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Particulate gravity currents along V-shaped valleys

Published online by Cambridge University Press:  17 July 2009

JOE J. MONAGHAN ,
CATHERINE MÉRIEUX ,
HERBERT E. HUPPERT  and
JOHN MANSOUR
JOE J. MONAGHAN*
Affiliation:
School of Mathematical Sciences, Monash University, Vic 3800, Australia
CATHERINE MÉRIEUX
Affiliation:
School of Mathematical Sciences, Monash University, Vic 3800, Australia
HERBERT E. HUPPERT
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CMS, Wilberforce Road, Cambridge CB3 0WA, UK
JOHN MANSOUR
Affiliation:
School of Mathematical Sciences, Monash University, Vic 3800, Australia
*
†Email address for correspondence: joe.monaghan@sci.monash.edu.au
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Abstract

This paper extends previous studies of saline gravity currents at high Reynolds number flowing along a tank with a V-shaped valley. We use experiments and a box model to determine the primary features of the flow. The particulate gravity currents were initiated by releasing a fixed volume of fluid consisting of pure water mixed with silicon carbide particles from a lock at one end of the tank. The resulting motion and deposit pattern differ significantly from those for the propagation of a particulate gravity current along a flat-bottomed tank. The front of the current, seen from above, is approximately parabolic (with axis parallel to the flow direction) in contrast to the current in a flat-bottomed tank where it is nearly a straight line perpendicular to the flow. This feature mimics the results for pure saline currents. When seen in profile the currents do not have a clearly defined raised head, which is a feature of the flat-bottomed currents. The mass deposited per unit area varies nearly monotonically with respect to distance down the tank, again in contrast to the case of the flat-bottomed tank. The exceptions to this are the two experiments which have the highest ratio of lock height to length. The mass deposited per unit area across the V-shaped valley is much larger in the central part of the valley than it is on the flanks for any position along the valley. We find that the results can be described with remarkable accuracy by a box model using a generalization of the equation for sedimentation from a turbulent medium due to Martin and Nokes. Our results further show that the factor used in the deposition rate equation which is commonly assumed to be 1 should be smaller, typically 0.7.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 631 , 25 July 2009 , pp. 419 - 440
Copyright
Copyright © Cambridge University Press 2009

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