The flow of high-Reynolds axisymmetric gravity currents of a stratified fluid into a stratified ambient: shallow-water and box model solutions |
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Authors: | T. Zemach M. Ungarish |
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Affiliation: | 1. Department of Computer Science, Tel-Hai College, Tel-Hai, Israel 2. Department of Computer Science, Technion, Haifa, 32000, Israel
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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. |
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