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Conformally mapped viscous gravity current

Robinson, TO; Eames, I; (2017) Conformally mapped viscous gravity current. Journal of Engineering Mathematics , 103 (1) pp. 77-86. 10.1007/s10665-016-9861-y. Green open access

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Abstract

We show how the conformal mapping technique can be applied to analyse specific problems in the context of viscous gravity current theory. We examine the edge of steady thin planar viscous gravity currents in the presence of complex external low Reynolds flows. In addition to the uniform ambient flow we look at the case of viscous gravity currents spreading in positively strained flows and around cylindrical bodies. These external flows exert shear stress on the gravity current, which drives it in the streamwise direction. The idealised conditions are re-created in the laboratory using a Hele–Shaw cell with a point source on the bottom plate where the saline is introduced into the flow. The mapped laboratory results are compared to a known similarity solution and the agreement is good. We conclude by identifying a broad class of viscous gravity current problems where this technique may be applied.

Type: Article
Title: Conformally mapped viscous gravity current
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s10665-016-9861-y
Publisher version: http://dx.doi.org/10.1007/s10665-016-9861-y
Language: English
Additional information: © The Author(s) 2016. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Keywords: Conformal mapping; Viscous gravity current; Similarity solution; Hele-Shaw cell; Potential flow
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Civil, Environ and Geomatic Eng
URI: https://discovery.ucl.ac.uk/id/eprint/1508353
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