Blue Holes and Froude Horizons: Circular Shallow Water Profiles for Astrophysical Analogs
arXiv:2101.06455 · doi:10.1103/PhysRevResearch.3.023119
Abstract
Interesting analogies between shallow water dynamics and astrophysical phenomena have offered valuable insight from both the theoretical and experimental point of view. To help organize these efforts, here we analyze systematically the hydrodynamic properties of backwater profiles of the shallow water equations with 2D radial symmetry. In contrast to the more familiar 1D case typical of hydraulics, %already for {even in} isentropic conditions, a solution with minimum-radius horizon for the flow emerges, similar to the black hole and white hole horizons, where the critical conditions of unitary Froude number provide a unidirectional barrier for surface waves. Beyond these time-reversible solutions, a greater variety of cases arises, when allowing for dissipation by turbulent friction and shock waves (i.e., hydraulic jumps) for both convergent and divergent flows. The resulting taxonomy of the base-flow cases may serve as a starting point for a more systematic analysis of higher-order effects linked, e.g., to wave propagation and instabilities, capillarity, variable bed slope, and rotation.
References in corpus (6)
- Measurement of stimulated Hawking emission in an analogue system
- Observation of negative-frequency waves in a water tank: A classical analogue to the Hawking effect?
- Experimental demonstration of the supersonic-subsonic bifurcation in the circular jump: A hydrodynamic white hole
- Horizons and Ergoregions in Superfluids
- Classical Hydrodynamics for Analogue Spacetimes: Open Channel Flows and Thin Films
- Free surface axially symmetric flows and radial hydraulic jumps