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Modelling gravity currents without an energy closure.

Konopliv, N. A. and Llewellyn-Smith, S. G. and McElwaine, J. N. and Meiburg, E. (2016) 'Modelling gravity currents without an energy closure.', Journal of fluid mechanics., 789 . pp. 806-829.

Abstract

We extend the vorticity-based modelling approach of Borden & Meiburg (Phys. Fluids, vol. 25 (10), 2013, 101301) to non-Boussinesq gravity currents and derive an analytical expression for the Froude number without the need for an energy closure or any assumptions about the pressure. The Froude-number expression we obtain reduces to the correct form in the Boussinesq limit and agrees closely with simulation data. Via detailed comparisons with simulation results, we furthermore assess the validity of three key assumptions underlying both our as well as earlier models: (i) steady-state flow in the moving reference frame; (ii) inviscid flow; and (iii) horizontal flow sufficiently far in front of and behind the current. The current approach does not require an assumption of zero velocity in the current.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1017/jfm.2015.755
Publisher statement:This article has been published in a revised form in Journal of Fluid Mechanics [http://doi.org/10.1017/jfm.2015.755]. This version is published under a Creative Commons CC-BY-NC-ND. No commercial re-distribution or re-use allowed. Derivative works cannot be distributed. © 2016 Cambridge University Press
Date accepted:20 December 2015
Date deposited:30 July 2019
Date of first online publication:26 January 2016
Date first made open access:30 July 2019

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