Self-similar behavior of non-planar non-circular gravity currents

This work reports some new aspects of non-planar non-circular gravity currents obtained from laboratory experiments, fully resolved simulations and box models. We show that these currents eventually reach a self-similar regime during which the local front propagation scales as the square root of time as in circular releases. In particular, the front has a self-similar shape that primarily depends on the aspect ratio of the initial release. The extended box model recently reported in [Zgheib \textit{et al.} 2014 \textit{Theor. Comput. Fluid Dyn.} \textbf{28}, 521-529] is used to propose a relation for the self-similar horizontal aspect ratio of the propagating front as a function of the initial horizontal aspect ratio. The experimental and numerical results are in good agreement with the proposed relation.