Karin Bryan

Bar-Trapped Edge Waves

Thesis Approved December 1996

Edge waves are shallow water waves which are trapped along the shoreline waveguide by reflection and refraction. The cross-shore pattern of nodes and antinodes in edge waves has long been hypothesized to have the right lengthscale to explain longshore bars. However, different frequencies and modes have antinodes in different locations, and there is little existing field data to suggest frequency and mode selection. A bar can also provide a local minimum in shallow water wave speed,
(where h is depth), needed to produce a separate waveguide, which can trap and amplify edge waves relative to the shoreline. These trapped solutions have similar shapes over the bar, regardless of frequency or wavenumber. Calculations of drift velocity, in the absence of phase locking, show drift convergence near the top of the bar, at the top of the bottom boundary layer; these bar-trapped waves may cause bar growth. Edge waves react to a longshore current as though it were a change in the bottom topography; the profile will be deeper for edge waves traveling with the current and shallower for edge waves traveling against the current, with the magnitude of the change dependent on the direction and the strength of the current shear relative to the bottom slope. For strong shears, the bottom can be changed to the degree of creating a virtual bar, on which edge waves can also be trapped and amplified. This could be a mechanism for moving a bar, or creating a bar on a plane beach.

These theories were tested using frequency-wavenumber spectra of the longshore component or orbital velocity from observations taken during the DELILAH experiment, October 1990, Duck, N.C. Continuous, unexplained, diagonal lines of variance have been observed in this data, and similar data from other experiments. Here, these diagonal lines are shown to be evidence of bar-trapped edge waves. These lines not only have the same frequency-wavenumber coordinates as bar-trapped edge waves, but also vary in a predictable manner with changes in the longshore current and depth profile. For example, when the effect of the current was strong enough to remove the effect of the bar in theoretical predictions, the diagonal line of variance disappeared. (The diagonal line reappeared, when this strong current shear moved shoreward into the trough, at high tide). On such days, when the edge wave shape is strongly controlled by current (or for example on a plane beach), the expected affect on topography is unclear because the location of edge wave trapping moves, when the longshore current profile changes with changes the tide. However, on days when the edge wave shape is strongly influenced by the bar, calculations of cross-shore drift, using the DELILAH data to obtain realistic magnitudes, show the drift should allow the bar to grow or maintain itself against gravity and other destructive forces.