Shallow-water models for gravity currents/intrusions in double-continuous-stratification systems

High-Reynolds-number Boussinesq gravity currents and intrusions systems, in which both the ambient and the propagating ``current'' are linearly stratified, are considered. The main focus is on a current of fixed volume released from a lock; the height ratio of the fluids $H$, and the stratification parameter of the ambient $S$, are quite general. It is shown that a one-layer shallow-water model, in which the internal stratification enters as a new dimensionless parameter, $\sigma \in [0,1]$, provides insightful results. In general, the speed of propagation decreases when the internal stratification becomes more pronounced ($\sigma$ increases), and in some cases the current runs out of driving force. This model is a versatile and robust self-contained prediction tool, which can be applied to both rectangular and axisymmetric geometries, and to quite general continuously- stratified systems.