  We impose a linearized Eulerian perturbation on a steady, shallow, radial
outflow of a liquid (water), whose local pressure function includes both the
hydrostatic and the Laplace pressure terms. The resulting wave equation bears
the form of a hydrodynamic metric. A dispersion relation, extracted from the
wave equation, gives an instability due to surface tension and the cylindrical
flow symmetry. Using the dispersion relation, we also derive three known
relations that scale the radius of the circular hydraulic jump in the outflow.
The first two relations are scaled by viscosity and gravity, with a
capillarity-dependent crossover to the third relation, which is scaled by
viscosity and surface tension. The perturbation as a high-frequency travelling
wave, propagating radially inward against the bulk outflow, is blocked just
outside the circular hydraulic jump. The amplitude of the wave also diverges
here because of a singularity. The blocking is associated with surface tension,
which renders the circular hydraulic jump a hydrodynamic white hole.
