Abstract

Sand ridges with longitudinal crests that have spacings of hundreds to thousands of metres have been observed forming on sandy 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 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 many shelves. On the shelves that we shall refer to as “wave-dominated”, a mechanism that may account for systems of sand ridges is associated with 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 outlined. The surface hydrodynamics is modelled by the nonlinear dispersive shallow-water theory. The wave-induced flux of sediment is calculated using the mass-transport velocity. The bed topography is then described using a continuity equation. This theoretical description results in a coupled system of nonlinear partial differential equations. This system may be simplified somewhat by using a model decomposition of the surface wave. The resulting equations are then approximated numerically in order to make quantitative predictions about field situations. The model has been tested against in situ measurements made on the Atlantic coast of the U.S.A. (the Delmarva and Virginia coastal shelves). 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 very long time required for the formation of fully-developed bars provides an a posteriori indication of the stability of these structures. Moreover, general trends in the onshore transport, and slow ridge migration due to shore retreat can also be predicted using this model.