  On the basis of the viscous Saint-Venant equations, hydraulic jumps in
laminar open channel flow are obtained as continuous shock structures. Thanks
to the inclusion of viscosity, the jumps are not abrupt, rendering the classic
patchwork via the Rankine-Hugoniot shock relations unnecessary. The jumps arise
as stable stationary solutions of the governing equations and lend themselves
excellently to a Dynamical Systems analysis, manifesting themselves as
near-parabolic trajectories in phase space. Based on this, we derive an
analytic expression for the jump length as a function of the Froude and
Reynolds numbers, reflecting the fact that both gravity and viscosity
contribute to the balance of forces that shape the jump. The paper concludes
with a numerical experiment confirming the stability of the jumps.
