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Modelling gravity currents without an energy closure

Konopliv, N.A.; Llewellyn-Smith, S.G.; McElwaine, J.N.; Meiburg, E.

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Authors

N.A. Konopliv

S.G. Llewellyn-Smith

E. Meiburg



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.

Citation

Konopliv, N., Llewellyn-Smith, S., McElwaine, J., & Meiburg, E. (2016). Modelling gravity currents without an energy closure. Journal of Fluid Mechanics, 789, 806-829. https://doi.org/10.1017/jfm.2015.755

Journal Article Type Article
Acceptance Date Dec 20, 2015
Online Publication Date Jan 26, 2016
Publication Date Jan 26, 2016
Deposit Date Oct 21, 2016
Publicly Available Date Jul 30, 2019
Journal Journal of Fluid Mechanics
Print ISSN 0022-1120
Electronic ISSN 1469-7645
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 789
Pages 806-829
DOI https://doi.org/10.1017/jfm.2015.755

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Copyright 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




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