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

Source: [Standing and travelling waves in the shallow-water circular hydraulic jump](<https://www.sota2.com/research/paper/68fa26862c2a3760193bac04>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T03:04:27.045Z

Authors: Arnab K. Ray, J. K. Bhattacharjee

Published: 2004-09-13T12:50:56.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0409315>)

[PDF](<https://arxiv.org/pdf/cond-mat/0409315.pdf>)