  Interesting analogies between shallow water dynamics and astrophysical
phenomena have offered valuable insight from both the theoretical and
experimental point of view. To help organize these efforts, here we analyze
systematically the hydrodynamic properties of backwater profiles of the shallow
water equations with 2D radial symmetry. In contrast to the more familiar 1D
case typical of hydraulics, %already for {even in} isentropic conditions, a
solution with minimum-radius horizon for the flow emerges, similar to the black
hole and white hole horizons, where the critical conditions of unitary Froude
number provide a unidirectional barrier for surface waves. Beyond these
time-reversible solutions, a greater variety of cases arises, when allowing for
dissipation by turbulent friction and shock waves (i.e., hydraulic jumps) for
both convergent and divergent flows. The resulting taxonomy of the base-flow
cases may serve as a starting point for a more systematic analysis of
higher-order effects linked, e.g., to wave propagation and instabilities,
capillarity, variable bed slope, and rotation.
