Resonant Response of Harbors (The Harbor Paradox Revisited) 



uAK=4+ln (4R/a) (eM« 1). 



(6.5) 



Combining (3.7) and (6.5) in (4.8), we obtain 



irA = 3.0135 + 2in(R/a) - in(kR) , 



(6.6) 



wherein k = k^s for n # 0, 



The resonant wavelength, \q- Zir/ko , Gq = Qo> and Pq for 

 the Helmholtz mode, as determined by (4.9a), (4.i0a), (4.12a), and 

 (4. 17) in conjunction with (6. 6) are given by the lowest curves In 

 each of Figs. 5-7. The higher curves in Figs. 5-7 are based on 

 (5.8) - (5.10) and illustrate the striking effects of an intervening 

 caneil on Helmholtz resonance. Qmsi a-S determined by (4.12), is 

 plotted in Fig. 8 for the first five modes. The rem.arkable sharpness 

 of the higher modes, vis-a-vis the Helmholtz mode, is borne out by 

 Lee's [1971] experiments. 



O.OI 



0.03 



0.1 



0.3 



b/R 



Fig. 5. Wavelength for Helmholtz resonance of circular harbor plus 

 canal (b= a for i = 0). The results are strictly valid only 

 for b/R « 1 and kgi « 1, but the corresponding errors 

 are not likely to exceed 5 - 10% for b/R < 1 and k©^ < 2 



111 



