Blue Holes and Froude Horizons: Circular Shallow Water Profiles for Astrophysical Analogs

TL;DR

This paper systematically analyzes 2D radial shallow water flow profiles, revealing horizons analogous to black holes, and explores various flow regimes including dissipation, shocks, and their implications for astrophysical analogs.

Contribution

It introduces a comprehensive classification of radial shallow water flows with horizons, extending understanding beyond 1D models and incorporating effects like dissipation and shocks.

Findings

Identification of horizon-like features in 2D shallow water flows.

Classification of flow regimes including dissipative and shock solutions.

Potential for modeling astrophysical phenomena using shallow water analogs.

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.