Hydraulic jumps on shear flows with constant vorticity

In this work, the influence of constant background vorticity on the properties of shock waves in a shallow water system are considered. It is shown that the flow-depth ratio of stationary shocks can be written as a function of two non-dimensional parameters: the Froude number, suitably defined in the presence of the shear flow, and a non-dimensional vorticity. Some properties of these hydraulic jumps are explored, and it is shown that stronger background vorticity has the effect of moderating the strength of the hydraulic jump.