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Generalised Serre–Green–Naghdi equations for open channel and for natural river hydraulics

In this paper, we present a new non-linear dispersive model for open channel and river flows. These equations are the second-order shallow water approximation of the section-averaged (three-dimensional) incompressible and irrotational Euler system. This new asymptotic model generalises the well-known one-dimensional Serre–Green–Naghdi (SGN) equations for rectangular section on uneven bottom to arbitrary channel/river section.