Miles 



< 



^4- 



Fig. 1. Schematic diagram of harbor opening on straight 

 coastline; t,j, X^^ and t,^ are, respectively, the 

 incident, specularly reflected, and scattered 

 waves 



(from X = 0) waves on the hypothesis of the monochromatic time 

 dependence exp (jcot), where ^ denotes free-surface displacement 

 (we omit the modifier complex amplitude of throughout the subse- 

 quent development), k is the wave number, and Vj = Z^j(0,0) is 

 a measure of the excitation of the harbor through M. By narrow, 

 we imply 



l/R « 1 and ka « 1 , 



(1.3a,b) 



where a is the width of M, and R is a characteristic dimension 

 of H. These restrictions imply that the motion within H is small, 

 and that the energy of the motion induced by Vj (or, more precisely, 

 by the pressure pgVj ) is dominantly kinetic and concentrated near 

 M (the narrowness of which implies locally high velocities), except i 

 in the spectral neighborhoods of the resonant frequencies of the 

 harbor. An appropriate measure of this dominant motion is the flow 

 through M, say I, which, by hypothesis (linearized theory) , must 

 be simply proportional to Vj , We regard Vj and I as the voltage 

 and current at the input terminals of an equivalent circuit and seek 

 a description of the resonant response of the harbor in terms of the 

 voltages induced in this equivalent circuit. 



The input impedance, Zj = Vj/l, for the configuration of 

 Fig, 1 may be resolved (see Fig, 2a) into a series combination of a 

 radiation impedance, Z|^= Rj^ + J^' ^^*^ ^ harbor impedance, 

 Z^= jXu, where R^| 1 1 , XJlp/co, and Xyjlj^/co are respectively 

 proportional to the power radiated from H through M (in the form 



96 



