The dynamics of a three-dimensional gravity current is investigated by both laboratory experiments and numerical simulations. The experiments take place in a rectangular tank, which is divided into two square reservoirs with a wall containing a sliding gate of width b. The two reservoirs are filled to the same height H, one with salt water and the other with fresh water. The gravity current starts its evolution as soon as the sliding gate is manually opened. Experiments are conducted with either smooth or rough surface on the bottom of the tank. The bottom roughness is created by gluing sediment material of different diameters to the surface. Five diameter values for the surface roughness and two salinity conditions for the fluid are investigated. The mathematical model is based on shallow-water theory together with the single-layer approximation, so that the model is strictly hyperbolic and can be put into conservative form. Consequently, a finite-volume-based numerical algorithm can be applied. The Godunov formulation is used together with Roe’s approximate Riemann solver. Comparisons between the numerical and experimental results show satisfactory agreement. The behavior of the gravity current is quite unusual and cannot be interpreted using the usual model framework adopted for two-dimensional and axisymmetric gravity currents. Two main phases are apparent in the gravity current evolution; during the first phase the front velocity increases, and during the second phase the front velocity decreases and the dimensionless results, relative to the different densities, collapse onto the same curve. A systematic discrepancy is seen between the numerical and experimental results, mainly during the first phase of the gravity current evolution. This discrepancy is attributed to the limits of the mathematical formulation, in particular, the neglect of entrainment in the mathematical model. An interesting result arises from the influence of the bottom surface roughness; it both reduces the front velocity during the second phase of motion and attenuates the differences between the experimental and numerical front velocities during the first phase of motion.

A two-layer, shallow-water model for three-dimensional (3D) gravity currents is proposed. The formulation results from the shallow-water-equations for two layers of immiscible liquids, subjected by the rigid-lid condition, so that the upper surface of the lighter layer remains perfectly flat during the motion. The arising pressure must be determined by solving the equations of motion, which is no problem for two-dimensional and axisymmetric gravity currents because the pressure is easily eliminated. In 3D gravity currents, the pressure is determined by solving a Poisson equation, together with momentum and mass balance equations. By means of a suitable scaling and a perturbation expansion, the equations are uncoupled from each other so that the problem is considerably simplified. Numerical results are compared with 3D lock-exchange release experiments. A comparison between numerical and experimental results of the gravity current indicates a fairly good agreement, whereas the results concerning the upper layer field variables shows that the numerical results are consistent with the experiments.

In this work, a numerical assessment of the suitability of a Single Relaxation Time (SRT) Lattice Boltzmann Method (LBM) model to simulate axisymmetric gravity currents is carried out. The model results are compared with both experimental data and other numerical models. The particular SRT formulation employed is known to converge, in the limit of low Knudsen number, to the two-layer 2D Shallow Water Equations (SWEs) set with a viscosity term featuring a closed theoretical formulation. Even with the lowest viscosity achievable by the method, its effect is shown to become important in most of the cases analysed, thus posing some serious constraints on possible application of the single relaxation time LBM method to simulate the lock-release generated-type gravity currents analysed here. The comparison with classical numerical models shows that the the viscous effects in the LBM model can be well reproduced employing coefficients derived from the above-mentioned theoretical formulation.