A stationary circular hydraulic jump, the limits of its existence and its gasdynamic analogue

We propose a theory of a steady circular hydraulic jump based on the shallow-water model obtained from the depth-averaged Navier-Stokes equations. The flow structure both upstream and downstream of the jump is determined by considering the flow over a plate of finite radius. The radius of the jump is found using the far-field conditions together with the jump conditions that include the effects of surface tension. We show that a steady circular hydraulic jump does not exist if the surface tension is above a certain critical value. The solution of the problem provides a basis for the hydrodynamic stability analysis of the hydraulic jump. An analogy between the hydraulic jump and a detonation wave is pointed out.