n(x,t) = a J (Y4x) cos (ot: 



2 (4) 



o x 



where 



J = zeroth order Bessel function 

 X = nondimensional offshore' distance 



11. The normally incident leaky wave theoretically has an infinity of 

 nodes and antinodes extending out to deep water and beyond. On the other 

 hand, the cross-shore structure of the trapped edge wave is exponentially 

 decaying offshore with maximum amplitude at the shoreline, the number of nodes 

 equaling the mode number of the wave. As shown in Table 1 and Figure 3, a 

 mode edge wave has only the exponential decay, whereas the mode 1 wave goes 

 through one phase change (the node) as it exponentially decays. The higher 

 modes have many nodes and antinodes and extend farther offshore. In fact, 

 their cross-shore structure looks very much like that of the normally incident 

 leaky wave close to shore. The physical dimensions of these waves also vary 

 with frequency and beach slope. This is shown in the nondimensional cross- 

 shore coordinate used in Figure 3; the cross-shore structure will be more 

 tightly trapped to the shoreline in dimensional scales for high frequencies 

 and shallow beach slopes. 



Table 1 



Offshore Description of the First Four 



Edge Wave Modes 



n <t>(x) 



1 ■ e" kx 



1 ( 1 - 2kx) • e" kx 



2 (1 - 4kx + 2k 2 x 2 ) • e~ kx 



3 (1 - 6kx + 6k 2 x 2 - « k 3 x 3 ) • e _kx 



10 



