Carrier, Shaw, and Miyata (1971) suggest an approximate method for 

 determining resonant wavelengths, for harbors with entrance channels, 

 which will be more generally applicable than equation (299). Their 

 method assumes that the resonant wavelength, L (L C = 0), for an equiva- 

 lent harbor of the same dimensions but having no entrance channel (L c = 

 0) , can be obtained. Correcting an error which appears in Carrier, Shaw, 

 and Miyata, the resonant wavelength for the harbor with an entrance chan- 

 nel is then given by the equation 



o 

 2tt 



L L, 



a b 



I/(L 

 o a 



0) 



(2tt) 



1/2 



(300) 



The resonant wavelength where L c 

 results (see Fig. 46). 



can be obtained using Miles' (1971) 



For a harbor with an entrance channel (Fig. 45), Miles (1971) indi- 

 cates that narrowing the entrance width or increasing the length of the 

 entrance channel will significantly increase the response of the harbor 

 to the Helmholtz mode, which may dominate tsunami response. This narrow- 

 ing or lengthening also has the effect of decreasing the resonant fre- 

 quency (Carrier, Shaw, and Miyata, 1971). Carrier, Shaw, and Miyata point 

 out that lengthening the entrance channel to a harbor also increases the 

 frictional resistance so amplification factors for a very long entrance 

 channel may be significantly reduced (although the resonant frequencies 

 would still be less than for a harbor without an entrance channel; i.e., 

 where L c = 0) . 



Seelig, Harris, and Herchenroder (1977) present a numerical means for 

 analyzing harbors responding to the Helmholtz mode of resonance. The 

 method uses a Runge-Kutta-Gill technique where 



dh 



b 



dt 



(301) 



hj, is the surface elevation of the water in the harbor above some arbi- 

 trary fixed datum, Q the flow rate through the entrance channel, and 

 Aj> the area of the harbor (A^, = Lj, B) . The governing differential 

 equation is 



where 



^a = _£ / jl . 



dt 



U, 2 " A 2 ) 



\ bo so' 





^ba 



£ 

 a 



1 (K 

 9 b 



V 



I F 

 9 



(302) 



(303) 



143 



