Abstract
It is well-known that near an infinite linear array of periodically spaced cylinders trapped waves of certain eigenfrequencies can exist. If there are only a finite number of cylinders in an infinite sea, trapping is imperfect. Simple harmonic incident waves can excite a nearly trapped wave at one of the eigen frequencies through a linear mechanism. However, the maximum amplification ratio increases monotonically with the number of the cylinders; hence the solution is singular in the limit of infinitely many cylinders. Recently, a nonlinear theory of subharmonic resonance of perfectly trapped waves has been completed. In this article the theory is further extended to random incident waves with a narrow spectrum centered near twice the natural frequency of the trapped wave. The effects of detuning and bandwidth of the spectrum are examined.
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References
Evans DV, Linton CM (1991) Trapped modes in open channels. J Fluid Mech. 225:153–175
Callan M, Linton CM, Evans DV (1991) Trapped modes in two-dimensional waveguides. J Fluid Mech 229:51–64
Linton CM, Evans DV (1992) Integral equations for a class of problems concerning obstacles in waveguides. J Fluid Mech 245:349–365
Evans DV, Levitin M, Vassiliev D (1994) Existence theorems for trapped modes. J Fluid Mech 261:21–31
Evans DV, Porter R (1997) Trapped modes about multiple cylinders in a channel. J Fluid Mech 339:331–356
Evans DV, Porter R (1998) Trapped modes embedded in the continuous spectrum. Q J Mech Appl Maths 52:263–274
Utsunomiya T, Taylor RE (1999) Trapped modes around a row of circular cylinders in a channel. J Fluid Mech 386:259–279
Maniar HD, Newman JN (1997) Wave diffraction by a long array of cylinders. J. Fluid Mech 339:309–330
Galvin CJ (1965) Resonant edge waves on laboratory beaches. EOS Trans. 46:112
Guza RT, Davis RE (1974) Excitation of edge waves by waves incident on a beach. J Geopys Res 79:1285–1291
Guza RT, Bowen AJ (1976) Finite amplitude Stokes edge waves. J Marine Res 34:269–293
Minzoni AA, Whitham GB (1977) On the excitation of edge wave on beaches. J Fluid Mech 79:273–287
Rockliff N (1978) Finite amplitude effects in free and forced edge waves. Math Proc Cambridge Philos Soc 83:463–479
Mei CC, Sammarco P, Chan ES, Procaccini C (1994) Subharmonic resonance of proposed storm Venice gates for Venice Lagoon. Proc R Soc London A 444:257–265
Sammarco P, Tran HH, Mei CC (1997a) Subharmonic resonance of Venice gates in waves. Part 1. Evolution equation and uniform incident waves. J Fluid Mech 349:295–325
Sammarco P, Tran HH, Gottlieb O, Mei CC (1997b) Subharmonic resonance of Venice gates in waves. Part 2. Sinusoidally modulated incident waves. J Fluid Mech 349:327–359
Vittori G (1998) Oscillating tidal barriers and random waves. J Hydraulic Engng 124:406–412
Li Y, Mei CC (2006) Subharmonic resonance of a trapped wave near a vertical cylinder in a channel. J Fluid Mech 561:391–416
Phillips O (1966) The dynamics of the upper ocean. Cambridge university press
Kinsman B (1984) Wind waves: their generation and propagation on the ocean surface. Dover, pp 330–331
Sveshnikov AA (1966) Applied methods of the theory of random functions. Pergamon press
Goda Y (2000) Random seas and design of maritime structures, 2nd edn. World Scientific, Singapore
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Dedicated to Professor J. N. Newman on his 70th birthday. We wish to express our profound admiration for Professor Newman’s scientific contributions and leadership in the ship-hydrodynamics discipline. The relation between this article and an early work of his reflects in part his impact on us.
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Li, Y., Mei, C.C. Subharmonic resonance of a trapped wave near a vertical cylinder by narrow-banded random incident waves. J Eng Math 58, 157–166 (2007). https://doi.org/10.1007/s10665-006-9120-8
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DOI: https://doi.org/10.1007/s10665-006-9120-8