American Geophysical Union Fall Meeting 2000
******************************************

A. Brad Murray, Olivier Arnoult, Andrew Ashton, Duke University

Feedbacks between perturbations on an initially straight shoreline and wave-driven alongshore sediment transport can theoretically cause an instability leading to the growth of finite-amplitude shoreline features.

Some models of the evolution of large-scale shoreline planforms have treated alongshore transport as a diffusive process. This treatment is appropriate when waves in deep water approach shore at near-normal incidence. A commonly used formula for alongshore sediment transport, based on the energy flux toward shore and the component of that flux directed alongshore, can be recast in terms of deep-water wave heights and angles relative to the local shoreline orientation (assuming linear shoaling and refraction over shore-parallel contours). Simple analysis shows that for any off-shore wave angle less than that which produces the maximum transport, perturbations away from a straight shoreline will be damped.

However, when offshore wave angles are greater than that which produces the maximum transport (which we will call "high angle waves"), a straight shoreline is unstable. In this case, moving in the down-drift direction near the crest of a shoreline perturbation, the angle between the shoreline and the offshore waves will be diverging from the angle that produces maximum transport. Thus, at the crest sediment transport will converge, and the amplitude of the perturbation will increase. This result depends only on the non-linearity (the existence of a maximum) in the relationship between alongshore transport and the angle of offshore waves relative to the local shoreline orientation.

We have developed a numerical model to investigate the long-term, finite-amplitude behaviors possible on sandy shorelines. This simple model is similar to one-line models used to predict intermediate-scale shoreline evolution. However, the algorithm is generalized to treat arbitrary local shoreline orientations.

In the model, growth in amplitude and wavelength of shoreline features occurs whenever high angle waves predominate in the long-term wave distribution. If this distribution also creates a net alongshore drift of sediment, because of a prevalence of waves approaching from either positive or negative angles (e.g. from the north more than the south on a generally east-facing coast), features also migrate. In this case, they can overtake each other and merge, or repel each other, depending on the disparity in size between two features. These processes can generate forms resembling the kilometer-scale sand waves observed on some natural shorelines, such as a section of Lake Ontario coast where high angle waves from one direction dominate. Numerical experiments show that even in the limit of a distribution with predominantly high-angle waves approaching equally often from positive and negative directions, interactions between features lead to perpetual growth of larger features and disappearance of smaller ones. In either the net-drift or symmetrical distribution case, the amplitude and wavelength of shoreline features can grow to the 100-kilometer scale of some capes and cuspate forelands, such as along the southeastern coast of North America. Such experiments, which involve homogeneous initial conditions and forcing, show that complex, large-scale shoreline features could arise from instabilities inherent in the relationship between alongshore sediment transport and local shoreline orientation.