Past exam of the waves and compressible flow course of the University of Oxford / 2023 / 3 / a / iii / Solution

Put $R=h_2/h_1>1$. The squared Froude numbers follow directly from the discharge relation:Thus the jump connects supercritical flow to subcritical flow. Long surface gravity waves have speed $\sqrt{gh}$ relative to the fluid, so the characteristic speeds in the stationary frame are $u\pm \sqrt{gh}$. Upstream both point with the flow; downstream one points against it. The jump changes whether long-wave information can propagate upstream through the local flow.