Asymptotic Analysis of non-Linear Sand Transport in Estuaries
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Asymptotic analysis is applied to a two-dimensional depth-averaged morphodynamic model for a tidally dominated estuary. The water motion is described by the depth-averaged shallow water equations and driven by an externally prescribed M2-tide. The sediment transport is determined by the tidal averages of suspended sediment and sediment as bed load transport. The linearized equations can quantitatively denote the tidal bar length, and can be used qualitatively to clarify the physical processes behind the instability of the sandy bed. The second- and third-order equations are used to capture the non-linear morphodynamics of the estuary. The elongation of troughs and the shallow cross-channel sandy bridges of sand are reproduced. A finite-amplitude equilibrium could not be found.