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Melting the roof of a chamber containing a hot, turbulently convecting fluid

Published online by Cambridge University Press:  21 April 2006

Herbert E. Huppert  and
R. Stephen J. Sparks
Herbert E. Huppert
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
R. Stephen J. Sparks
Affiliation:
Department of Earth Sciences, University of Cambridge, Downing Site, Cambridge CB2 3EQ, UK
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Abstract

The input of a hot, turbulently convecting fluid to fill a chamber can result in the roof of the chamber melting. The rate of melting of the roof is here analysed experimentally and theoretically. Three separate cases are considered. The melt may be heavier than the fluid and initially sink through it. The intense motion in the fluid then mixes the falling melt in with it. Alternatively, the melt may be less dense than the fluid and form a separate layer between the roof and the fluid. This melt layer can itself be in quite vigorous convective motion. An intermediate case is shown to be possible, wherein the melt is initially denser than the fluid, and sinks. As its temperature increases and its density decreases, it becomes less dense than the surrounding fluid and rises. Experimental simulations of each of these three cases are described. The experiments employ a roof of either wax or ice which is melted by the aqueous salt solution beneath it. The second case, that of a light melt, has important geological applications. It describes the melting of the continental crust by the emplacement of a hot, relatively dense input of fluid basaltic rock. Both the basaltic layer and the resultant granitic melt layer crystallize and increase their viscosities as they cool. These effects are incorporated into the analysis and the rate of melting and the temperatures of the two layers are calculated as functions of time. The process is exemplified by the formation of the Cerro Galan volcanic system in Northwestern Argentina over the last 5 million years. An Appendix analyses the thermal history of the fluid in a chamber that does not melt and compares the results obtained with those derived previously.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 188 , March 1988 , pp. 107 - 131
Copyright
© 1988 Cambridge University Press

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