On the slumping of high Reynolds number gravity currents in two-dimensional and axisymmetric configurations

The behaviour of an inviscid gravity current of finite volume which is released from behind a lock and then propagates over a horizontal boundary is considered, for the elucidation of the initial ‘slumping’ phase during which the nose propagates with a constant velocity. The shallow-water two-layer model is used and the necessary front condition is provided, for comparisons, by four different correlations for the nose Froude function. Analytical and numerical results are presented, which reveal the essential flow-field features for various values of the governing dimensionless parameter H, the initial depth ratio of the outer embedding fluid to that of the dense fluid in the lock. It is shown that in the two-dimensional configuration a clear-cut slumping stage develops for any value of H, but for H<2 this stage is complicated by jumps of the interface (backward and forward moving bores) and constrained maximal nose velocity. The two-layer model provides good qualitative and quantitative agreements with previously published measurements, but the one-layer model mispredicts the dependency of the slumping distance on H. In the axisymmetric configuration a clear-cut slumping stage develops only for values of H close to 1 (shallow ambient), and persists for a relatively short time and distance. The effect of the Froude correlations and implementation to box-model approximations are also discussed.