Hostname: page-component-745bb68f8f-f46jp Total loading time: 0 Render date: 2025-01-11T00:14:39.020Z Has data issue: false hasContentIssue false
  • English
  • Français

Melting driven by vigorous compositional convection

Published online by Cambridge University Press:  26 April 2006

Ross C. Kerr
Ross C. Kerr
Affiliation:
Research School of Earth Sciences, The Australian National University, Canberra, ACT 0200, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

The melting of a solid in contact with a hot fluid is quantified for the case in which a difference between the densities of the fluid and of the melted solid is able to drive vigorous compositional convection. A scaling analysis is first used to obtain a theoretical expression for the melting rate that is valid for a certain range of Stefan numbers. This expression is then compared with melting velocities measured in laboratory experiments in which ice and wax are melted when they are overlain or underlain by hot aqueous solutions. The melting velocities are consistent with the theoretical expression, and are found to depend on the heats of solution that are released when the melted solids mix with the solutions. The experiments also indicate that, for vigorous convection to occur during the melting of a floor, the unstable compositional buoyancy needs to be at least twice the stabilizing thermal buoyancy.

An important geological situation in which melting occurs is when large volumes of basaltic magma are intruded into the Earth's continental crust. The theoretical and experimental results are used and extended to examine quantitatively the melting of the floor and walls of the magma chamber, and of crustal blocks that fall into the chamber.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 280 , 10 December 1994 , pp. 255 - 285
Copyright
© 1994 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bird, R. B., Stewart, W. E. & Lightfoot, E. N. 1960 Transport Phenomena. John Wiley & Sons.
Brandeis, G. & Jaupart, C. 1986 On the interaction between convection and crystallization in cooling magma chambers. Earth Planet. Sci. Lett. 77, 345–361.Google Scholar
Brandeis, G., Jaupart, C. & Allègre, C. J. 1984 Nucleation, crystal growth and the thermal regime of cooling magmas. J. Geophys. Res. 89, 10161–10177.Google Scholar
Bruce, P. M. & Huppert, H. E. 1989 Thermal control of basaltic fissure eruptions. Nature 342, 665–667.Google Scholar
Campbell, I. H. 1977 A study of macro-rhythmic layering and cumulate processes in the Jimberlana intrusion, Western Australia. I. The upper layered series. J. Petrol. 18, 183–215.Google Scholar
Campbell, I. H. 1985 The difference between oceanic and continental tholeiites: a fluid dynamic explanation. Contrib. Mineral. Petrol. 91, 37–43.Google Scholar
Campbell, I. H. 1986 A fluid dynamic model for potholes of the Merensky Reef. Econ. Geol. 81, 1118–1125.Google Scholar
Campbell, I. H. & Turner, J. S. 1987 A laboratory investigation of assimilation at the top of a basaltic magma chamber. J. Geol. 95, 155–172.Google Scholar
Carslaw, H. S. & Jaeger, J. C. 1986 Conduction of Heat in Solids. Oxford University Press.
Carte, A. E. 1961 Air bubbles in ice. Proc. Phys. Soc. 77, 757–768.Google Scholar
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops and Particles. Academic Press.
Cox, K. G. & Mitchell, C. 1988 Importance of crystal settling in the differentiation of Deccan Traps basaltic magmas. Nature 333, 447–449.Google Scholar
Daly, R. A. 1933 Igneous Rocks and the Depths of the Earth. Hafner.
Davaille, A. & Jaupart, C. 1993 Transient high Rayleigh number thermal convection with large viscosity variations. J. Fluid Mech. 253, 141–166.Google Scholar
DePaolo, D. J. 1985 Isotopic studies of processes in mafic magma chambers: I. The Kiglapait Intrusion, Labrador. J. Petrol. 26, 925–951.Google Scholar
Fang, D. & Hellawell, A. 1988 The surface morphology of crystals melting under solutions of different densities. J. Cryst. Growth 92, 364–370.Google Scholar
Fink, J. H. & Griffiths, R. W. 1990 Radial spreading of viscous-gravity currents with solidifying crust. J. Fluid Mech. 221, 485–509.Google Scholar
Huppert, H. E. 1989 Phase changes following the initiation of a hot turbulent flow over a cold solid surface. J. Fluid Mech. 198, 293–320.Google Scholar
Huppert, H. E. & Sparks, R. S. J. 1985 Cooling and contamination of mafic and ultramafic magmas during ascent through continental crust. Earth Planet. Sci. Lett. 74, 371–386.Google Scholar
Huppert, H. E. & Sparks, R. S. J. 1988a The fluid dynamics of crustal melting by injection of basaltic sills. Phil. Trans. R. Soc.: Edinb. Earth Sci. 79, 237–243.Google Scholar
Huppert, H. E. & Sparks, R. S. J. 1988b Melting the roof of a chamber containing a hot, turbulently convecting fluid. J. Fluid Mech. 188, 107–131.Google Scholar
Huppert, H. E. & Sparks, R. S. J. 1988c The generation of granitic magmas by intrusion of basalt into continental crust. J. Petrol. 29, 599–624.Google Scholar
Irvine, T. N. 1970 Heat transfer during solidification of layered intrusions. I. Sheets and sills. Can. J. Earth. Sci. 7, 1031–1061.Google Scholar
Jafarpur, K. & Yovanovich, M. M. 1992 Laminar free convective heat transfer from isothermal spheres: a new analytical method. Intl J. Heat Mass Transfer 35, 2195–2201.Google Scholar
Katsaros, K. B., Liu, W. T., Businger, J. A. & Tillman, J. E. 1977 Heat transport and thermal structure in the interfacial boundary layer measured in an open tank of water in turbulent free convection. J. Fluid Mech. 83, 311–335.Google Scholar
Kerr, R. C. 1994 Dissolving driven by vigorous compositional convection. J. Fluid Mech. 280, 287–302.Google Scholar
Kerr, R. C. & Lister, J. R. 1991 The effects of shape on crystal settling and on the rheology of magmas. J. Geol. 99, 457–467.Google Scholar
Kerr, R. C. & Lister, J. R. 1992 Further results for convection driven by the differential sedimentation of particles. J. Fluid Mech. 243, 227–245.Google Scholar
Kuo, L.-C. & Kirkpatrick, R. J. 1985 Kinetics of crystal dissolution in the system diopside-forsterite-silica. Am. J. Sci. 285, 51–90.Google Scholar
Lesher, C. E. 1990 Decoupling of chemical and isotopic exchange during magma mixing. Nature 344, 235–237.Google Scholar
Lister, J. R. 1990 Buoyancy-driven fluid fracture: similarity solutions for the horizontal and vertical propagation of fluid-filled cracks. J. Fluid Mech. 217, 213–239.Google Scholar
Lister, J. R. & Kerr, R. C. 1989 The effect of geometry on the gravitational instability of a buoyant region of viscous fluid. J. Fluid Mech. 202, 577–594.Google Scholar
Lister, J. R. & Kerr, R. C. 1991 Fluid-mechanical models of crack propagation and the application to magma transport in dykes. J. Geophys. Res. 96, 10049–10077.Google Scholar
Martin, D. & Campbell, I. H. 1988 Laboratory modeling of convection in magma chambers: crystallization against sloping floors. J. Geophys. Res. 93, 7974–7988.Google Scholar
Martin, D. & Nokes, R. 1988 Crystal settling in a vigorously convecting magma chamber. Nature 332, 534–536.Google Scholar
Martin, D. & Nokes, R. 1989 A fluid-dynamical study of crystal settling in convecting magmas. J. Petrol. 30, 1471–1500.Google Scholar
Morse, S. A. 1969 Geology of the Kiglapait Intrusion, Labrador. Mem. Geol. Soc. Am. 112.Google Scholar
Nilson, R. H., McBirney, A. R. & Baker, B. H. 1985 Liquid fractionation. Part II: Fluid dynamics and quantitative implications for magmatic systems. J. Volcanol. Geotherm. Res. 24, 25–54.Google Scholar
Odé, H. 1966 Gravitational instability of a multi-layered system. PhD thesis, University of Utrecht.
Oxtoby, D. W. 1990 New perspectives on freezing and melting. Nature 347, 725–730.Google Scholar
Philpotts, A. R. & Asher, P. M. 1993 Wallrock melting and reaction effects along the Higganum Diabase Dyke in Connecticut: contamination of a continental flood basalt feeder. J. Petrol. 34, 1029–1058.Google Scholar
Ryan, M. P. 1987 Neutral buoyancy and the mechanical evolution of magmatic systems. In Magmatic Processes: Physicochemical Principles, Spec. Publ. 1 (ed. B. O. Mysen), pp. 259–287. The Geochemical Society, University Park, PA.
Sparks, R. S. J. & Huppert, H. E. 1984 Density changes during fractional crystallization of basaltic magmas: fluid dynamic implications. Contrib. Mineral. Petrol. 85, 300–309.Google Scholar
Sparks, R. S. J. & Marshall, L. A. 1986 Thermal and mechanical constraints on mixing between mafic and silicic magmas. J. Volcanol. Geotherm. Res. 29, 99–124.Google Scholar
Stewart, B. W. & DePaolo, D. J. 1990 Isotopic studies of processes in mafic magma chambers: II. The Skaergaard Intrusion, East Greenland. Contrib. Mineral. Petrol. 104, 125–141.Google Scholar
Stewart, B. W. & DePaolo, D. J. 1992 Diffusive isotopic contamination of mafic magma by coexisting silicic liquid in the Muskox Intrusion. Science 255, 708–711.Google Scholar
Tritton, D. J. 1977 Physical Fluid Dynamics. Van Nostrand Reinhold.
Turner, J. S. 1979 Buoyancy Effects in Fluids. Cambridge University Press.
Turner, J. S. & Campbell, I. H. 1986 Convection and mixing in magma chambers. Earth Sci. Rev. 23, 255–352.Google Scholar
Wager, L. R. & Brown, G. M. 1968 Layered Igneous Rocks. Edinburgh: Oliver & Boyd.
Washburn, E. W. (ed.) 1926 International Critical Tables of Numerical data: Physics, Chemistry and Technology. National Academic Press.
Weast, R. C. (ed.) 1989 CRC Handbook of Chemistry and Physics. CRC Press.
Wilson, J. R. & Larsen, S. B. 1985 Two-dimensional study of a layered intrusion: the Hyllingen Series, Norway. Geol. Mag. 122, 97–124.Google Scholar
Woods, A. W. 1991 Fluid mixing during melting. Phys. Fluids A 3, 1393–1404.Google Scholar
Woods, A. W. 1992 Melting and dissolving. J. Fluid Mech. 239, 429–448.Google Scholar