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 flow rate Q, kinematic viscosity {\nu} and surface tension {\gamma}. 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.