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

Matière et Systèmes Complexes, CNRS and Université Paris Diderot UMR 7057 - Bâtiment Condorcet, 10 rue Alice Domon et Léonie Duquet, 75013 Paris, France

Received: 23 June 2014
Accepted: 10 August 2014

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 the flow rate Q, the kinematic viscosity ν and the surface tension γ. Combining this result with a lubrication description of the outer flow leads, under appropriate conditions, to a new and simple law ruling the jump radius , in excellent agreement with our experimental data. This unexpected result raises an unsolved question to all available models.