Energy balances for propagating gravity currents: homogeneous and stratified ambients

Abstract

The exchange of energy for an inviscid gravity current which is released from a lock and then propagates over a horizontal boundary is considered. Attention is focused on effects due to stratification in the ambient. The investigation uses both a one-layer shallow-water model and Navier–Stokes finite-difference simulations. There is good agreement between these two approaches for the energy of the dense fluid (the current). The results indicate that with respect to the behaviour of energy as a function of time we can distinguish between: ($a$) currents propagating at supercritical speed (with respect to the fastest internal wave in the ambient), including a nose propagating into an unstratified ambient; and ($b$) currents propagating at subcritical speed, including the strongest effective stratification for which the density at the base of the ambient is equal to that of the current. The stratification enhances the accumulation of potential energy in the ambient and reduces the energy decay (dissipation) of the two-fluid system. The interaction of the internal waves with the head of the current in the subcritical case has no significant influence on the energy balance of the current.