Averaging theory for the structure of hydraulic jumps and separation in laminar free-surface flows

We present a simple viscous theory of free-surface flows in boundary layers, which can accommodate regions of separated flow. In particular, this yields the structure of stationary hydraulic jumps, both in their circular and linear versions, as well as structures moving with a constant speed. Finally, we show how the fundamental hydraulic concepts of subcritical and supercritical flow, originating from inviscid theory, emerge at intermediate length scales in our model.