RESONANT RESPONSE OF HARBORS 

 (THE HARBOR PARADOX REVISITED) 



John W. Miles 



University of California 

 San DiegOj California 



I. INTRODUCTION 



We consider the surface- wave response of a harbor to a 

 prescribed, Incident wave In an exterior half-space on the hypo- 

 thesis of linearized, shallow- water theory, an Ideal fluid, and a 

 narrow inouth, Invoking the equlvcilent- circuit techniques that have 

 proved so efficient In attacking analogous problems in acoustics 

 and electronnagnetlc theory. These techniques offer significant 

 advantages In practice: (1) the sub-problems of external radiation, 

 channel coupling, and Internal resonance may be attacked separately; 

 (11) the equivalent- circuit parameters may be expressed as homo- 

 geneous, quadratic forms that may be simply approximated without 

 solving the complete boundary- value problem; (111) observed values 

 (Including those from model experiments) of dominant parameters, 

 such as resonant frequencies, may be Incorporated In preference 

 to, or In place of, theoretical values; (Iv) empirically determined 

 dissipation parameters (resistances) may be Incorporated; (v) ana- 

 log computation, both conceptual and electrical, may be Invoked to 

 expedite understanding of the resonant response. 



Referring to Fig, 1 , we consider a harbor H that opens to 

 the sea through a narrow mouth M In a straight coastline, x = 0. 

 Let 



; (x,y) =i V. exp {- jk (x cos 9. + y sin 9; )} (1.1) 



and 



;r=;i(-x,y) (1.2) 



be the complex annplltudes of the Incident and specularly reflected 



1 



A more detailed version of this work has been published elsewhere 



[Miles, 1971] . 



95 



