Modelling intrusions through quiescent and moving ambients

Johnson, Christopher G. and Hogg, Andrew J. and Huppert, Herbert E. and Sparks, R. Stephen J. and Phillips, Jeremy C. and Slim, Anja C. and Woodhouse, Mark J. (2015) Modelling intrusions through quiescent and moving ambients. Journal of Fluid Mechanics, 771. pp. 370-406. ISSN 0022-1120, ESSN: 1469-7645 DOI 10.1017/jfm.2015.180

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Abstract

Volcanic eruptions commonly produce buoyant ash-laden plumes that rise through the stratified atmosphere. On reaching their level of neutral buoyancy, these plumes cease rising and transition to horizontally spreading intrusions. Such intrusions occur widely in density-stratified fluid environments, and in this paper we develop a shallow-layer model that governs their motion. We couple this dynamical model to a model for particle transport and sedimentation, to predict both the time-dependent distribution of ash within volcanic intrusions and the flux of ash that falls towards the ground. In an otherwise quiescent atmosphere, the intrusions spread axisymmetrically. We find that the buoyancy-inertial scalings previously identified for continuously supplied axisymmetric intrusions are not realised by solutions of the governing equations. By calculating asymptotic solutions to our model we show that the flow is not self-similar, but is instead time-dependent only in a narrow region at the front of the intrusion. This non-self-similar behaviour results in the radius of the intrusion growing with time \textrm3/4$ , rather than \textrm2/3$ as suggested previously. We also identify a transition to drag-dominated flow, which is described by a similarity solution with radial growth now proportional to \textrm5/9$ . In the presence of an ambient wind, intrusions are not axisymmetric. Instead, they are predominantly advected downstream, while at the same time spreading laterally and thinning vertically due to persistent buoyancy forces. We show that close to the source, this lateral spreading is in a buoyancy-inertial regime, whereas far downwind, the horizontal buoyancy forces that drive the spreading are balanced by drag. Our results emphasise the important role of buoyancy-driven spreading, even at large distances from the source, in the formation of the flowing thin horizontally extensive layers of ash that form in the atmosphere as a result of volcanic eruptions.

Item Type: Article
Uncontrolled Keywords: 2015AREP; IA768
Subjects: 99 - Other
Divisions: 02 - Geodynamics, Geophysics and Tectonics
Journal or Publication Title: Journal of Fluid Mechanics
Volume: 771
Page Range: pp. 370-406
Identification Number: 10.1017/jfm.2015.180
Depositing User: Sarah Humbert
Date Deposited: 21 Jul 2016 17:33
Last Modified: 21 Jul 2016 17:33
URI: http://eprints.esc.cam.ac.uk/id/eprint/3566

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