Modification of edge waves by barred-beach topography

A numerical model to calculate edge-wave profiles and wavelengths for arbitrary bottom profiles and given frequency was developed utilizing the model wave equation of Berkhoff (1972). Following Smith and Sprinks (1975), surface profiles and longshore wave numbers were found for fixed wave periods using an eigenvalue approach. The model was verified by calculating profiles and dispersion for a plane beach of mild slope, and comparing results with the analytic solution of Eckart (1951) and Ursell (1952). The model was then applied to the case of a beach with multiple offshore bars, with bar positions determined by the antinodal positions of a standing incident wave of a set frequency. Calculation of surface profiles for a range of frequencies using a fixed beach indicated that antinodes of the edgewave profiles tend to be trapped by the bars, suggesting the possibility that bars affect the long-wave climate in such a way as to lead to self-maintenance over extended periods. No effect of the bars on the dispersion relationship was found, and it was concluded that, for the particular beach profile used, the edge waves respond to the mean beach slope over the offshore length of the profile.