Trapping and Near-trapping by Arrays of Cylinders in Waves.
D. V. Evans and R. Porter (to appear in J. Eng. Maths, Special Issue on
Ocean Mechanics, January 1998)
In this paper, a survey is given of some recent developments and
discoveries concerning the trapping of waves by arrays of vertical
circular cylinders. In particular, we exmaine the cases when there is a
circular arrangement of cylinders and both finite and infinite periodic
linear arrays of identical cylinders. Only for the infinite array is
there pure trapping of waves -- known as Rayleigh-Bloch or edge waves
-- which, for particular dominant wavenumbers, reduce to the well-known
trapped mode solutions for a cylinder between two parallel walls having
either Neumann or Dirichlet conditions upon them. This latter case
is considered separately and some new results are presented. In the
circular array and finite linear array the concept of near-trapping is
introduced where large resonant motions are found to occur at certain
frequencies of the incident wave field. In the case of the finite linear
array, these near-trapping frequencies are related to the Rayleigh-Bloch
trapped wave frequencies for the infinite array. Finally, the case when
there are two or more lines of cylinders in the linear array is examined.
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