10. Since both leaky and edge waves have velocity components that 

 reflect at the shoreline, they have a standing structure of nodes and anti- 

 nodes in the crossshore (Figure 3). Note the similarity between modes, 



EDGE WAVES 



REFLECTED NORMALLY 



INCIDENT WAVE 



Figure 3. The offshore structure of edge wave modes to 3 

 plotted in terms of nondimensional offshore distance x 



particularly near the shore. Note further that the standing incident wave, an 

 example of the leaky waves, also looks similar. This structure for an edge 

 wave is defined by the cross-shore amplitude function <t> in Equation 1 and 

 can be analytically determined for a few simple beach profiles. On a plane 

 beach of slope 6 , it takes the form 



<t>(x) = e" kx L (2kx) 



(3) 



where 



L - Laguerre polynomial of order n 

 n = the mode number of the edge wave (Eckart 1951) 

 The cross-shore functions for the first few modes are listed in Table 1. The 

 mathematical solution for a normally incident leaky wave on a plane beach 

 (Lamb 1932; Suhayda 197*0 is 



