Analytical solutions for long-time steady state Boussinesq gravity currents flowing along a horizontal boundary of finite length

This paper presents analytical solutions to the theoretical problem proposed by Ellison and Turner. Their equations describe the longitudinal evolution of a miscible gravity current when it reaches a steady state. The solutions here proposed allow the evolution of the velocity, height and density of the current to be calculated solely from the local Richardson number. The latter is obtained using a universal function F that can be tabulated or plotted whatever the release conditions. The solutions are then extended to configurations in which a jump appears, and finally for several entrainment laws available in the literature.