The trapping of surface waves by multiple submerged horizontal
cylinders.
R. Porter & D. V. Evans (to appear in Journal of Engineering
Maths)
The existence of edge waves, or trapped modes, travelling above a
single long horizontal submerged cylinder is well established using the
linearised theory of water waves. In the present paper, the possibility
of wave-trapping by multiple submerged horizontal circular cylinders
is considered. The trapped mode solutions are constructed by means
of a multipole approach combined with an addition formula for Bessel
functions and requires finding the non-trivial solutions of a real
infinite system of algebraic equations. We briefly return to the case of
a single submerged cylinder, reproducing results for symmetric trapped
modes and also discovering a new set of antisymmetric modes providing
the cylinder is sufficiently close to the free surface. A large range
of results are presented for multiple cylinders.
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