Advanced numerical methods have been proposed to study planar gravity currents in complex geometries or bathymetries, e.g. ( Reference Cantero, Lee, Balachandar and Garcia2007). Direct numerical simulations (DNS) have been used to shed light on the dynamics and the instabilities of axisymmetric constant-volume gravity currents, as in Cantero et al. ( Reference Cuthbertson, Laanearu, Wåhlin and Davies2012, Reference Cuthbertson, Lundberg, Davies and Laanearu2014) and Ottolenghi, Cenedese & Adduce ( Reference Ottolenghi, Cenedese and Adduce2017 b) on continuous-inflow gravity currents in rotating tanks illustrate the complexity of the necessary experimental arrangement even in the case of planar flows. Recent experiments described by Cuthbertson et al. Reference Hallworth, Huppert, Phillips and Sparks1996). This is because of the relative feasibility of field or laboratory experiments and the availability of numerical and analytical similarity solutions for the associated initial value problem in the context of shallow water theory (see e.g. currents generated by the release of a constant volume of a dense fluid. Hallworth, Huppert & Ungarish Reference Hallworth, Huppert and Ungarish2001 Huppert Reference Huppert2006 Ungarish Reference Ungarish2009 Dai & Wu Reference Dai and Wu2016), refers to constant-volume flows, i.e. Most of the knowledge on axisymmetric currents, (e.g. The reader is referred to the classical introduction of Simpson ( Reference Simpson1997) for a general review of the several possible manifestations of gravity currents in nature and in laboratory, and to Meiburg, Radhakrishnan & Nasr-Azadani ( Reference Meiburg, Radhakrishnan and Nasr-Azadani2015) for a comprehensive description of the methods and models used to describe them. in the case of turbid or cold river waters flowing into lakes or coastal areas under calm wind conditions. Such currents may be found when positively buoyant water plumes impinge on a level of stable stratification or when heavy fluids are spilled on the sea bottom, e.g. The spreading of three-dimensional, unconfined gravity currents is a primary concern in many environmental problems in hydraulics, coastal dynamics, oceanography and meteorology. 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 own environmental relevance. The identification of the inertial–buoyancy regime in the presence of hydrodynamic 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. 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 adoption of the slumping model of Huppert & Simpson ( J. Fluid Mech., vol. 99 (04), 1980, pp. 785–799), which is here extended to the case of constant-flow-rate cylindrical currents, allows reconciling of the different theories about the initial radial spreading in the context of different asymptotic regimes. 13, 1979, pp. 1241–1247), conducted for purely axially symmetric, constant inflow, gravity currents. The viscous–buoyancy phase is in good agreement with the model of Huppert ( J. Fluid Mech., vol. 121, 1982, pp. 43–58), while the inertial phase is consistent with the experiments of Britter ( Atmos. 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. In the latter case a typical ring structure is visible in the density and velocity fields. Depending on the Grashof number, the shocks can either be isolated or produced continuously. The flow is characterised by the presence of lobe and cleft instabilities and hydrodynamic shocks. In particular, the circular frontline spreads like a constant-flow-rate, axially symmetric gravity current about a virtual source translating along the symmetry axis. The study shows that, after an initial transient, the flow can be separated into an axisymmetric expansion and a globally translating motion. Unconfined three-dimensional gravity currents generated by lock exchange using a small dividing gate in a sufficiently large tank are investigated by means of large eddy simulations under the Boussinesq approximation, with Grashof numbers varying over five orders of magnitudes.
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