Numerical simulations of lock-exchange compositional gravity current

Abstract

Compositional gravity current flows produced by the instantaneous release of a finite-volume, heavier lock fluid in a rectangular horizontal plane channel are investigated using large eddy simulation. The first part of the paper focuses on the evolution of Boussinesq lock-exchange gravity currents with a large initial volume of the release during the slumping phase in which the front of the gravity current propagates with constant speed. High-resolution simulations are conducted for Grashof numbers $\sqrt {Gr}$ = 3150 (LGR simulation) and $\sqrt {Gr}$ = 126000 (HGR simulation). The Grashof number is defined with the channel depth h and the buoyancy velocity ub = $\sqrt {g'h}$ (g′ is the reduced gravity). In the HGR simulation the flow is turbulent in the regions behind the two fronts. Compared to the LGR simulation, the interfacial billows lose their coherence much more rapidly (over less than 2.5h behind the front), which results in a much faster decay of the large-scale content and turbulence intensity in the trailing regions of the flow. A slightly tilted, stably stratified interface layer develops away from the two fronts. The concentration profiles across this layer can be approximated by a hyperbolic tangent function. In the HGR simulation the energy budget shows that for t > 18h/ub the flow reaches a regime in which the total dissipation rate and the rates of change of the total potential and kinetic energies are constant in time. The second part of the paper focuses on the study of the transition of Boussinesq gravity currents with a small initial volume of the release to the buoyancy–inertia self-similar phase. When the existence of the back wall is communicated to the front, the front speed starts to decrease, and the current transitions to the buoyancy–inertia phase. Three high-resolution simulations are performed at Grashof numbers between $\sqrt {Gr}$ = 3 × 104 and $\sqrt {Gr}$ = 9 × 104. Additionally, a calculation at a much higher Grashof number ($\sqrt {Gr}$ = 106) is performed to understand the behaviour of a bottom-propagating current closer to the inviscid limit. The three-dimensional simulations correctly predict a front speed decrease proportional to t−α (the time t is measured from the release time) over the buoyancy–inertia phase, with the constant α approaching the theoretical value of 1/3 as the current approaches the inviscid limit. At Grashof numbers for which $\sqrt {Gr}$ > 3 × 104, the intensity of the turbulence in the near-wall region behind the front is large enough to induce the formation of a region containing streaks of low and high streamwise velocities. The streaks are present well into the buoyancy–inertia phase before the speed of the front decays below values at which the streaks can be sustained. The formation of the velocity streaks induces a streaky distribution of the bed friction velocity in the region immediately behind the front. This distribution becomes finer as the Grashof number increases. For simulations in which the only difference was the value of the Grashof number ($\sqrt {Gr}$ = 4.7 × 104 versus $\sqrt {Gr}$ = 106), analysis of the non-dimensional bed friction velocity distributions shows that the capacity of the gravity current to entrain sediment from the bed increases with the Grashof number. Past the later stages of the transition to the buoyancy–inertia phase, the temporal variations of the potential energy, the kinetic energy and the integral of the total dissipation rate are logarithmic.