Numerical Simulation of Gravity Current Descending a Slope into a Linearly Stratified Environment
Publication: Journal of Hydraulic Engineering
Volume 140, Issue 12
Abstract
The accurate prediction of the dilution and motion of the produced denser water (e.g., discharge of concentrated brine generated during solution mining and desalination) is of importance for environmental protection. Boundary conditions and ambient stratification can significantly affect the dilution and motion of gravity currents. In this study, a multiphase model was applied to simulate the gravity current descending a slope into a linearly stratified ambient. The turbulence model was used to better simulate the near-bed motion. The mathematical model, the initial and boundary conditions, and the details of the numerical scheme are described here. The time-dependent evolution of the gravity current, the flow thickness, and the velocity and density field were simulated for a range of flow parameters. Simulations show that the Kelvin–Helmholtz (K-H) billows are generated at the top of the trailing fluid by the interfacial velocity shear. The K-H instability becomes weaker with the slope distance from the source because of the decrease in interfacial velocity shear along the slope. The ambient stratification restricts and decreases the current head velocity as it descends the slope, which differs from the situation in the homogenous ambient while the head velocity remains in an approximately steady state. Motion of the descending flow into the stratified ambient has two stages: initial acceleration and deceleration at a later stage based on the balance of inertial, buoyancy, and friction forces. When the descending current approaches the initial neutral position at a later stage, it separates from the slope and spreads horizontally into the environment. The simulated results, such as vertical velocity and density profiles and front positions, agree well with the measurements, indicating that the mathematical model can be successfully applied to simulate the effect of the boundary conditions and ambient stratification on the dilution and propagation of gravity currents.
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Acknowledgments
The research reported in this paper is financially supported by the UK Engineering and Physical Sciences Research Council (EPSRC: EP/G066264/1). The constructive and insightful comments and suggestions made by three anonymous reviewers and the associate editor have significantly improved the quality of the final paper.
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Published In
Journal of Hydraulic Engineering
Volume 140 • Issue 12 • December 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Oct 4, 2013
Accepted: Jul 24, 2014
Published online: Sep 3, 2014
Published in print: Dec 1, 2014
Discussion open until: Feb 3, 2015
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