Constant Froude number in a circular hydraulic jump and its implication on the jump radius selection

Abstract

The properties of a standard hydraulic jump depend critically on a Froude number Fr defined as the ratio of the flow velocity to the gravity waves speed. In the case of a horizontal circular jump, the question of the Froude number is not well documented. Our experiments show that Fr measured just after the jump is locked on a constant value that does not depend on flow rate Q, kinematic viscosity ν and surface tension γ. Combining this result to a lubrication description of the outer flow yields, under appropriate conditions, a new and simple law ruling the jump radius RJ : $R_J(ln(\frac{R_{\infty }}{R_J}){)}^{3/8}\sim Q^{5/8}{\nu }^{-3/8}$, in excellent agreement with our experimental data. This unexpected RJ result asks an unsolved question to all available models.

5 pages, 3 figures

References in corpus (3)

• Measurement of stimulated Hawking emission in an analogue system
• Experimental demonstration of the supersonic-subsonic bifurcation in the circular jump: A hydrodynamic white hole
• Orbits and reversals of a drop rolling inside a horizontal circular hydraulic jump

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• Surface tension and instability in the hydrodynamic white hole of a circular hydraulic jump
• Preventing sinking of a disk by leveraging the boundary jump phenomenon