  Rotation of non-circular hydraulic jumps is a recent experimental observation
that lacks a theory based on first principles. Here we furnish a basic theory
of this phenomenon founded on the shallow-water model of the circular hydraulic
jump. The breaking of the axial symmetry morphs the circular jump into a
polygonal state. Variations on this state rotate the polygon in the azimuthal
direction. The dependence of the rotational frequency on the flow rate and on
the number of polygon vertices agrees with known experimental results. We also
predict how the rotational frequency varies with viscosity. Finally, we
establish a correspondence between the rotating polygonal structure and the
Hawking effect in an analogue white hole. The rotational frequency of the
polygons affords a direct estimate of the frequency of the thermal Hawking
radiation.
