Axisymmetric gravity currents at high Reynolds number: On the quality of shallow-water modeling of experimental observations

The motion of an axisymmetric gravity current that is released from a lock and then propagates over a horizontal boundary is considered. Attention is focused on the interpretation of the experimentally observed propagation (for Boussinesq systems at high Reynolds number) by means of the shallow-water inviscid model. Comparisons of the theoretical one-layer model results with previously published measurements of M. A. Hallworth, H. E. Huppert, and M. Ungarish [J. Fluid Mech. 447, 1 (2001)] and M. D. Patterson, J. E. Simpson, S. B. Dalziel, and G. J. F. van Heijst [Phys. Fluids 18, 046601 (2006)] prove that the model provides reliable insights and fairly accurate predictions (sometimes even better than obtained by full Navier-Stokes simulations) of distance of propagation and shape of interface, except for a very short initial phase. The limit of validity of the inviscid approximation is calculated, and it is shown that the above-mentioned experiments are within it. Some apparent discrepancies and scatter of various results are briefly discussed, and some reconciliations are suggested.