Miles 



is the radiation impedance of the harbor mouth. The equivalent 

 circuit corresponding to (3.2) is sketched in Fig. 2a. 



The velocity distribution in M for ka « 1 corresponds to 

 that for potential flow. Normalizing this distribution according to 

 (2. lib), we obtain 



f{y) = Tr-'[(ia)^- y^]-"'^ (|y|<a). (3.5) 



Substituting (3.5) into (3.4) and invoking ka « 1, we obtain 



Zm= (w/c^)[i + jA^(ka)] (ka « 1), (3.6) 



where 



TrA^^= ln[8/(vka)] , (3.7) 



and In -y = 0. 577. . . is Euler's constant. 



IV. RESONANT RESPONSE 



An appropriate measure of the response of the harbor to a 

 prescribed incident wave is the mean-square elevation, say or^, as 

 determined W averaging over both space and time (the temporal 

 average of t, is iKI )• 



(r^=iA'' r lU^dA. (4.1) 



Substituting % into (4. 1) from (2. 7) , invoking (2.8) for G and (2.11) 

 for u, carrying out the integration over A with the aid of (2.9c), 

 and invoking (2.14) for Zn = Vn/l, where Vp is the voltage induced 

 across Zn by I, we obtain 



2 



(T 



= i^l»-r,'|V„|^-i|V,|^^C^U), (4.2) 



where 



-1/2 1,, /,, I -1/2 



GnCf) = fin |Vn/Vi | = fin |Zn/(ZM+ Z^) | (4.3) 



is the amplification factor for the n'th mode, and 



/C = k^A = w^(A/gh) (4.4) 



104 



