The circular jump as a hydrodynamic white hole

Abstract

Surface waves in classical fluids experience a rich array of black/white hole horizon effects. The dispersion relation depends on the characteristics of the fluid as well as on the fluid depth and the wavelength regime. We focus on the shallow-water regime, and discuss the experimental proof that the circular hydraulic jump marks the transition between a supercritical and a subcritical flow regime. This finally confirms a theoretical conjecture formulated by Lord Rayleigh nearly 100 years ago. It also confirms that the circular jump corresponds to the spontaneous formation of a hydrodynamic white hole, with interesting characteristics from the point of view of analogue gravity. We study the dispersive regime, mention some lessons about the trans-Planckian issue and describe possible directions for future work.