2D Large-Eddy Simulation of Lock-Exchange Gravity Current Flows at High Grashof Numbers

Lock-exchange gravity current flows produced by the instantaneous release of a heavy fluid are investigated by means of high-resolution two-dimensional (2D) large-eddy simulation (LES) using a dynamic subgrid scale model for Grashof numbers $\left(\mathsf{Gr}\right)$ up to ${10}^{12}$ . The model is validated using 2D direct numerical simulation results for the classical lock-exchange gravity current flow in an infinite channel with no-slip walls. Then the model is applied to study lock-exchange flows for the case in which the heavier (lock) fluid is initially situated in between a vertical end wall and the lock barrier. Three cases with different aspect ratios of the initial lock fluid are considered for Grashof numbers of the order of ${10}^9–{10}^{10}$ . It is found that 2D LES is able to capture most of the physics observed in experiments including the evolution of the head, as well as the formation of coherent billow structures at the apex of the head due to growth of the Kelvin-Helmholtz (KH) instabilities. However, due to the fact that three-dimensional instabilities cannot develop in 2D simulations, the coherence of these KH billows in the latter stages of the evolution of the current is found to be stronger compared to the experiment where mixing is sensibly higher at the interface between the current and the surrounding fluid. The LES simulations accurately capture the front and bore velocities in the slumping phase and predict that during the inviscid self-similar phase the front speed decay is proportional to $t^{-1∕3}$ , which is consistent with theory, where $t$ =time. A LES simulation at a Grashof number closer to the inviscid range $(\mathsf{Gr}={10}^{12})$ shows that the evolution of the current and the structure of the head region are qualitatively similar to those observed at lower Grashof numbers $(\mathsf{Gr}>{10}^8)$ . The energy balance shows that the higher front velocity in the $\mathsf{Gr}={10}^{12}$ simulation is due to the fact that the amount of mixing (dissipation) decays with the Grashof number. This allows a larger fraction of the potential energy to be converted into kinetic energy. The flow fields are also used to obtain the distributions of the bed shear stress which determine the amount of sediment entrained by a compositional gravity current propagating over a loose bed.