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

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 nu and the surface tension gamma. 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 R-J : R-J ( ln( R-infinity/ R-J)) (3/ 8) similar to Q (5/ 8)nu (-3/ 8) g(-1/ 8), in excellent agreement with our experimental data. This unexpected result raises an unsolved question to all available models. Copyright (C) EPLA, 2014