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

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

2004-09-13

arxiv.org/abs/cond-mat/0409315v3

Physics Letters A, Vol. 371, Pg. 241, Year 2007

Physics

Condensed Matter

Other Condensed Matter

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

Scientific paper

10.1016/j.physleta.2007.07.073

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.

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