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

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, σ ∈ [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.

Modeling Gravity and Turbidity Currents: Computational Approaches and Challenges

“…The effects of density stratification may be important not just in the ambient but also within the current itself. Again, box models and shallow water models for such stratified currents were developed by Zemach and Ungarish [120]. This importance of stratification within the current was explored in depth in the computational "turbidity current with a roof" model of Balachandar and colleagues [121].…”