On the shock transition, the hydraulic jump, and vortex breakdown

Abstract

The normal shock, hydraulic jump, and vortex breakdown have a common feature: they are all marked by a transition from a supercritical to a subcritical flow state. These phenomena are due to the nonlinearity of the flow, and it will be shown that viscosity also plays an essential role. This paper demonstrates explicitly how viscosity enters into these flows, The treatment of normal shock served a starting illustration. Then an equation governing the phenomenon of hydraulic jump is derived with the inclusion of the effect of viscosity. It is explicitly shown that supercritical flow is not stable and has to go through a transition to a conjugate subcritical flow state downstream. Similar treatment is also applied to vortex breakdown with largely similar results.