G. Vittori

On the formation of sand waves and sand banks

A fully three-dimensional model is proposed for the generation of tidal sand waves and sand banks from small bottom perturbations of a flat seabed subject to tidal currents. The model predicts the conditions leading to the appearance of both tidal sand waves and sand banks and determines their main geometrical characteristics. A finite wavelength of both sand waves and sand banks is found around the critical conditions, thus opening the possibility of performing a weakly nonlinear stability analysis able to predict the equilibrium amplitude of the bottom forms. As shown by previous works on the subject, the sand wave crests turn out to be orthogonal to the direction of the main tidal current. The present results also show that in the Northern Hemisphere sand bank crests are clockwise or counter-clockwise rotated with respect to the main tidal current depending on the counter-clockwise or clockwise rotation of the velocity vector induced by the tide. Only for unidirectional or quasi-unidirectional tidal currents are sand banks always counter-clockwise rotated. The predictions of the model are supported by comparisons with field data. Finally, the mechanisms leading to the appearance of sand waves and sand banks are discussed in the light of the model findings. In particular, it is shown that the growth of sand banks is not only induced by the depth-averaged residual circulation which is present around the bedforms and is parallel to the crests of the bottom forms: a steady drift of the sediment from the troughs towards the crests is also driven by the steady velocity component orthogonal to the crests which is present close to the bottom and can be quantified only by a three-dimensional model. While the former mechanism appears to trigger the formation of counter-clockwise sand banks only, the latter mechanism can give rise to both counter-clockwise and clockwise rotated sand banks.

Crescentic bedforms in the nearshore region

A wave of small amplitude is considered which approaches a straight beach normally and which is partially reflected at the coastline. By assuming that the local depth is much smaller than the length of the incoming wave, the shallow water equations are used to determine the water motion. The surf zone width is assumed to be small compared to the length of the incoming wave and hence the effect of wave breaking is included only parametrically. The time development of the cohesionless bottom is described by the Exner continuity equation and by an empirical sediment transport rate formula which relates the sediment flux to the steady currents and wave stirring. It is shown that the basic-state solution, which does not depend on the longshore coordinate, may be unstable with respect to longshore bedform perturbations, so that rhythmic topographies form. The instability process is due to a positive feedback mechanism involving the incoming wave, synchronous edge waves and the bedforms. The growth of the bottom perturbations is related to the presence of steady currents caused by the interaction of the incoming wave with synchronous edge waves which in turn are excited by the incoming wave moving over the wavy bed. For natural beaches the model predicts two maxima in the amplification rate: one is related to incoming waves of low frequency, the other to wind waves. Thus two bedforms of different wavelengths can coexist in the nearshore region with longshore spacings of a few hundred and a few tens of metres, respectively. To illustrate the potential validity of the model, its results are compared with field data. The overall agreement is fairly satisfactory.

Linear evolution of sandwave packets

We investigate how a local topographic disturbance of a flat seabed may become morphodynamically active, according to the linear instability mechanism which gives rise to sandwave formation. The seabed evolution follows from a Fourier integral, which can generally not be evaluated in closed form. As numerical integration is rather cumbersome and not transparent, we propose an analytical way to approximate the solution. This method, using properties of the fastest growing mode only, turns out to be quick, insightful, and to perform well. It shows how a local disturbance develops gradually into a sandwave packet, the area of which increases roughly linearly with time. The elevation at the packet?s center ultimately tends to increase, but this may be preceded by an initial stage of decrease, depending on the spatial extent of the initial disturbance. In the case of tidal asymmetry, the individual sandwaves in the packet migrate at the migration speed of the fastest growing mode, whereas the envelope moves at the group speed. Finally, we apply the theory to trenches and pits and show where results differ from an earlier study in which sandwave dynamics have been ignored.