Sequent depths at the abrupt change in porosity at the transition between unobstructed and vegetated open channel flows

In this paper, a new set of depth-integrated double-averaged Navier–Stokes equations (DIDANS equations), which describe 1D unsteady vegetated flow, is derived. The equations are used to derive an analytical expression relating flow depths just before and just after the interface between free flow and a vegetation patch, known as the sequent depths. The expression can be used to determine whether a prescribed flow depth on one side of the interface is physically possible and, if so, to determine the sequent depth on the other side. The procedure can be included in undergraduate Engineering Hydraulics courses and textbooks, and may also be useful for PhD students, practitioners and model developers. It can be incorporated into numerical models of open-channel flows with vegetation patches to define appropriate boundary conditions and test the accuracy of numerical solutions.