Tunneling of the blocked wave in a circular hydraulic jump

The formation of a circular hydraulic jump in a thin liquid layer involves the creation of a horizon where the incoming wave (surface ripples) is blocked by the fast flowing fluid. That there is a jump at the horizon is due to the viscosity of the fluid which is not relevant for the horizon formation. By using a tunneling formalism developed for the study of the Hawking radiation from black holes, we explicitly show that there will be an exponentially small tunneling of the blocked wave across the horizons as anticipated in studies of “analog gravity”.