On the Migration of Tidal Dunes (Sand Waves)

A morphological model to predict the formation of tidal dunes (sand waves) and their migration is described. The analysis assumes that the appearance of the bedforms is due to the growth of the most unstable component of an initially random perturbation of small amplitude, forced by a uniform tidal flow. Results are presented for a unidirectional tide, even though the analysis can be easily extended to an elliptical tide. The wavelength of the fastest growing component of the bottom perturbation is found to fall in the range of the wavelengths of the tidal dunes observed in the field. The forcing tidal flow contains both the M4 and Z0 constituents, which are superimposed to the main M2 constituent and the bottom forms are found to migrate either in the direction of the residual current or in the opposite direction, depending on the parameters of the hydrodynamic and morphodynamic problems. A comparison of the theoretical results with field data shows that the model provides fair predictions of both the geometrical characteristics of the tidal dunes (sand waves) and of their migration speed.