Resonant Response of Harbors (The Harbor Paradox Revisited) 



The period for the Helmholtz mode is given by 



i/p ^ i/p 

 To = \o/c = 27r(A/gh)"'/Co . (6.7) 



Choosing R = 1000' and h = 20', we obtain Tq = ZX^/ttR minutes, 

 which approximates typical tsunami periods (20 - 40 minutes) for 

 Xq/ZttR in the range of 5-10 (see Fig. 5). We infer that a large 

 harbor with a short entrance (i /R « 1) or a small harbor with a 

 canal (i /R ~ 0.3 - 3) may act as a Helmholtz resonator under 

 tsunami excitation. 



REFERENCES 



Bartholomeusz , E. F. , "The reflexion of long waves at a step," 

 Proc. Camb. Phil. Soc. , 54, 106-18, 1958. 



Carrier, G. F. , Shaw, R. P. and Miyata, M. , "The response of 

 narrow mouthed harbors in a straight coastline to periodic 

 incident waves , " J. Appl. Mech. (in press), 1970. 



Garrett, C. J. R. , "Bottomless harbors," J. Fluid Mech. , ^3, 

 443-49, 1970. 



Lamb, H. , Hydrodynamics , Cambridge Unlvers Ity Press , 1932. 



Lee, J. J. , "Wave induced oscillations in harbors of arbitrary 

 shape, " J. Fluid Mech., 45, 375-93, 1971. 



Miles, J. W. , "The analysis of plane discontinuities in cylindrical 

 tubes," Parts I and II. J. Acoust. Soc. Am. , \J_, 259-71, 

 272-84, 1946. 



Miles, J. W. , "The coupling of a cylindrical tube to a half- infinite 

 space," J. Acoust. Soc. Am. , 20 , 6 52-64, 1948. 



Miles, J. W. , "Surface-wave scattering matrix for a shelf," 

 J. Fluid Mech., 23, 755-67, 1967. 



Miles, J. W. , "Resonant response of harbors: an equivalent- circuit 

 analysis," J. Fluid Mech. , 46, 241-65, 1971, 



Miles, J. W. and Munk, W. H. , "Harbor paradox," J. Waterways 

 Harb. Dlv. , Am. Soc. Civ. Engrs , 87, 111-30, 1961. 



Morse, P. M. , Vibration and Sound , New York: McGraw-Hill, 1948. 



Rayleigh, Lord, Theory of Sound, New York: Dover, 1945. 



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