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Double-diffusive convection

Published online by Cambridge University Press:  20 April 2006

Herbert E. Huppert  and
J. Stewart Turner
Herbert E. Huppert
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW
J. Stewart Turner
Affiliation:
Research School of Earth Sciences, Australian National University, Canberra ACT 2600
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Abstract

In this paper we present a rather personal view of the important developments in double-diffusive convection, a subject whose evolution has been the result of a close interaction between theoreticians, laboratory experimenters and sea-going oceano-graphers. More recently, applications in astrophysics, engineering and geology have become apparent. In the final section we attempt to draw some general conclusions and suggest that further progress will again depend on a close collaboration between fluid dynamicists and other scientists.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 106 , May 1981 , pp. 299 - 329
Copyright
© 1981 Cambridge University Press

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References

Arons, A. B. 1980 The scientific work of Henry Stommel. Evolution of Physical Oceanography (ed. B. A. Warren & C. Wunsch). Massachusetts Institute of Technology Press.
Baker, D. J. 1971 Density gradients in a rotating stratified fluid: experimental evidence for a new instability. Science 172, 1029–1031.CrossRefGoogle Scholar
Baines, W. D. & Turner, J. S. 1968 Turbulent buoyant convection from a source in a confined region. J. Fluid Mech. 37, 51–80.Google Scholar
Chen, C. F., Briggs, D. G. & Wirtz, R. A. 1971 Stability of thermal convection in a salinity gradient due to lateral heating. Int. J. Heat Mass. Trans. 14, 57–65.Google Scholar
Chen, C. F. & Turner, J. S. 1980 Crystallization in a double-diffusive system. J. Geophys. Res. 85, 2573–2593.Google Scholar
Cooper, J. W. & Stommel, H. 1968 Regularly spaced steps in the main thermocline near Bermuda. J. Geophys. Res. 73, 5849–5854.Google Scholar
Cooper, L. N. H. 1967 Stratification in the deep ocean. Sci. Progr. 55, 73–90.Google Scholar
Copley, S. M., Giamei, A. F., Johnson, S. M. & Hornbecker, M. H. 1970 The origin of freckles in unidirectionally solidified castings. Metal Trans. 1, 2193–2204.Google Scholar
Coriell, S. R., Cordes, M. R., Boettinger, W. J. & Sekerka, R. F. 1980 Convective and interfacial instabilities during unidirectional solidification of a binary alloy. J. Crystal Growth 49, 13–28.Google Scholar
Da Costa, L. N., Knobloch, E. J. & Weiss, N. O. 1981 Oscillations in double-diffusive convection. J. Fluid Mech. (to appear).Google Scholar
Elder, J. W. 1969 Numerical experiments with thermohaline convection. Phys. Fluids Suppl. 12, II. 194–197.Google Scholar
Fay, J. A. & MacKenzie, J. J. 1972 Cold cargo. Environment 14, 21–29.Google Scholar
Fedorov, K. N. 1970 The stepped structure of temperature inversions in the ocean. Izv. Akad. Nauk. S.S.S.R., Fizika atmosfery i okeana 6, 1178–1188.Google Scholar
Fedorov, K. N. 1976 The thermohaline finestructure of the ocean. (English translation, Pergamon, 1978.)
Fischer, H. 1971 The dilution of an undersea sewage cloud by salt fingers. Water Res. 5, 909–915.Google Scholar
Goldreich, P. & Schubert, G. 1967 Differential rotation in stars. Astrophys. J. 150, 571–587.Google Scholar
Gordon, A. L., Georgi, D. T. & Taylor, H. W. 1977 Antarctic polar front zone in the western Scotia Sea—Summer 1975. J. Phys. Oceanog 7, 309–328.Google Scholar
Gregg, M. C. 1980 The three-dimensional mapping of a small thermohaline intrusion. J. Phys. Oceanog. 10, 1468–1492.Google Scholar
Gregg, M. C. & Briscoe, M. G. 1979 Internal waves, finestructure, microstructure, and mixing in the ocean. Rev. Geophys. Space Phys. 17, 1524–1548.Google Scholar
Gregg, M. C. & Cox, C. S. 1972 The vertical microstructure of temperature and salinity. Deep-Sea Res. 19, 355–376.Google Scholar
Griffiths, R. W. 1979 The transport of multiple components through thermohaline diffusive interfaces. Deep-Sea Res. 26, 383–397.Google Scholar
Groves, G. W. 1959 Flow estimate for the perpetual salt fountain. Deep-Sea Res. 5, 209–214.Google Scholar
Herring, J. 1963 Investigation of problems in thermal convection. J. Atmos. Sci. 20, 325–338.Google Scholar
Hoare, R. E. 1966 Problems in heat transfer in Lake Vanda, a density stratified Antarctic Lake. Nature 210, 787–789.Google Scholar
Holyer, J. 1981 On the collective instability of salt fingers. J. Fluid Mech. (in the press).Google Scholar
Huppert, H. E. 1971 On the stability of a series of double-diffusive layers. Deep-Sea Res. 18, 1005–1021.Google Scholar
Huppert, H. E. 1976 Transitions in double-diffusive convection. Nature 263, 20–22.Google Scholar
Huppert, H. E. & Josberger, E. G. 1980 The melting of ice in cold stratified water. J. Phys. Oceanog. 10, 953–960.Google Scholar
Huppert, H. E. & Linden, P. F. 1976 The spectral signature of salt-fingers. Deep-Sea Res. 23, 909–914.Google Scholar
Huppert, H. E. & Linden, P. F. 1979 On heating a stable salinity gradient from below. J. Fluid Mech. 95, 431–464.Google Scholar
Huppert, H. E. & Manins, P. C. 1973 Limiting conditions for salt-fingering at an interface. Deep-Sea Res. 20, 315–323.Google Scholar
Huppert, H. E. & Moore, D. R. 1976 Nonlinear double-diffusive convection. J. Fluid Mech. 78, 821–854.Google Scholar
Huppert, H. E. & Sparks, R. S. J. 1980 Restrictions on the composition of mid-ocean ridge basalts: a fluid dynamical investigation. Nature 286, 46–48.CrossRefGoogle Scholar
Huppert, H. E. & Sparks, R. S. J. 1981 The fluid dynamics of a basaltic magma chamber replenished by influx of hot, dense ultrabasic magma. Contributions to Mineralogy and Petrology (in the press).
Huppert, H. E. & Turner, J. S. 1972 Double-diffusive convection and its implications for the temperature and salinity structure of the ocean and Lake Vanda. J. Phys. Oceanog. 2, 456–461.Google Scholar
Huppert, H. E. & Turner, J. S. 1978 Melting icebergs. Nature 271, 46–48.Google Scholar
Huppert, H. E. & Turner, J. S. 1980 Ice blocks melting into a salinity gradient. J. Fluid Mech. 100, 367–384.Google Scholar
Huppert, H. E. & Turner, J. S. 1981 A laboratory model of a replenished magma chamber. Earth & Planetary Sci. Lett. (in the press).Google Scholar
Hurle, D. & Jakeman, E. 1969 Significance of the Soret effect in the Rayleigh-Jeffrey's problem. Phys. Fluids 12, 2704–2705.Google Scholar
Hurle, D. T. J. & Jakeman, E. 1971 Soret-driven thermosolutal convection. J. Fluid Mech. 47, 667–687.Google Scholar
Jacobs, S. S., Huppert, H. E., Holdsworthy, G. & Drury, D. J. 1981 Thermohaline steps induced by melting of the Erebus glacier tongue. J. Geophys. Res. (in the press).Google Scholar
Jevons, W. S. 1857 On the cirrous form of cloud. London, Edinburgh and Dublin Phil. Mag. & J. Sci. IV. 14, 22–35.Google Scholar
Joyce, T. M., Zenk, W. E. & Toole, J. 1978 The anatomy of the Antarctic Polar Front in the Drake Passage. J. Geophys. Res. 83, 6093–6113.Google Scholar
Lambert, R. B. & Sturges, W. 1977 A thermohaline staircase and vertical mixing in the thermocline. Deep-Sea Res. 24, 211–222.Google Scholar
Linden, P. F. 1971 Salt fingers in the presence of grid-generated turbulence. J. Fluid Mech. 49, 611–624.Google Scholar
Linden, P. F. 1973 On the structure of salt fingers. Deep-Sea Res. 20, 325–340.Google Scholar
McBirney, A. R. 1980 Mixing and unmixing of magmas. J. Volcanol. & Geotherm. Res. 7, 357–371.Google Scholar
McBirney, A. R. & Noyes, R. M. 1979 Crystallization and layering of the Skaergaard intrusion. J. Pet. 20, 487–554.Google Scholar
McDougall, T. J. 1981 Double-diffusive convection with a nonlinear equation of state. Prog. Oceanog. (in the press).Google Scholar
McIntyre, M. E. 1970a Diffusive destabilization of a baroclinic circular vortex. Geophys. Fluid Dynamics 1, 19–57.Google Scholar
McIntyre, M. E. 1970b Role of diffusive overturning in nonlinear axisymmetric convection in a differentially heated rotating annulus. Geophys. Fluid Dynamics 1, 58–89.Google Scholar
McKenzie, D. P. & Richter, F. M. 1981 Parameterized thermal convection in a layered region and the thermal history of the Earth. J. Geophys. Res. (in the press).Google Scholar
Magnell, B. 1976 Salt fingers observed in the Mediterranean outflow region (34° N, 11° W) using a towed sensor. J. Phys. Oceanog. 6, 511–523.Google Scholar
Malkus, W. V. R. 1954 The heat transport and spectrum of thermal turbulence. Proc. Roy. Soc. A 225, 196–212.Google Scholar
Marzec, C. J. & Spiegel, E. A. 1980 Ordinary differential equations with strange attractors. SIAM J. Appl. Math. 38, 403–421.Google Scholar
May, R. M. 1976 Simple mathematical models with very complicated dynamics. Nature 261, 459–467.Google Scholar
Mendenhall, C. E. & Mason, M. 1923 The stratified subsidence of fine particles. Proc. Nat. Acad. Sci. U.S.A. 9, 199–202.Google Scholar
Merceret, F. J. 1977 A possible manifestation of double-diffusive convection in the atmosphere. Boundary-Layer Met. 11, 121–123.Google Scholar
Molcard, R. & Williams, A. J. 1975 Deep stepped structure in the Tyrrhenian Sea. Mem. Soc. r. Sci. Liège 7, 191–210.Google Scholar
Munns, R. G., Stanley, R. J. & Densmore, C. D. 1967 Hydrographic observations of the Red Sea brines. Nature 214, 1215–1217.Google Scholar
Neal, V. T., Neshyba, S. & Denner, W. 1969 Thermal stratification in the Arctic Ocean. Science, 166, 373–374.Google Scholar
Neshyba, S., Neal, V. T. & Denner, W. 1971 Temperature and conductivity measurements under ice island T-3. J. Geophys. Res. 76, 8107–8120.Google Scholar
Piacsek, S. A. & Toomre, J. 1980 Nonlinear evolution and structure of salt fingers. Marine Turbulence (ed. J. C. J. Nihoul), pp. 193–219. Elsevier.
Pingree, R. D. 1971 Regularly spaced instrumental temperature and salinity structures. Deep-Sea Res. 18, 841–844.Google Scholar
Preston, B. N., Laurent, T. C., Comper, W. D. & Checkley, G. J. 1980 Rapid polymer transport in concentrated solutions through the formation of ordered structures. Nature 287, 499–503.Google Scholar
Prigogine, I. & Rice, S. A. 1975 Advances in Chemical Physics XXXII. Wiley.
Proctor, M. R. E. 1981 Steady subcritical thermohaline convection. J. Fluid Mech. 105, 507–521.Google Scholar
Richter, F. M. 1979 Focal mechanisms and seismic energy release of deep and intermediate earthquakes in the Tonga-Kermadec region and their bearing on the depth extent of mantle flow. J. Geophys. Res. 84, 6783–6795.CrossRefGoogle Scholar
Ruddick, B. R. & Turner, J. S. 1979 The vertical length scale of double-diffusive intrusions. Deep-Sea Res. 26, 903–913.Google Scholar
Sarsten, J. A. 1972 LNG stratification and rollover. Pipeline and Gas. J. Sept. 1972, 37–39.Google Scholar
Schaefer, J. T. 1975 Nonlinear biconstituent diffusion: a possible trigger of convection. J. Atmos. Sci. 32, 2278–2284.Google Scholar
Schmitt, R. W. 1981 Form of the temperature—salinity relationship in the Central water: evidence for double-diffusive mixing. J. Phys. Oceanog. (in the press).Google Scholar
Schmitt, R. W. & Evans, D. L. 1978 An estimate of the vertical mixing due to salt fingers based on observations in the North Atlantic Central water. J. Geophys. Res. 83, 2913–2919.Google Scholar
Spiegel, E. A. 1971 Convection in stars. II. Basic Boussinesq convection. Ann. Rev. Astron. Astrophys. 9, 323–352.Google Scholar
Spiegel, E. A. 1972 Convection in stars. II. Special effects. Ann. Rev. Astron. Astrophys. 10, 261–304.Google Scholar
Stern, M. E. 1960 The 'salt fountain’ and thermohaline convection. Tellus 12, 172–175.Google Scholar
Stern, M. E. 1969 Collective instability of salt fingers. J. Fluid Mech. 35, 209–218.Google Scholar
Stern, M. E. 1976 Maximum buoyancy flux across a salt finger interface. J. Mar. Res. 34, 95–110.Google Scholar
Stern, M. E. & Turner, J. S. 1969 Salt fingers and convecting layers. Deep-Sea Res. 16, 497–511.Google Scholar
Stevenson, D. J. & Turner, J. S. 1979 Fluid models of mantle convection. The Earth: its Origin, Evolution and Structure (ed. M. W. McElhinny), pp. 227–263. Academic.
Stommel, H. 1962 Examples of mixing and self stimulated convection on the S, T diagram (in Russian). Okeanologiya 2, 205–209.Google Scholar
Stommel, H., Arons, A. B. & Blanchard, D. 1956 An oceanographical curiosity: the perpetual salt fountain. Deep-Sea Res. 3, 152–153.Google Scholar
Stommel, H. & Fedorov, K. N. 1967 Small-scale structure in temperature and salinity near Timor and Mindanao. Tellus 19, 306–325.Google Scholar
Straus, J. M. 1972 Finite amplitude doubly-diffusive convection. J. Fluid Mech. 56, 353–374.Google Scholar
Swallow, J. C. 1965 Hot salty water. Oceanus 11, 3–5.Google Scholar
Tabor, H. 1979 Non-convecting solar ponds. Phil. Trans. Roy. Soc. A 295, 423–433.Google Scholar
Tait, R. I. & Howe, M. R. 1968 Some observations of thermohaline stratification in the deep ocean. Deep-Sea Res. 15, 275–280.Google Scholar
Tait, R. I. & Howe, M. R. 1971 Thermohaline staircase. Nature 231, 178–179.Google Scholar
Thorpe, S. A., Hutt, P. K. & Soulsby, R. 1969 The effect of horizontal gradients on thermohaline convection. J. Fluid Mech. 38, 375–400.Google Scholar
Turner, J. S. 1965 The coupled turbulent transports of salt and heat across a sharp density interface. Int. J. Heat Mass Trans. 8, 759–767.Google Scholar
Turner, J. S. 1967 Salt fingers across a density interface. Deep-Sea Res. 14, 599–611.Google Scholar
Turner, J. S. 1968 The behaviour of a stable salinity gradient heated from below. J. Fluid Mech. 33, 183–200.Google Scholar
Turner, J. S. 1974 Double-diffusive phenomena. Ann. Rev. Fluid Mech. 6, 37–56.Google Scholar
Turner, J. S. 1978 Double-diffusive intrusions into a density gradient. J. Geophys. Res. 83, 2887–2901.Google Scholar
Turner, J. S. 1979 Buoyancy Effects in Fluids. Cambridge University Press.
Turner, J. S. 1980 A fluid-dynamical model of differentiation and layering in magma chambers. Nature 285, 213–215.Google Scholar
Turner, J. S. 1981 The influence of molecular processes on turbulence and mixing in the ocean. Proc. 2nd Int. Conference on Turbulence in the Ocean (ed. J. D. Woods). Springer.
Turner, J. S. & Chen, C. F. 1974 Two-dimensional effects in double-diffusive convection. J. Fluid Mech. 63, 577–592.Google Scholar
Turner, J. S. & Gustafson, L. B. 1978 The flow of hot saline solutions from vents in the sea floor—some implications for exhalative massive sulfide and other ore deposits. Economic Geology 73, 1082–1100.CrossRefGoogle Scholar
Turner, J. S. & Gustafson, L. B. 1981 Fluid motions and compositional gradients produced by crystallization or melting at vertical boundaries. J. Vulcanol. & Geotherm. Res. (in the press).Google Scholar
Turner, J. S. & Stommel, H. 1964 A new case of convection in the presence of combined vertical salinity and temperature gradients. Proc. Nat. Acad. Sci. U.S.A. 52, 49–53.Google Scholar
Turner, J. S., Shirtcliffe, T. G. L. & Brewer, P. G. 1970 Elemental variations of transport coefficients across density interfaces in multiple diffusive systems. Nature 228, 1083–1084.Google Scholar
Veronis, G. 1965 On finite amplitude instability in thermohaline convection. J. Mar. Res. 23, 1–17.Google Scholar
Veronis, G. 1968 Effect of a stabilizing gradient of solute on thermal convection. J. Fluid Mech. 34, 315–336.Google Scholar
Wager, L. R. & Brown, G. M. 1967 Layered Igneous Rocks. Edinburgh: Oliver and Boyd.
Williams, A. J. 1974 Salt fingers observed in the Mediterranean outflow. Science, 185, 941–943.Google Scholar