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Environmental Fluid Mechanics

, Volume 12, Issue 4, pp 347–359 | Cite as

The flow of high-Reynolds axisymmetric gravity currents of a stratified fluid into a stratified ambient: shallow-water and box model solutions

  • T. Zemach
  • M. Ungarish
Original Article

Abstract

We consider the axisymmetric flow (in a full cylinder or a wedge) of high-Reynolds-number Boussinesq gravity currents and intrusions systems in which both the ambient and the propagating “current” are linearly stratified. The main focus is on a current of fixed volume released from a cylinder lock; the height ratio of the fluids H, and the stratification parameter of the ambient S, are quite general. We develop a one-layer shallow-water model. The internal stratification enters as a new dimensionless parameter, \({\sigma \in [0, 1]}\). In general, the time-dependent motion is obtained by standard finite-difference solutions; a self-similar analytical solution exists for S = 0. We show that, in general, the speed of propagation decreases when the internal stratification becomes more pronounced (σ increases). We also developed a box-model approximation, and show that the resulting radius of propagation is in good agreement with the more rigorous shallow-water prediction.

Keywords

Gravity current Axisymmetric flow Stratified Shallow-water 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Computer ScienceTel-Hai CollegeTel-HaiIsrael
  2. 2.Department of Computer ScienceTechnionHaifaIsrael

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