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Viscous lock-exchange in rectangular channels

Viscous lock-exchange in rectangular channels

Authors :
Jerome Martin
Laurent Talon
N. Rakotomalala
Dominique Salin
Fluides, automatique, systèmes thermiques (FAST)
Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)
Source :
Journal of Fluid Mechanics, Journal of Fluid Mechanics, Cambridge University Press (CUP), 2011, 673, pp.132-146. ⟨10.1017/S0022112010006208⟩
Publication Year :
2011
Publisher :
HAL CCSD, 2011.

Abstract

In a viscous lock-exchange gravity current, which describes the reciprocal exchange of two fluids of different densities in a horizontal channel, the front between two Newtonian fluids spreads as the square root of time. The resulting diffusion coefficient reflects the competition between the buoyancy driving effect and the viscous damping, and depends on the geometry of the channel. This lock-exchange diffusion coefficient has already been computed for a porous medium, a 2D Stokes flow between two parallel horizontal boundaries separated by a vertical height, H, and, recently, for a cylindrical tube. In the present paper, we calculate it, analytically, for a rectangular channel (horizontal thickness b, vertical height, H) of any aspect ratio (H/b) and compare our results with experiments in horizontal rectangular channels for a wide range of aspect ratios (1/10-10). We also discuss the 2D Stokes-Darcy model for flows in Hele-Shaw cells and show that it leads to a rather good approximation, when an appropriate Brinkman correction is used.<br />Comment: 16 pages,7 figures

Details

Language :
English
ISSN :
00221120 and 14697645
Database :
OpenAIRE
Journal :
Journal of Fluid Mechanics, Journal of Fluid Mechanics, Cambridge University Press (CUP), 2011, 673, pp.132-146. ⟨10.1017/S0022112010006208⟩
Accession number :
edsair.doi.dedup.....c08518825a8b3595dfc9c6738862e70e
Full Text :
https://doi.org/10.1017/S0022112010006208⟩