Impact of boundary conditions on entrainment and transport in gravity currents

Gravity currents have been studied numerically and experimentally both in the laboratory and in the ocean. The question of appropriate boundary conditions is still challenging for most complex flows. Gravity currents make no exception—appropriate, physically and mathematically sound boundary conditions are yet to be found. This task is further complicated by the technical limitations imposed by the current oceanographic techniques. In this paper, we make a first step toward a better understanding of the impact of boundary conditions on gravity currents. Specifically, we use direct numerical simulations to investigate the effect that the popular Neumann, and less popular Dirichlet boundary conditions on the bottom continental shelf have on the entrainment and transport of gravity currents. The finding is that gravity currents under these two different boundary conditions differ most in the way they transport heat from the top towards the bottom. This major difference occurs at medium temperature ranges. Entrainment and transport at high temperatures also show significant differences.