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.
When strong tidal currents are present, tidal bedforms i.e. undulations of the sea bottom are observed which are characterized by wavelengths much longer than the water depth. Two different bedforms are observed, namely tidal dunes (also named sand waves) and sand banks (also named tidal ridges). The wavelength of the tidal dunes is of the order of ten times the water depth and the crests of the bottom forms are almost perpendicular to the oscillating tidal current. Moreover, tidal dunes are often observed to migrate in the direction of the residual current, even though example of bottom forms migrating against it do exist (Allen, 1994; Stride, 1982). On the other hand, the wavelength of sand banks is of the order of hundred times the water depth and their crests are almost aligned with the main direction of the tidal current, usually forming small counter-clockwise angles. Moreover, sand banks hardly move (Allen 1994; Dyer & Huntley, 1999). The height of tidal dunes is of a few metres, even though there are tidal dunes which are characterized by height up to tens of metres (Van Landeghem et al. 1999). On the other hand, sand banks have much larger heights which may be a significant fraction of the local water depth. Hulscher et al. (1993) pointed out that the presence of both tidal dunes and sand banks is highly correlated with the presence of intense tidal currents. While the migration of sand banks is negligible, tidal dunes have significant migration speeds which can reach tens of metres per year. The predictions of the migration of tidal dunes is relevant for the offshore industry and the maintenance of navigation channels. Indeed, a pipeline, on a sea bottom characterized by the presence of tidal dunes, may experience large free spans which can induce oscillations, fatigue phenomena and, under certain conditions, even the buckling of the pipeline or its break. Therefore pipelines, in areas where tidal dunes are expected to be present, are often buried at a significant depth below the level of the expected troughs of the dunes, which is an expensive operation. Moreover, migrating tidal dunes can move large volumes of sand in shipping channels thus decreasing the local water depth and asking for periodic dredging activities. Finally, migrating tidal dunes can decrease the local sea bottom level and mine the stability of offshore structures, as wind mill parks and oil platforms. The horizontal length scales of sand banks and sand waves are quite different from the length of the tidal wave and Hulscher et al. (1993) suggested that the appearance of tidal dunes and sand banks might be due to a free instability of the morphodynamic system describing the interaction between the currents induced by tide propagation and the cohesionless sea bottom. Hence, they concluded that the process which leads to the formation of these bottom forms can be investigated by means of a linear stability analysis. Stability analyses aimed at investigating the formation of tidal dunes and sand banks were formulated by different authors (Huthnance, 1982a, b; Hulscher et al., 1993; Hulscher, 1996; Besio et al. 2006). However, these models consider symmetrical tidal currents and the bottom forms predicted by the stability analyses do not migrate. The model by Besio et. al (2006) is presently extended to take into account more than one tidal constituent, thus allowing to predict the speed of migration of tidal dunes.