Abstract
The numerical solutions for the dispersion of linear, shallow‐water edge waves are compared with observed alongshore wavenumber‐frequency spectra of edge wave variance to examine their prediction of the effects of nonplanar bathymetry and moderate mean alongshore currents. Field observations were made at the two Southern California Nearshore Sediment Transport Study field sites, Torrey Pines (1978) and Leadbetter (1980) beaches. On Torrey Pines beach, where the bathymetry is very planar except for a concave (steepening landward) beach face, observed departures from the analytical plane beach dispersion solution, attributed to the concave face, are predicted by numerical dispersion solutions using the measured cross‐shore depth profile. On both beaches, asymmetry in observed dispersion curves of upstream and downstream progressing edge waves are well predicted by numerical dispersion solutions using the cross‐shore profile of measured mean alongshore current. Spectra of the alongshore velocity component from both beaches show changes in edge wave mode dominance with increased frequency. Oltman‐Shay and Guza (1987) demonstrated that mode dominance transition with frequency, as observed from a fixed offshore location, is associated with the seaward decay of edge waves and that the approximate frequency of mode transition is predicted by the profile solutions for edge wave variance and the assumption of equal shoreline elevation variance amongst modes. A submerged concave beach face at Torrey Pines beach is shown to alter the predicted cross‐shore scaling of the edge wave profiles from that predicted when mean water is below the concave beach face, and therefore to alter the mode transition frequency predictions. Different mode transition frequencies are observed in spectra from data runs with mean water levels both above and below the concave beach face, and the differences are shown to be reasonably predicted using edge wave profile solutions for the measured beach profile. For these data, observed and predicted mode transition frequencies did not change appreciably in the presence of mean alongshore current, implying that large changes in cross‐shore scaling of the edge wave profiles did not occur. However, as has been previously shown by Howd et al. (1992), there are also local edge wave profile shape changes because of the cross‐shore shear of the mean alongshore current. Verification of these predicted local shape changes can not be made with these data. Confidence in cross‐shore profile solutions is of practical importance for estimates of shoreline variances from offshore measurements. On these two beaches, estimates using both numerical solutions for the measured depth and current profiles, and analytical solutions for plane beach approximations typically differ by only 10 to 40%.
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