the shoreline some of the wave energy is reflected shoreward from the 

 transition in water depth at the seaward limit of the shelf. This is 

 further illustrated in Figure 33 where d s is the water depth at the 

 toe of the nearshore slope, d2 the water depth at the seaward limit of 

 the shelf, dj the water depth at the seaward limit of the steep tran- 

 sition in water depth, Sj the slope of the steep transition, S2 the 

 slope of the shelf, and S 3 the nearshore slope. 



Wave Reflected Seaward 

 from Shoreline 



Wave Reflected Shoreward 

 from Depth Transition 



Shoreline 



] s 2 Nearshore Slope 



Steep Transition 



Figure 33. Reflected waves on a shelf. 



The wave reflected shoreward from the steep transition may be ir 

 radians out of phase with the wave transmitted seaward across the tran- 

 sition. However, the actual phase difference will depend on the geometry 

 of the shelf and transition, and the water depth. This was illustrated 

 in example problem 5. For perfect reflection, the wave reflected from 

 the shoreline will be in phase with the initial wave incident on the 

 shoreline. The time, t , for the wave to travel the distance, a g , 

 from the steep transition to the nearshore slope will be the same as the 

 time required for the reflected wave from the nearshore slope to travel 

 back to the steep transition in depth. Therefore, where the wave re- 

 flected from the transition is ir radians out of phase with the incident 

 wave, resonance will occur if 



nT 



2t = -=- 

 s 2 



(205) 



where T is the incident wave period, and n = 1, 2, 3, . . . 



Noting that C = /gd where d g < d < d 2 , for a wave with a normal 

 angle of incidence, 



f dx 

 "Jo C 



(206) 



99 



