Numerical simulation of gravity current descending a slope into a linearly stratified environment.

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 is applied to simulate the gravity current descending a slope into a linearly stratified ambient. The k- turbulence model is used to better simulate the near bed motion. The mathematical model, initial and boundary conditions and the details of the numerical scheme are described. The time-dependent evolution of the gravity current, the flow thickness and the velocity and density field are simulated for a range of flow parameters. Simulations show that the Kelvin–Helmholtz billows are generated at the top of trailing fluid by the interfacial velocity shear. The K-H type instability becomes weaker with the slope distance from the source due to the decrease of the interfacial velocity shear along slope. The ambient stratification restricts and decreases the current head velocity as it descends slope, which differs from the situation in homogenous ambient while the head velocity remains an approximately steady state. Motion of the descending flow into the stratified ambient has two stages: initial acceleration and deceleration at later stage based on the balance of inertial, buoyancy and friction forces. When the descending current approaches the initial neutral position at later stage, it separates from the slope and spreads horizontally into 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 condition and ambient stratification on the dilution and propagation of gravity currents.