Sand bars in tidal channels. Part 1. Free bars

We investigate the basic mechanism whereby bars form in tidal channels or estuaries. The channel is assumed to be long enough to allow neglect of the effects of end conditions on the process of bar formation. In this respect, the object of the present analysis differs from that of Schuttelaars & de Swart (1999) who considered bars of length scaling with the finite length of the tidal channel. The channel bottom is assumed to be cohesionless and consisting of uniform sediments. Bars are shown to arise from a mechanism of instability of the erodible bed subject to the propagation of a tidal wave. Sediment is assumed to be transported both as bedload and as suspended load. A fully three-dimensional model is employed both for the hydrodynamics and for sediment transport. At the leading order of approximation considered, the effects of channel convergence, local inertia and Coriolis forces on bar instability are shown to be negligible. Unlike fluvial free bars, in the absence of mean currents tidal free bars are found to be non-migrating features (in the mean). Instability arises for large enough values of the mean width to depth ratio of the channel, for given mean values of the Shields parameter and of the relative channel roughness. The role of suspended load is such as to stabilize bars in the large-wavenumber range and destabilize them for small wavenumbers. Hence, for large values of the mean Shields stress, it turns out that the first critical mode (the alternate bar mode) is characterized by a very small value of the critical width to depth ratio. Furthermore, the order-M mode being characterized by a critical value of the width to depth ratio equal to m times the critical value for the first mode, it follows that for large values of the mean Shields stress several unstable modes are simultaneously excited for relatively low values of the aspect ratio. This suggests that the actual bar pattern observed in nature may arise from an interesting nonlinear competition among different unstable modes.