Résumé
Zenkovitch (1959) first described cuspate spits as a limited category of shore-connected features that result from symmetrical wind/ wave forcings and/or peculiar initial shore configuration. Later on, Asthon et al. (2001) and Asthon and Murray (2006) proned that cuspate spits, flying spits and other shoreline features derive from instabilities inherent in the relationship between alongshore sediment transport and local shoreline orientation. They exhibited a comprehensive weakly non-linear theory for cuspate and spit dynamics, and gave a striking numerical solutions to the problem. Recently, Bouchette et al. (2014) provided an alternative explicit formulation for the growth of cuspate spits through time. From this last formulation, it was demonstrated that there exists an exact relationship between the amplitude, the length of a cuspate on one side, and the longshore diffusivity and the time on the other side. In the present work, we explore how this relationship can be used to predict various coastal characteristics at decadal/geological time scales as soon as a cuspate develops in the area concerned. This formulation can be considered as a method for the datation of a cuspate spit. Alternatively, it can allow to estimate the mean fluxes of sediment trapped along the shore. The model is validated thanks to a comparison with observed cuspates. The cuspate law suggests that the length of the cuspate and its amplitude may be related through a power law (to the power of three). We demonstrate that this power law is not a simple mathematical result but does exist in the nature. The occurrence of a power law suggests also that more underlying physics remain to be analysed in the process of nucleation and growth of cuspate spits.