The unsteady radial flow of a relatively dense fluid released from an axisymmetric lock is analyzed when it freely drains over an edge and when it generates a gravity current propagating over a horizontal surface. In both situations when modeled using the shallow water equations, despite initiation from rest within a lock, the flow thins, accelerates, and becomes supercritical in a region close to the symmetry axis. For free drainage, this alters the outflow, while for radial gravity currents, it leads to the formation of an internal jump connecting rapidly moving fluid to more tranquil flow at the front. Both scenarios share the same supercritical flow structure, which is related to their initiation from lock-release conditions and is a function of axisymmetry; the phenomenon is not found in analogous two-dimensional flows. Through analysis and numerical integration of the governing equations, the common onset and consequences of supercriticality are revealed in both flows, as well as, the progression of the fluid motions to self-similar states that develop at late times.

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• Geophysical fluid dynamics
• Stratified geophysical flows