The relaxation time for viscous and porous gravity currents following a change in flux

Ball, T. V. and Huppert, H. E. and Lister, JR and Neufeld, J. A. (2017) The relaxation time for viscous and porous gravity currents following a change in flux. Journal of Fluid Mechanics, 821. pp. 330-342. ISSN 0022-1120, ESSN: 1469-7645 DOI https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/relaxation-time-for-viscous-and-porous-gravity-currents-following-a-change-in-flux/1000433B94ABAC5BA41D6ABD106A68C2

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Abstract

© 2017 Cambridge University Press. The equilibration time in response to a change in flux from Q to Λ Q after an injection period T applied to either a low-Reynolds-number gravity current or one propagating through a porous medium, in both axisymmetric and one-dimensional geometries, is shown to be of the form τ =Tf (Λ), independent of all the remaining physical parameters. Numerical solutions are used to investigate f(Λ) for each of these situations and compare very well with experimental results in the case of an axisymmetric current propagating over a rigid horizontal boundary. Analysis of the relaxation towards self-similarity provides an illuminating connection between the excess (deficit) volume from early times and an asymptotically equivalent shift in time origin, and hence a good quantitative estimate of τ. The case Λ = 0 of equilibration after ceasing injection at time T is a singular limit. Extensions to high-Reynolds-number currents and to the case of a constant-volume release followed by constant-flux injection are discussed briefly.

Item Type: Article
Uncontrolled Keywords: 2017AREP; IA72
Subjects: 02 - Geodynamics, Geophysics and Tectonics
Divisions: 02 - Geodynamics, Geophysics and Tectonics
12 - PhD
Journal or Publication Title: Journal of Fluid Mechanics
Volume: 821
Page Range: pp. 330-342
Identification Number: https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/relaxation-time-for-viscous-and-porous-gravity-currents-following-a-change-in-flux/1000433B94ABAC5BA41D6ABD106A68C2
Depositing User: Sarah Humbert
Date Deposited: 30 Apr 2018 10:59
Last Modified: 03 Dec 2018 12:08
URI: http://eprints.esc.cam.ac.uk/id/eprint/4258

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