–76
Gargett AE, Sanford TS, Osborn TR (1979) Surface mixing layers in the Sargasso Sea. J Phys Oceanogr 9:1090–1111
Gargett AE, Osborn TR, Nasmyth PW (1984) Local isotropy and the decay of turbulence in a stratified fluid. J Fluid Mech 144:231–280
Garrett C (1990) The role of secondary circulation in boundary mixing. J Geophys Res 95:3181–3188
Garrett C (1991) Marginal mixing theories. Atmos Ocean 29:313–331
Gill AE (1982) Ocean atmosphere dynamics. Academic Press, New York
Gloor M, Wüest A, Münnich M (1994) Benthic boundary mixing and resuspension induced by internal seiches. Hydrobiologia 284:59–68
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
Gregg MC (1987) Diapycnal mixing in the thermocline: a review. J Geophys Res 92:5249–5286
Gregg MC, Sanford TB (1988) The dependence of.turbulent dissipation on stratification in a diffusively stable thermocline. J Geophys Res 93:12381–12392
Gust G (1982) Tools for oceanic small-scale, highfrequency flows: metal-clad hot wires. J Geophys Res 87:447–455
Gust G, Weatherly GL (1985) Velocities, turbulence and skin friction in a deep-sea logarithmic layer. J Geophys Res 90:4779–4792
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
Hinze JO (1975) Turbulence, 2nd edn. McGraw-Hill, New York, 618 pp
Horn W, Mortimer CH, Schwab DJ (1986) Windinduced internal seiches in Lake Zurich observed and modeled. Limnol Oceanogr 31:1232–1254
Horsch GM, Stefan HG (1988) Convective circulation in littoral water due to surface cooling. Limnol Oceanogr 33: 1068–1083
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
Hutchinson GE (1957) A treatise on limnology. Wiley, New York
Hutter K (1983) Hydrodynamics of lakes. Springer, Berlin, Heidelberg, New York
Imberger J (1985) The diurnal mixed layer. Limnol Oceanogr 30:737–770
Imberger J, Patterson JC (1990) Physical Limnology. Advances in applied mechanics. Academic Press, Cambridge, pp 303–475
Imboden DM (1981) Tracer and mixing in the aquatic environment. Swiss Federal Institute of Technology, Ziirich
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
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
Imboden DM, Joller T (1984) Turbulent mixing in the hypolimnion of Baldeggersee (Switzerland) traced by natural radon-222. Limnol Oceanogr 29:831–844
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
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
Joseph J, Sendner H (1958) Uber die horizontale Diffusion im Meer. Dtsch Hydrogr Z 11:49–77
Kelvin L, Thomson SW (1875) On an alleged error in Laplace’s theory of the tides. Philes Mag 4:227–242
Kierstead H, Slobodkin LB (1953) The size of water masses containing plankton blooms. J Mar Res 12:141–147
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
Kuhn W (1979) Aus Wärmehaushalt und Klimadaten berechnete Verdunstung des Zürichsees. Vierteljahresschr Naturforsch Ges Zür 123:261–283
Kullenberg G (1972) Apparent horizontal diffusion in stratified vertical shear flow. Tellus 24:17–28
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
Kunze E (1987) Limits on growing, finite length salt fingers: a Richardson number constraint. J Mar Res 45:533–556
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
Langmuir I (1938) Surface motion of water induced by wind. Science 87:119–123
LeBlond PH, Mysak LA (1978) Waves in the ocean. Elsevier, Amsterdam
Ledwell JR, Watson AJ, Law CS (1993) Evidence for slow mixing across the pycnocline from an openocean tracer-release experiment. Nature 364: 701–703
Leeder MR (1983) On the dynamics of sediment suspension by residual Reynolds stresses – confirmation of Bagnold’s theory. Sedimentology 30:485–491
Leibovich S (1983) The form and dynamics of Langmuir circulations. Annu Rev Fluid Mech 15 :391–427
Lemmin U (1987) The structure and dynamics of internal waves in Baldeggersee. Limnol Oceanogr 32:43–61
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
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
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
Lighthill J (1978) Waves in fluids. Cambridge Univ Press, Cambridge
Lombardo CP, Gregg MC (1989) Similarity scaling of ε and X in a convecting surface boundary layer. J Geophys Res 94:6273–6284
Marti DE, Imboden DM (1986) Thermische Energieflüsse an der Wasseroberfläche: Beispiel Sempachersee. Schweiz Z Hydrol 48:196–229
McDougall TJ (1987a) Thermobaricity, cabbeling and water mass conversion. J Geophys Res 92: 5448–5464
McDougall TJ (1987b) Neutral surfaces. J Phys Oceanogr 17: 1950–1964
McDougall TJ, Taylor JR (1984) Flux measurements across a finger interface at low values of the stability ratio. J Mar Res 42:1–14
Miller MC, McCave IN, Komar PD (1977) Threshold of sediment motion under unidirectional currents. Sedimentology 24:507–527
Mortimer CH (1974) Lake hydrodynamics. Verh Int Verein LimnoI20:124–197
Mortimer CH (1975) Substantive corrections to SIL communications (IVL Mitteilungen) Numbers 6 and 20. Verh Int Verein Limnol 19:60–72
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
Münnich M (1993) On the influence of bottom topography on the vertical structure of internal seiches. Diss No 10434, ETH Zürich
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
Murthy CR (1976) Horizontal diffusion characteristics in Lake Ontario. J Phys Oceanogr 6:76–84
Mysak LA, Salvadé G, Hutter K, Scheiwiler T (1983) Lake of Lugano and topographic waves. Nature 306:46–48
Newman FC (1976) Temperature steps in Lake Kivu: a bottom heated saline lake. J Phys Oceanogr 6: 157–163
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
Oakey NS, Elliott JA (1982) Dissipation within the surface mixed layer. J Phys Oceanogr 12: 171–185
Okubo A (1967) The effect of shear in an oscillatory current on horizontal diffusion from an instantaneous source. Limnol Oceanogr 1:194–204
Okubo A (1971) Oceanic diffusion diagrams. Deep-Sea Res 18:789–802
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
Osborn TR (1974) Vertical profiling of velocity microstructure. J Phys Oceanogr 4:109–115
Osborn TR (1980) Estimates of the local rate of vertical diffusion from dissipation measurements. J Phys Oceanogr 10:83–89
Osborn TR, Cox CS (1972) Oceanic fine structure. Geophys Fluid Dyn 3:321–345
Padman L, Dillon TM (1987) Vertical heat fluxes through the Beaufort Sea thermohaline staircase. J Geophys Res 92:10799–10806
Pahl-Wostl C, Imboden D (1990) DYPHORA – A dynamic model for the rate of photosynthesis of algae. J Plankton Res 12: 1207–1221
Patterson JC (1987) A model for convective motions in reservoir side arm. Proc XXII, IAHR Congr Lausanne 1987, pp 68–73
Peeters F (1994) Horizontale Mischung in Seen. Diss No 10476 ETH Zürich, p 147
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
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
Peters H, Gregg MC, Toole JM (1988) On the parametrization of equatorial turbulence. J Geophys Res 93:1199–1218
Platt T, Denman KL (1975) Spectral analysis in ecology. Annu Rev Ecol Syst 6:189–210
Powell T, Jassby A (1974) The estimation of vertical eddy diffusivities below the thermocline in lakes. Water Resour Res 10:191–198
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
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
Richardson LF (1926) Atmospheric diffusion on a distance-neighbour graph. Proc R Soc A 110: 709–737
Sanderson B, Perry K, Pederson T (1986) Vertical diffusion in meromictic Powell Lake, British Columbia. J Geophys Res 91:7647–7655
Saylor JH, Huang JCK, Reid RO (1980) Vortex modes in southern Lake Michigan. J Phys Oceanogr 10: 1814–1823
Schlatter JW (1991) Schwefelhexafluorid als Tracer zum Studium von Mischungsprozessen in Seen. Diss No 9596, ETH Zürich
Schmitt RW (1979) Flux measurements on salt fingers at an interface. J Mar Res 37:419–436
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
Shay TJ, Gregg MC (1986) Convectively driven turbulent mixing in the upper ocean. J Phys Oceanogr 16: 1777–1798
Shields A (1936) Anwendung der Aehnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung. Mitt Preuss Versuchsanst Wasserbau Schiffbau 26, Berlin. pp 1–26
Siegenthaler C, Sturm M (1991) Slump induced surges and sediment transport in Lake Uri, Switzerland. Verh Int Verein Limnol 24:955–958
Soloviev A V (1990) Coherent structures at the ocean surface in convectively unstable conditions. Nature 346:157–160
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
Spigel RH, Imberger J (1980) The classification of mixed-layer dynamics in lakes of small to medium size. J Phys Oceanogr 10:1104–1121
Steele JH (1974) Spatial heterogeneity and population stability. Nature 248:83
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
Stein horn I (1985) The disappearance of the long term meromictic stratification of the Dead Sea. Limnol Oceanogr 30:451–462
Stern ME (1976) Maximum buoyancy flux across a salt finger interface. J Mar Res 34:95–110
Stern ME, Turner JS (1969) Salt fingers and convecting layers. Deep-Sea Res 16:497–511
Stocker T, Hutter K (1987) Topographic waves in channels and lakes on the f-plane. Springer, Berlin, Heidelberg, New York
Stull RB (1984) Transilient turbulence theory. Part l. The concept of eddy mixing across finite distances. J Atmos Sci 41:3351–3367
Stull RB (1986) Transilient turbulence theory. Part 3. Bulk dispersion rate and numerical stability. J Atmos Sci 43:50–57
Stull RB (1988) An introduction to boundary layer meteorology. Kluwer, Dordrecht
Swinbank WC (1963) Long-wave radiation from clear skies. Q J R Meteorol Soc 89:339–348
Taylor GI (1953) Dispersion of soluble matter in solyent‘ flowing slowly through a tube. Proc R Soc Lond A 219:186–203
Thorpe SA (1969) Experiments on the stability of stratified shear flows. Radio Sci 4: 1327–1332
Thorpe SA (1977) Turbulence and mixing in a Scottish loch. Philos Trans R Soc Lond Ser A 286: 125–181
Thorpe SA (1988) The dynamics of the boundary layers of the deep ocean. Sci Prog 72:189–206
Toole JM, Polzin KL, Schmitt RW (1994) Estimates of diapycnal mixing in the abyssal ocean. Science 264:1120–1123
Turner JS (1965) The coupled turbulent transports of salt and heat across a sharp density interface. Int J Heat Mass Transfer 8:759–767
Turner JS (1967) Salt fingers across a density interface. Deep-Sea Res 14:599–611
Turner JS (1968) The behavior of a stable salinity gradient heated from below. J Fluid Mech 33: 183–200
Turner JS (1973) Buoyancy effects in fluids. Cambridge Univ Press, Cambridge
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
Van Senden DC, Imboden OM (1989) Internal seiche pumping between sill-separated basins. Geophys Astrophys Fluid Dyn 48: 135–150
Weatherly GL (1972) A study of the bottom boundary layer of the Florida current. J Phys Oceanogr 2: 54–72
Wehrli B (1993) Chemie am Seegrund. Vierteljahresschr Naturforsch Ges Zürich 138:1–11
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
Wiegand RC, Chamberlain V (1987) Internal waves of the second vertical mode in a stratified lake. Limnol Oceanogr 32:29–42
Wimbush M, Munk W (1970) The benthic boundary layer. In: Maxwell AE, (ed) The sea, vol 4. Interscience, New York, pp 731–758
Woods JD (1968) Wave-induced shear instability in the summer thermocline. J Fluid Mech 32:791–800
Woods AW (1991) Boundary-driven mixing. J Fluid Mech 226:625–654
Wroblewski JS, O’Brien JJ (1976) A spatial model of phytoplankton patchiness. Mar BioI 35:161–175
Wüest A (1987) Ursprung und Grösse von Mischungsprozessen im Hypolimnion natürlicher Seen. Diss No 8350, ETH Zürich
Wüest A (1994) Interaktionen in Seen: Die Biologie als Quelle dominanter physik ali scher Kräfte. Limnologica 24:93–104
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
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
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
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
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
Young WR, Rhines PB, Garrett CJR (1982) Shear-flow dispersion, internal waves and horizontal mixing in the ocean. J Phys Oceanogr 12:515–527
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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
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