Energy balances for the collision of gravity currents of equal strengths

Abstract

Collision of two counterflowing gravity currents of equal densities and heights was investigated by means of three-dimensional high-resolution simulations with the goal of understanding the flow structures and energetics in the collision region in more detail. The lifetime of collision is approximately $3 \tilde {H}/\tilde {u}_f$ , where $\tilde {H}$ is the depth of heavy and ambient fluids, and $\tilde {u}_f$ is the front velocity of the approaching gravity currents, and the lifetime of collision can be divided into three phases. During Phase I, $-0.2 \leqslant (\tilde {t}-\tilde {t}_c) \tilde {u}_f/\tilde {H} \leqslant 0.5$ , where $\tilde {t}$ is the time, and $\tilde {t}_c$ is the time instance at which the two colliding gravity currents have fully osculated, geometric distortions of the gravity current fronts result in stretching of pre-existing vorticity in the wall-normal direction inside the fronts, and an array of vertical vortices extending throughout the updraught fluid column develop along the interface separating the two colliding gravity currents. The array of vertical vortices is responsible for the mixing between the heavy fluids of the two colliding gravity currents and for the production of turbulent kinetic energy in the collision region. The presence of the top boundary deflects the updraughts into the horizontal direction, and a number of horizontal streamwise vortices are generated close to the top boundary. During Phase II, $0.5 \leqslant (\tilde {t}-\tilde {t}_c) \tilde {u}_f/\tilde {H} \leqslant 1.2$ , the horizontal streamwise vortices close to the top boundary induce turbulent buoyancy flux and break up into smaller structures. While the production of turbulent kinetic energy weakens, the rate of transfer of energy to turbulent flow due to turbulent buoyancy flux reaches its maximum and becomes the primary supply in the turbulent kinetic energy in Phase II. During Phase III, $1.2 \leqslant (\tilde {t}-\tilde {t}_c) \tilde {u}_f/\tilde {H} \leqslant 2.8$ , the collided fluid slumps away from the collision region, while the production of turbulent kinetic energy, turbulent buoyancy flux and dissipation of energy attenuate. From the point of view of energetics, the production of turbulent kinetic energy and turbulent buoyancy flux transfers energy away from the mean flow to the turbulent flow during the collision. Our study complements previous experimental investigations on the collision of gravity currents in that the flow structures, spatial distribution and temporal evolution of the mean flow and turbulent flow characteristics in the collision region are presented clearly. It is our understanding that such complete information on the energy budgets in the collision region can be difficult to attain in laboratory experiments.