TRAPPED WAVES OVER SYMMETRICAL THIN BODIES

Explicit relations are derived for the dependence of the longshore wavenumber on the wave frequency of symmetric trapped waves or edge waves travelling near the cutoff frequency over submerged horizontally symmertric thin bodies or near-vertical Results for particular geometries are presented and shown to agree with certain explict solutions for edge waves over sloping beaches or trapped waves over a submerged narrow shelf, or a semicircular mound on the sea bed. Similar results are obtained for thin bodies extending vertically throughout the depth in open channels or for thin cross-sections in an acoustic wave guide.