On gravity currents confined by porous boundaries in containers of general cross-sections

Environmental Fluid Mechanics - We consider an inertial (large Reynolds number) gravity current (GC) released from a lock of length $$x_0$$ and height $$h_0$$ into an ambient fluid of height...     

A steady-state model for asymmetric intrusive gravity currents in a linearly stratified ambient

The behavior of the steady intrusive gravity current of thickness h and density ρ _c which propagates with speed U at the neutral buoyancy level of a long horizontal channel of height H into a stratified ambient fluid whose density increases linearly from ρ _o to ρ _b is investigated. The intrusive and the ambient fluids are assumed to be asymmetric with respect to the neutral-buoyancy level. The Boussinesq, high-Reynolds number two-dimensional configuration is considered. Long’s model combined with the flow-force balance over the width of the channel and the pressure balances over a density current are used to obtain the desired results. It is shown that the intrusion velocity decreases with decreasing the asymmetry of the system and approaches its minimum for the symmetric configuration (however, the difference of speed between asymmetric and symmetric configurations shows no significant differences).     

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

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.