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The effects of temperature-dependent viscosity on flow in a cooled channel with application to basaltic fissure eruptions

Published online by Cambridge University Press:  26 April 2006

Jonathan J. Wylie  and
John R. Lister
Jonathan J. Wylie
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW, UK
John R. Lister
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW, UK
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Abstract

A theoretical description is given of pressure-driven viscous flow of an initially hot fluid through a planar channel with cold walls. The viscosity of the fluid is assumed to be a function only of its temperature. If the viscosity variations caused by the cooling of the fluid are sufficiently large then the relationship between the pressure drop and the flow rate is non-monotonic and there can be more than one steady flow for a given pressure drop. The linear stability of steady flows to two-dimensional and three-dimensional disturbances is calculated. The region of instability to two-dimensional disturbances corresponds exactly to those flows in which an increase in flow rate leads to a decrease in pressure drop. At higher viscosity contrasts some flows are most unstable to three-dimensional (fingering) instabilities analogous, but not identical, to Saffman-Taylor fingering. A cross-channel-averaged model is derived and used to investigate the finite-amplitude evolution.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 305 , 25 December 1995 , pp. 239 - 261
Copyright
© 1995 Cambridge University Press

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