Separation of particle-laden gravity currents down a slope in linearly stratified environments

Abstract

Particle-laden gravity currents down a slope in stratified fluid are important processes in lake, estuary, and ocean environments. By conducting direct numerical simulations, this study investigates the detailed dynamic features of lock-exchange particle-laden gravity currents down a slope in linearly stratified environments. The front velocity, separation depth, water entrainment ratio, and energy budget are quantitatively analyzed. This evolutionary process can be divided into three stages, i.e., the acceleration stage, deceleration stage, and separation stage, if the relative stratification parameter is larger than unity. At the acceleration stage, as the collapse of the dense fluid leads to fast entrainment of ambient water into the current, the entrainment ratios have large values, while the settling velocity and the ambient stratification are shown to have less impact on both the entrainment ratios and the front velocity. At the deceleration stage, a larger slope angle, a weaker ambient stratification, and a smaller settling velocity bring a greater front velocity. At the separation stage, the head of the current leaves the slope and intrudes into the environment; meanwhile, the dense fluid at the body of the current also intrudes into the ambient water because the density contrast has largely been reduced due to water entrainment, particle settling, and the density increase in the ambient fluid. A predictive model is developed to determine the separation depth by considering the presence of particles. The fingerlike horizontal intrusions enhance the entrainment effect between the current and the ambient water. A stronger ambient stratification suppresses the conversion of the potential energy to the kinetic energy, while a larger settling velocity accelerates the conversion of the kinetic energy to the dissipated energy.