and the wavelength is 



L = CjT = 171.5 x 60 x 60 = 617,400 meters (384 miles) 



From equation (178), wave instability is given by 

 (a 1 L 1 ) 1/2 > 2d 2 

 (a x x 617,400) 1/2 > 2 x 200 



a. > 0.26 meter (0.85 foot) 



Waves with a deepwater amplitude less than 0.26 meter will not 

 decompose. 



************************************* 



Using the results of Mason and Keulegan (1944), the above examples 

 illustrate that the longer period tsunamis are much more likely to 

 decompose where the waves have the same height in the deep ocean. 



Street, Burgess, and Whitford (1968) investigated solitary waves 

 passing from an initial water depth, over a steep slope, and into a 

 shallower water depth. They obtained results similar to those of other 

 investigators, showing that each wave changed from a single wave into a 

 train of several waves. In some instances, there was also a significant 

 increase in wave height. Defining the initial water depth as di, the 

 shallower depth as d2, the initial wave height as H^, and the wave 

 height in the shallower water depth as H.£, as the ratio di/d2 increased, 

 relative wave height H^/H^ reached a maximum value for any initial wave 

 height H^ and then decreased. As H^/di decreased, the maximum value 

 of H^/H^ became greater and occurred at a higher value of d 1 /d 2 . The 

 locus of the maximum values of wave enhancement , H^/H^ , are shown in 

 Figure 29 with the results for the solitary wave experiments. 



Madsen and Mei's (1969) numerical results for the propagation of 

 long waves give the results shown in Figure 26 for a solitary wave 

 passing over a slope and onto a shelf. The numerical results of Street, 

 Chan, and Fromm (1970) give the results shown in Figure 27 for a solitary 

 wave, and the results shown in Figure 28 for a train of waves. Goring 

 (1978) has also recently carried out experiments on solitary waves 

 propagating onto a shelf. His results are similar to those of Street, 

 Chan, and Fromm (1970) and Madsen and Mei (1969). 



In all cases where a single wave produced a series of wave crests, 

 the first wave crest of the series was the highest . It may be presumed 

 that a number of initial wave crests will produce the same number of 

 groups of wave crests, each having a high initial wave followed by smaller 

 waves. The numerical work of Street, Chan, and Fromm (1970) for wave 

 trains is inconclusive in this regard as Figure 28 shows the additional 

 wave crests, but does not separate the waves into groups associated with 

 the initial crests. 



86 



