On inwardly propagating high-Reynolds-number axisymmetric gravity currents

The behaviour of an axisymmetric inviscid gravity current, which is released from a lock near the outer wall of a circular container and then propagates towards the centre over a horizontal boundary, is considered. Shallow-water and box-model theoretical analyses and experimental results are presented and compared. The resulting motion predicted by the shallow-water model displays interesting differences with the previously reported outward propagation of an axisymmetric current, as well as with propagation in a two-dimensional rectangular geometry. The current initially develops the usual decelerating motion with a nose-up tail-down shape, but when the nose reaches about half of the outer radius the confining geometry opposes the further decrease of the height and velocity of the nose. The box-model approximation, which omits the inclination of the interface, is unable to reproduce the hindering (and eventual reversal) effect of the geometrical confinement on the decrease of the nose velocity during the inward propagation.