Shallow-water approach to the circular hydraulic jump

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Abstract
We show that the circular hydraulic jump can be qualitatively understood using simplified equations of the shallow-water type which include viscosity. We find that the outer solutions become singular at a finite radius and that this lack of asymptotic states is a general phenomenon associated with radial flow with a free surface. By connecting inner and outer solutions through a shock, we obtain a scaling relation for the radius Rj of the jump, Rj ∼ Q⅝v⅜g⅛, where Q is the volume flux, v is the kinematic viscosity and g is the gravitational acceleration. This scaling relation is valid asymptotically for large Q. We discuss the corrections appearing at smaller Q and compare with experiments.

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