Numerical simulation of axisymmetric three-dimensional gravity currents generated by lock-exchange

Abstract

The unconfined three-dimensional gravity current generated by lock-exchange using a small dividing gate in a sufficiently large tank is investigated through a series of large eddy simulations under the Boussinesq approximation. The study shows that, after an initial transient, the flow can be separated into an axisymmetric expansion and a globally translating motion. In particular, the circular frontline spreads like a constant flow-rate, axial symmetric gravity current about a virtual source translating along the symmetry axis. The flow is characterised by the presence of lobe and cleft instabilities and hydrodynamical shocks. Depending on the Grashof number, the shocks can either be isolated or produced continuously. In the latter case a typical ring structure is visible in the density and velocity fields. The analysis of the frontal spreading of the axisymmetric part of the current indicates the presence of three regimes, namely, a slumping phase, an inertial-buoyancy equilibrium regime and a viscous-buoyancy equilibrium regime. The viscousboundary phase is well in accord with the model of Huppert [1982], while the inertial phase is consistent with the experiments of [Britter, 1979], conducted for purely axial symmetric, constant inflow, gravity currents. The adoption of the slumping model of Huppert and Simpson [1980], which is here extended to the case of constant-flow-rate cylindrical currents, allows reconciling di↵erent theories about the initial radial spreading in the context of di↵erent asymptotical regimes. As expected, the slumping phase is governed by the Froude number at the lock’s gate, whereas the transition to the viscous phase depends on both the Froude number at the gate and the Grashof number. The identification of the inertial-buoyancy regime in the presence of hydrodynamical shocks for this class of flows is important, due to the lack of analytical solutions for the similarity problem in the framework of shallow water theory. This fact has considerably slowed the research on variable-flow-rate axisymmetric gravity currents, as opposed to the rapid development of the knowledge about cylindrical constant volume and planar gravity currents, despite their great environmental relevance. The results are relevant for the assessment of many environmental processes, among which the near-field spreading of riverine freshwater in coastal waters and the dispersion associated with severe cases of oil spill at sea.