Published online by Cambridge University Press: 31 January 2011
A simple idealized model is proposed to predict the appearance of alternate bottom forms in tidal channels. The model is based on the linear stability analysis of the flat seabed driven by tidal currents. The hydrodynamics is described by means of the full three-dimensional continuity and Reynolds equations. To quantify turbulent stresses, the Boussinesq assumption is introduced and an algebraic model is used for the eddy viscosity. The morphodynamics is described by the Exner equation and a simple sediment transport predictor. When applied to tidal channels, the model predicts the appearance of alternate bottom forms if the channel width is larger than a critical value. This finding agrees with previous analyses. However, the results obtained show the existence of two different modes. Close to the conditions of incipient sediment motion or when the suspended load is intense, the model suggests the appearance of an alternate sequence of shoals and pools (the first mode), characterized by a wavelength which might be comparable with the horizontal excursion of the tide. However, under such circumstances, to provide accurate quantitative results, the model should be extended to include the effects of the local acceleration and of the possible variations of the depth and width of the channel, which are neglected in the analysis. In all the other conditions, the model predicts the appearance of a second mode, presently termed tidal alternate bars. This mode is geometrically similar to the first mode, i.e. it is characterized by depositional and erosional areas which are found in an alternate arrangement, but it has significantly shorter wavelengths. In this case, the wavelength of the bedforms scales with the water depth. The physical mechanism generating tidal alternate bars appears to be the same as that generating tidal dunes, and it cannot be described by means of a depth-averaged approach.
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