Long-period waves on a natural beach

A field experiment is described in which three two-component electromagnetic flowmeters were used to measure simultaneously the longshore (υ) and onshore-offshore (u) velocity components along a line normal to the shoreline and up to 100 m offshore. Spectral analysis of the data from this experiment reveals the presence of a set of discrete spectral peaks of low frequency (0.014–0.05 Hz) which dominate over the wind wave peak close to the shoreline and which decay in amplitude with distance from the shore. The amplitudes of the velocity components for each of the four lowest-frequency (and clearest) peaks have been plotted against distance from the shoreline and are found to compare satisfactorily with the calculated edge wave amplitude variation for the beach. Phases between u, υ at one flowmeter and between u, u at different distances offshore have also been found from cross spectra and confirm that the peaks are due to edge waves. It is suggested that each of these low-frequency peaks corresponds to a progressive edge wave mode at the cutoff frequency for the beach. Ball (1967) and Guza and Inman (1975) calculate that the cutoff frequency υ for an edge wave of mode n should be proportional to n(n + 1 )1/2, where the constant of proportionality is dependent on the subaqueous beach profile. The frequencies of the four lowest-frequency peaks agree well with the predicted frequencies for the lowest modes of cutoff edge waves (n = 1, · · ·, 4), and the observed offshore decay of amplitude at each frequency indicates that assigning the peaks to these modes is correct. Energy exchange between these cutoff modes, through nonlinear interaction, is also suggested by the results. The significance of observing progressive edge waves on this beach is briefly discussed.