Trapped modes about multiple cylinders in a channel
D. V. Evans and R. Porter, 1997, Journal of Fluid Mechanics
339, 331--356.
The trapped modes which can occur in a long narrow wave channel
containing any number of different-sized bottom-mounted circular cylinders
arbitrarily-spaced along the centreline of the channel are considered. The
modes, all of which are antisymmetric with respect to the centre plane of
the channel are of two types; Neumann modes, in which the fluid has normal
velocity zero on the channel walls corresponding to a localised sloshing
near the cylinders, and Dirichlet modes, in which the dynamic pressure
vanishes on the channel walls. These latter modes have no physical meaning
in the water-wave context but have been observed in a related acoustic
context where the same governing equations and boundary conditions apply.
It is shown that in general there are <= N trapped modes for any
configuration of N cylinders, the precise number depending critically
on the geometry of the configuration. Both types are of importance in
predicting the exciting forces on individual cylinders within a large
but finite periodic arrangement of cylinders.
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