The hydraulic jump and the shallow-water equations

Abstract

This is a study of the shallow-water equations in the context of standing hydraulic jumps in a planar geometry. The inviscid solutions are reviewed and it is demonstrated that the commonly used vertical averaging procedure leads to a closure problem. Inconsistencies associated with the vertical averaging procedure are also pointed out. We thus show that the recent solutions of the boundary-layer shallow-water equations provided in Dasgupta and Govindarajan (Phys Fluids 22:108–112, 2010) are consistent and correct.