where c is a coupling coefficient reevaluated by Guza and Bowen and 

 given in Table 3 in dimensionless form, a e the dimensional critical 

 incident wave amplitude, v the dimensional kinematic viscosity, and 

 the values N 1 and N2 define n for w 1 and <d 2 , respectively. 

 The dimensionless value of ky used in Table 3 and equation (219) is 

 given by 



K = k * 7-7-77 (220) 



y y o*) 2 



where k$ is the dimensional wave number of the edge wave defined by 

 equation (213) and w* the dimensional radian frequency, 2ir/T, of the 

 incident wave, The dimensionless values of o^ and oj 2 used in Table 

 3 and equation (219) are given by 



CO* co* 



1 0)* z CO* 



where <o* and to| are the dimensional values. Table 3 shows that the 

 number of* edge wave pairs would increase as the incident wave amplitude 

 increases, i.e., the primary pair (Nj = N 2 = 0) would be excited while 

 the wave is still some distance from the shoreline and the other pairs 

 would be excited closer to the shoreline as the wave amplitude increases. 

 Therefore, the primary pair of edge waves would experience the greatest 

 growth. 



************** EXAMPLE PROBLEM 16 *************' 



GIVEN : A tsunami with a period of 20 minutes approaches the shoreline 

 on a constant shelf slope S 2 = 0.001 ($ = 0.001). It is assumed that 

 the nearshore slope is steep enough for the wave to reflect strongly 

 from the shoreline. 



FIND : 



(a) The wave periods and wavelengths of the first three edge wave 

 pairs (N x = l5 N 2 = 0), (N x = 0, N 2 = 1), and (Nj = 0, N 2 = 2) , and 



(b) the wave amplitudes necessary to excite the first three edge 

 wave pairs . 



SOLUTION : 



(a) From Table 3 



(N x = 0, N 2 = 0) coj = 0.5 co 



2Tr - 0.5 2JL= 0.5 2ir 



T, T 20 x 60 



104 



