Standing and travelling waves in the shallow-water circular hydraulic jump

Abstract

A wave equation for a time-dependent perturbation about the steady shallow-water solution emulates the metric an acoustic white hole, even upon the incorporation of nonlinearity in the lowest order. A standing wave in the sub-critical region of the flow is stabilised by viscosity, and the resulting time scale for the amplitude decay helps in providing a scaling argument for the formation of the hydraulic jump. A standing wave in the super-critical region, on the other hand, displays an unstable character, which, although somewhat mitigated by viscosity, needs nonlinear effects to be saturated. A travelling wave moving upstream from the sub-critical region, destabilises the flow in the vicinity of the jump, for which experimental support has been given.

9 pages, REVTeX, Additional treatment on travelling waves. Extensively revised in the publised version. Contains a full new section on the role of nonlinearity

References in corpus (6)

• On the Universality of the Hawking Effect
• Hydraulic/Shock-Jumps in Protoplanetary Disks
• Hydraulic Jump in One-dimensional Flow
• Critical properties and stability of stationary solutions in multi-transonic pseudo-Schwarzschild accretion
• The hydraulic jump as a white hole
• Horizons and Ergoregions in Superfluids

Cited by in corpus (14)

• Analogue Gravity
• Experimental demonstration of the supersonic-subsonic bifurcation in the circular jump: A hydrodynamic white hole
• The role of flow geometry in influencing the stability criteria for low angular momentum axisymmetric black hole accretion
• Perturbations on steady spherical accretion in Schwarzschild geometry
• On Spin Dependence of Relativistic Acoustic Geometry
• Classical Hydrodynamics for Analogue Spacetimes: Open Channel Flows and Thin Films
• Quasi-viscous accretion flow -- I: Equilibrium conditions and asymptotic behaviour
• Axially Symmetric Accretion of Fractal Medium onto Rotating Black Holes and the emergence of the Acoustic Manifold
• Implications of nonlinearity for spherically symmetric accretion
• Nonlinear variations in axisymmetric accretion
• Acoustic horizons in nuclear fluids
• The circular jump as a hydrodynamic white hole
• Surface tension and instability in the hydrodynamic white hole of a circular hydraulic jump
• Dissipation and acoustic tunnelling about the sonic horizon of Bondi accretion