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The propagation of high-Reynolds-number non-Boussinesq gravity currents in axisymmetric geometry

Published online by Cambridge University Press:  24 December 2009

MARIUS UNGARISH
MARIUS UNGARISH*
Affiliation:
Department of Computer Science, Technion, Haifa 32000, Israel
*
†Email address for correspondence: unga@cs.technion.ac.il
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Abstract

We consider the propagation of a non-Boussinesq gravity current in an axisymmetric configuration (full cylinder or wedge). The current of density ρc is released from rest from a lock of radius r0 and height h0 into an ambient fluid of density ρa in a container of height H. When the Reynolds number is large, the resulting flow is governed by the parameters ρc/ρa and H* = H/h0. We show that the one-layer shallow-water model, carefully combined with a Benjamin-type front condition, provides a versatile formulation for the thickness and speed of the current, without any adjustable constants. The results cover in a continuous manner the range of light ρc/ρa ≪ 1, Boussinesq ρc/ρa ≈ 1, and heavy ρc/ρa ≫ 1 currents in a fairly wide range of depth ratio, H*. We obtain finite-difference solutions for the propagation and show that a self-similar behaviour develops for large times. This reveals the main features, in particular: (a) The heavy current propagates faster and its front is thinner than that for the light counterpart; (b) For large time, t, both the heavy and light currents spread like t1/2, but the thickness profiles display significant differences; (c) The energy-constrained propagation with the thickness of half-ambient-depth (when H* is close to 1) is a very limited occurrence, in contrast to the rectangular geometry counterpart in which this effect plays a major role. The predictions of the simple model are supported by some axisymmetric Navier–Stokes finite-difference simulations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 643 , 25 January 2010 , pp. 267 - 277
Copyright
Copyright © Cambridge University Press 2009

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References

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