A new front condition for non-Boussinesq gravity currents

A new front condition for gravity currents in a two-layer shallow water framework with a free surface is developed by applying the theory of the weak formulation to a first order system of four partial differential equations written in conservation form. The Rankine–Hugoniot jump conditions are applied and a relation between the velocity and the height of the shock is obtained. Laboratory experiments on lock-release non-Boussinesq gravity currents are performed and the front propagation and the free surface displacement are evaluated. Front velocities, predicted by the present mathematical model, are compared to both laboratory measurements and the predictions of the Benjamin formula, which is based on the rigid lid approximation. The new jump condition is in a good agreement with the laboratory measurements, while the Benjamin formula exhibits an overestimation of the shock velocity in the non-Boussinesq cases. In addition, the free surface displacement near the shock predicted by the new model is in agreement with the laboratory measurements.