Gravity Currents Produced by Lock Exchanges: Experiments and Simulations with a Two-Layer Shallow-Water Model with Entrainment

Abstract

This paper presents the investigation of gravity currents by both laboratory experiments and a mathematical model. Eleven lock-exchange experiments, in which lock position, the initial current height, and density varied, were carried out to test the model validity and to compare laboratory results with previous expressions found in the literature. A two-layer shallow-water model was used to simulate all the runs. This model is new if compared with previous shallow-water models used to simulate gravity currents, because it accounts for both the entrainment and the free surface. A modified Turner’s formula is used to model the entrainment between the two fluids. The developed shallow-water models with and without entrainment are also compared, showing a better agreement when mixing is accounted for. Also, the effect of the free surface is shown by comparing the developed two-layer shallow-water model with a free surface and two different single-layer models with a rigid-lid approximation. Laboratory experiments and model simulations, accounting for both the entrainment and the free surface, are in good agreement. Front velocities, measured during the slumping phase, were compared with both predicted ones and previous expressions found in the literature, showing in most of the cases better result when the developed model is used.