Continuous hydraulic jumps in laminar channel flow

Abstract

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.

References in corpus (5)

• Averaging theory for the structure of hydraulic jumps and separation in laminar free-surface flows
• On the origin of the hydraulic jump in a thin liquid film
• Experimental demonstration of the supersonic-subsonic bifurcation in the circular jump: A hydrodynamic white hole
• The hydraulic jump as a white hole
• Surface tension and the origin of the circular hydraulic jump in a thin liquid film