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A numerical investigation of horizontal viscous gravity currents

Hallez, Yannick and Magnaudet, Jacques A numerical investigation of horizontal viscous gravity currents. (2009) Journal of Fluid Mechanics, vol. 630 . pp. 71-91. ISSN 0022-1120

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Official URL: http://dx.doi.org/10.1017/S0022112009006454

Abstract

We study numerically the viscous phase of horizontal gravity currents of immiscible fluids in the lock-exchange configuration. A numerical technique capable of dealing with stiff density gradients is used, allowing us to mimic high-Schmidt-number situations similar to those encountered in most laboratory experiments. Plane two-dimensional computations with no-slip boundary conditions are run so as to compare numerical predictions with the ‘short reservoir’ solution of Huppert (J. Fluid Mech., vol. 121, 1982, pp. 43–58), which predicts the front position lf to evolve as t1/5, and the ‘long reservoir’ solution of Gratton & Minotti (J. Fluid Mech., vol. 210, 1990, pp. 155–182) which predicts a diffusive evolution of the distance travelled by the front xf ~ t1/2. In line with dimensional arguments, computations indicate that the self-similar power law governing the front position is selected by the flow Reynolds number and the initial volume of the released heavy fluid. We derive and validate a criterion predicting which type of viscous regime immediately succeeds the slumping phase. The computations also reveal that, under certain conditions, two different viscous regimes may appear successively during the life of a given current. Effects of sidewalls are examined through three-dimensional computations and are found to affect the transition time between the slumping phase and the viscous regime. In the various situations we consider, we make use of a force balance to estimate the transition time at which the viscous regime sets in and show that the corresponding prediction compares well with the computational results.

Item Type:Article
Additional Information:Thanks to Cambridge University Press. The definitive version is available at http://journals.cambridge.org/action/login The original PDF of the article can be found at Journal of Fluid Mechanics : http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=5876652
Audience (journal):International peer-reviewed journal
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Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT
Université de Toulouse > Université Paul Sabatier-Toulouse III - UPS
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Deposited By:Yannick Hallez

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