Miles (1972) indicates that for waves passing from a Continental 

 Shelf into a harbor, where the dimensions of the harbor and the entry 

 channel are small compared to the local wavelength of the tsunami, the 

 response of the harbor is essentially restricted to the Helmholtz mode; 

 i.e., the lowest mode of resonance. The harbor undergoes a pumping 

 motion where the water level in the harbor is assumed to rise and fall 

 uniformly across the total area of the harbor (Carrier, Shaw, and Miyata, 

 1971). The water passing through the entry channel is assumed to have a 

 high velocity, represented as kinetic energy; the water in the harbor has 

 a much lower velocity, and the rise and fall of the water level in the 

 harbor is represented as potential energy. 



Carrier, Shaw, and Miyata (1971) show that the wave number, 

 Helmholtz resonance is represented 



for 



!*(*„!). 



1/2 



(299) 



where L a is the length of the entrance channel (Fig. 45). The term 

 (b/ir) in (k G b/2) in the denominator represents the effect of energy 

 radiation from the seaward end of the entrance channel (Rayleigh, 1945; 

 Miles, 1948). Equation (299) is restricted to very limited cases, and 

 Figure 46 shows a comparison of equation (299) and the results of Miles 

 (1971) for a harbor with a zero-length entrance channel (L e = 0). Figure 

 46 shows that equation (299) will generally predict resonant wavelengths 

 that are too short (and therefore predicted resonant periods with values 

 lower than the actual resonant periods) . 



Figure 45. Harbor with an entrance channel 



141 



