Dam-break release of a gravity current in a stratified ambient

The 'dam-break' initial behaviour of an inviscid gravity current which is released from a lock and then propagates over a horizontal boundary at the base of a stratified ambient fluid is considered. Analytical and finite-difference solutions of the one-layer shallow-water equations are developed and compared for the linear stratification in a rectangular channel case, and corroborated by numerical solutions of the full two-dimensional Navier-Stokes equations. Extensions of the shallow-water solution to non-linear stratification, release from an elliptical reservoir, and axisymmetric geometry are also presented. The results indicate that the shallow-water formulation captures well the essential features of the motion, which are qualitatively similar to the non-stratified case, but with details modified by the stratification; in particular, the forward propagation of the head and the backward spread of the depression wave are reduced when the stratification increases.