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

International audienceThe properties of a standard hydraulic jump depend critically on a Froude number F r 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 F r 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 to a lubrication description of the outer flow yields, under appropriate conditions, to a new and simple law ruling the jump radius R J : R J (ln(R∞/R J))^3/8 ∼ Q^5/8 ν^−3/8 g^−1/8 , in excellent agreement with our experimental data. This unexpected result asks an unsolved question to all available models