will have peaks and nodes in the seaward direction in addition to the 

 peaks and nodes in the longshore direction. 



Edge waves 



Reflected normally 



incident wave 



Figure 34. Offshore profiles of edge waves 

 (from Guza and Inman, 1975). 



Guza and Davis (1974) carried out a theoretical investigation of the 

 mechanism of edge wave generation by normally incident, shallow-water 

 waves on a constant beach slope. They define the longshore wavelength 

 of the edge wave by the longshore wave number, k y , given by 



y- 



where 



* -7 



y l. 



y \ y) 



g(2n + 1) tan 8 



(2n + 1) B « 1 



(213) 



(214) 



Lj, is the wavelength of the edge wave, Tj, the period of the edge wave, 

 and B the angle of the nearshore slope in radians. Guza and Davis 

 attribute the generating mechanism to a nonlinear interaction between 

 the incident wave and a pair of progressive edge waves with frequencies 

 defined by to, and to 9 where to = 2ir/T and 



CO = to, + (0, 



(215) 



i.e., the incident wave frequency is equal to the sum of the two edge 

 wave frequencies. The two edge waves have the same wavelength, but 

 propagate in opposite directions along the shoreline. Therefore, the 

 edge wave pair forms a standing wave. This standing wave will always 

 have a frequency equal to one-half the incident wave frequency (a period 

 twice the incident wave period) even though the frequencies of the edge 

 wave pairs may vary, as shown in Table 3. Where the frequencies of the 

 two progressive edge waves forming the pair are different, the nodes and 

 antinodes of the standing wave will move in the direction of the edge 

 wave with the higher frequency (shorter period) . Defining the edge 

 wave with the lower frequency by 



102 



