# Gravity currents with double stratification: a numerical and analytical investigation

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## Abstract

We consider high-Reynolds-number Boussinesq gravity current and intrusion 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 rectangular lock; the height ratio of the fluids \(H\), the stratification parameter of the ambient \(S\), and the internal stratification parameter of the current, \(\sigma \), are quite general. We perform two-dimensional Navier–Stokes simulation and compare the results with those of a previously-published one-layer shallow-water model. The results provide insights into the behavior of the system and enhance the confidence in the approximate model while also revealing its limitations. The qualitative predictions of the model are confirmed, in particular: (1) there is an initial “slumping” stage of propagation with constant speed \(u_N\), after which \(u_N\) decays with time; (2) for fixed \(H\) and \(S\), the increase of \(\sigma \) causes a slower propagation of the current; (3) for some combinations of the parameters \(H,S, \sigma \) the fluid released from the lock lacks initially (or runs out quickly of) buoyancy “driving power” in the horizontal direction, and does not propagate like a gravity current. There is also a fair quantitative agreement between the predictions of the model and the simulations concerning the spread of the current.

## Keywords

Gravity current Intrusion Stratified Shallow water Computational fluid dynamics## Notes

### Acknowledgments

MU acknowledges the hospitality of the Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan, where a part of this research was conducted.

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