Grain sorting effects on the formation of tidal sand waves

Abstract

A model is developed to investigate the process which leads to the formation of sand waves in shallow tidal seas characterized by a heterogeneous sea bed composition. The main goal of the analysis is the evaluation of the effects that a graded sediment has on the formation of the bottom forms and the investigation of the sorting process induced by the growth of the bottom forms. The analysis is based on the study of the stability of the flat bed configuration, i.e. small amplitude perturbations are added to the flat bottom and a linear analysis of their time development is made. For an oscillatory tidal current dominated by one tidal constituent, the results show that the graded sediment can stabilize or destabilize the flat bottom configuration with respect to the uniform sediment case, depending on the standard deviation σ* of the grain size distribution and on the ratio between the horizontal tidal excursion and the water depth. For moderate values of , i.e. values just larger than the critical value for which the sediment is moved and sand waves appear, the presence of a sand mixture stabilizes the flat bed. On the other hand, for large values of , the mixture has a destabilizing effect. In both cases the effect that a sand mixture has on the stability of the flat bed configuration is relatively small. Moreover, for moderate values of , the fine fraction of the mixture tends to pile up at the crests of the bottom forms while the coarse fraction moves towards the troughs. For large values of , the grain size distribution depends on the value of σ*. The results are physically interpreted and provide a possible explanation of the apparently conflicting field observations of the grain size distribution along the sand wave profile, carried out in the North Sea.