Gravity currents propagating at the base of a linearly stratified ambient

Abstract

Gravity currents produced from a full-depth lock release propagating at the base of a linearly stratified ambient are investigated by means of newly conducted three-dimensional high-resolution simulations in conjunction with corresponding two-dimensional simulations and laboratory experiments. A passive tracer is implemented in the simulations to quantitatively measure the energies associated with the current and the ambient. The density of heavy fluid within the lock is ρ̃C, the density in the ambient of depth H̃ varies linearly from ρ̃b at the bottom to ρ̃0 at the top, and the ambient has an intrinsic frequency Ñ. Attention is focused on the initial slumping stage, during which the gravity currents propagate at a constant velocity Ṽ and the internal Froude number is defined as Fr=Ṽ/ÑH̃. The dynamics of the subcritical gravity currents, i.e., Fr<1/π, and the supercritical gravity currents, i.e., Fr>1/π, are qualitatively different and are examined with the help of three-dimensional and two-dimensional high-resolution simulations. For the subcritical gravity currents, the flow is dominated by the internal wave, the Kelvin–Helmholtz vortices are inhibited, and the two-dimensional simulation agrees well with and serves as a good surrogate model for the three-dimensional simulation in the slumping stage. For the supercritical gravity currents, the Kelvin–Helmholtz vortices are pronounced and prone to breakup into three-dimensional structures in the slumping stage. On the one hand, for the supercritical gravity currents, the kinetic energy associated with the current and the potential energy associated with the ambient are accurately captured by the two-dimensional simulation. On the other hand, the transition distance for the slumping stage and dissipation rate in the system are underpredicted while the kinetic energy associated with the ambient and the potential energy associated with the current are overpredicted by the two-dimensional simulation for the supercritical gravity currents. Therefore, information derived from the two-dimensional simulation for the supercritical gravity currents must be treated with care. The high-resolution simulations in this study also complement the existing shallow-water formulation, which has been reported to agree well with the two-dimensional simulations with good physical assumptions and simple mathematical models.