Guza and Bowen (1975) investigated edge waves generated by incident 

 waves at some arbitrary angle of incidence, a , with the shoreline 

 (see Fig. 30) . Defining a parameter 



y = sin a tan g (221) 



the longshore wave numbers, k 1 and k 2 , of the primary edge wave pair 

 (N. = 0, N„ = 0) are given as 



k l = a f a (1 + 2 ^ t 222 ^ 



1 4g tan g 

 and 



2 



k 2 = Z — I a (1 - 2y) (223) 



z 4g tan g v ' 



when the angle of incidence, a,, is small, and where co is the radian 

 frequency of the incident wave. Where oij = 0, equations (222) and (223) 

 reduce to equation (214) . The standing edge wave where a, > will pro- 

 gress along the shoreline, and the drift speed, cj, of a node or anti- 

 node of the prd-mary edge wave pair is now given as 



c d . _ (224) 



Gallagher (1971) shows that an increase in the angle of incidence, 

 aj_, will produce greater edge wave energy at higher frequencies (shorter 

 periods) . 



Guza and Bowen (1976) discuss the height of the edge waves occurring 

 along a coastline. They show that the maximum edge wave amplitude at the 

 shoreline is theoretically three times the amplitude of the incident wave 

 for a straight coastline. Gallagher (1971) indicates that energy would 

 be lost because of bottom friction and the disperison caused by irregu- 

 larities in the coastline. Guza and Bowen (1976) indicate that edge wave 

 growth is limited by radiation of energy to deep water and by finite- 

 amplitude demodulation; i.e., as the edge waves increase in height their 

 natural frequency increases and no longer matches the forcing frequency. 

 From equation (213) and the work of Munk, Snodgrass, and Gilbert (1964) 

 relating trapped modes to leaky modes, it can be seen that leaky modes 

 (i.e., edge waves radiating energy to deep water) will only occur on 

 steep nearshore slopes. These nearshore slopes are very short in com- 

 parison to the tsunami wavelength, and are not of concern here. The 

 edge waves associated with the tsunami are assumed to occur over the 

 wider and flatter shelf slope shown in Figure 33. 



A progressive edge wave moving along a coastline may be reflected 

 from an obstacle such as a large headland. Guza and Bowen (1975) demon- 

 strate that this could produce a standing edge wave with higher amplitudes 

 near the obstacle. Reflection could also occur from a depth discontinuity 

 such as a submarine canyon in the manner described in Section VI, 3. 



107 



