Mathematics – Logic
Scientific paper
Aug 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986esrv...23..255t&link_type=abstract
Earth Science Reviews, Volume 23, Issue 4, p. 255-352.
Mathematics
Logic
46
Scientific paper
This paper reviews advances made during the last seven years in the application of fluid dynamics to problems of igneous petrology, with emphasis on the laboratory work with which the authors have been particularly involved. Attention is focused on processes in magma chambers which produce diversity in igneous rocks, such as fractional crystallization, assimilation and magma mixing. Chamber geometry, and variations in the density and viscosity of the magma within it, are shown to play a major role in determining the dynamical behaviour and the composition of the erupted or solidified products. Various convective processes are first reviewed, and in particular the phenomenon of double-diffusive convection. Two types of double-diffusive interfaces between layers of different composition and temperature are likely to occur in magma chambers. A diffusive interface forms when a layer of hot dense magma is overlain by cooler less dense magma. Heat is transported between the layers faster than composition, driving convection in both layers and maintaining a sharp interface between them. If a layer of hot slightly less dense magma overlies a layer of cooler, denser but compositionally lighter magma, a finger interface forms between them, and compositional differences are transported downwards faster than heat (when each is expressed in terms of the corresponding density changes). Processes leading to the establishment of density, compositional and thermal gradients or steps during the filling of a magma chamber are considered next. The stratification produced, and the extent of mixing between the inflowing and resident magmas, are shown to depend on the flow rate and on the relation between the densities and viscosities of the two components. Slow dense inputs of magma may mix very little with resident magma of comparable viscosity as they spread across the floor of the chamber. A similar pulse injected with high upward momentum forms a turbulent “fountain”, which is a very efficient mechanism for magma mixing, as is a turbulent plume of less dense magma rising through the host magma to the top of the chamber. The form of convection in the filled magma chamber is controlled by the shape and size of the chamber, the viscosity of the magma (through the Rayleigh number which is usually high in the early stages of cooling), and by processes at the boundary which produce lighter or denser fluid than that in the interior of the chamber. Compositional convection due to fluid released by crystallization often dominates over thermal convection. If crystallization at the bottom of a funnel-shaped chamber releases a light magma, this convects away from the floor, causing turbulent convection which tends to homogenize the overlying melt. If the magma released is dense, it flows down the sloping floor and stratifies the magma at the base of the chamber. Convection driven by crystallization in an inverted funnel has the reverse effect, e.g. dense fluid released at the sloping roof now has a homogenizing influence. Assimilation of wall rocks can also lead to identical dynamical effects and thus to zoning in magma chambers. Melting of a light roof, for instance, can produce a layer of cool felsic magma overlying the hotter more basic magma in the lower part of the chamber, with a diffusive interface between them. Assimilation has also been discussed for other geometries: assimilation of the walls of dykes, sills and lava flows can occur when the flow is hot and turbulent, whereas if the flow is laminar the magma will chill against the adjacent rocks and protect them from assimilation. When the magma in a chamber is layered, crystallization can cause the composition and density to change in several ways which may lead to mixing. A crystallizing lower layer of hot dense magma can evolve till it has the density of the magma above it, causing sudden overturning and thorough mixing. On the other hand, with a much more viscous layer above, light fluid is released continuously during crystallization and rises to the top of the chamber with little mixing. Overturning of a gas-rich mafic lower layer into a cooler silicic layer can cause a sudden quenching, with the rapid release of gas which could trigger an explosive eruption. Mixing can also occur during eruption, as two layers are drawn up simultaneously from a stratified chamber when a critical flow velocity is exceeded, and they then mix in the outlet vent. Laboratory experiments suggest, however, that magma mixing is inhibited by large viscosity differences, both during the filling and emptying of a magma chamber. Scaling these results to magmas indicates that a basaltic magma can flow into the bottom of a chamber containing rhyolite with little or no mixing between them, and that these two magma types can also flow out through the same exit vent with limited mixing. Each of the phenomena discussed in this review has been studied, at least in a qualitative way, using laboratory experiments to identify and understand a significant physical process occurring in magma chambers. The field of geological fluid mechanics and its application to these problems is still very new, and further advances seem assured as new phenomena are identified and more detailed and quantitative analogue experiments are developed to study them.
Campbell Ian H.
Turner Stewart J.
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