The analogue Hawking effect in rotating polygonal hydraulic jumps

Abstract: 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.