Abstract

Long-crested sand ridges with successive crest-to-crest distances of hundreds to thousands of metres are known to form on shelves. The stability of these sand bodies suggests that they may be time-averaged responses to the complex hydrodynamics of their environment. Consideration of the large scales involved seems to indicate that locally-generated storm waves are not responsible for these structures. Such disturbances may indeed modify existing bars, but do not appear to contribute essentially to the formation and mean features of sand ridges. On “wavedominated” shelves, a mechanism that may account for systems of sand ridges is associated with the development of infragravity waves (waves with periods of 0.5 to 5 min).

A description of the formation of bars on shelves by the propagation of infragravity waves is proposed. The hydrodynamics of the surface are modelled by a nonlinear, dispersive, shallow-water theory. The wave-induced flux of sediment is calculated using an associated mass-transport velocity. The bed topography is then described using a continuity equation. Such a theoretical description results in a coupled system of nonlinear partial differential equations. This system may be simplified somewhat by using a modal decomposition of the surface wave. The resulting equations are then approximated numerically in order to make quantitative predictions about field situations.

The model was tested against measurements made in situ on the Atlantic coast of the U.S.A. (the Delmarva coastal shelf). The agreement between the predictions and the measurements was sufficiently good to warrant some confidence in the mechanism inherent in the model’s derivation. Specifically, the successive crest-to-crest distances, which in the model depend only on the mean bed slope and the incident wave conditions, agree quite well with measured values. The long time scale for formation of fully-developed bars that is a property of the model provides an a posteriori indication of the stability of these structures. Moreover, general trends in onshore transport and in slow ridge migration due to shore retreat can also be predicted using this model.