Near-trapping of water waves by circular arrays of vertical
cylinders
by D. V. Evans and R. Porter, 1997, Applied Ocean Research, 19,
83-89.
The effect of incident waves on arrays of identical bottom-mounted
circular cylinders arranged either in a line or a circle are
considered. The present paper is motivated by the recent work of Maniar \&
Newman (1997) who show how large forces can be generated on long linear
arrays at certain frequencies corresponding to trapped modes present in
an infinite periodic linear array. This problem is revisited here where
it is shown that these trapped modes correspond to standing wave solutions
of the more general Rayleigh-Bloch waves along a periodic infinite linear
array. Numerical evidence is also provided for two new pure trapped modes
above the cut-off for the infinite array, existing only for particular
geometries. The analysis for the infinite linear array motivates the
idea of `near trapping' in circular arrays in which it is assumed that
adjacent cylinders only differ by a change in phase characterised by
an integer, $p$. Using the interaction theory of Linton \& Evans (1990)
it is shown how large peaks in the forces on circular arrays of $4$, $5$
and $6$ cylinders develop as the gap between the cylinders is reduced and
the peaks are shown to correspond to particular values of $p$ by examining
the complex roots of the near-trapping system. The largest forces appear
to arise when the near-trapped mode corresponds to a standing wave motion,
in agreement with the largest forces in linear arrays.
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