Trapped modes embedded in the continuous spectrum
by D.V. Evans and R. Porter, 1998, Q. J. Mech. Appl. Math. 52(1),
263-274
The existence of trapped modes due to rigid obstacles placed
symmetrically
in between parallel walls having either Neumann or Dirichlet conditions
imposed upon them are well known to occur for frequencies below the
continuous spectrum or channel cut-off and for a range of geometric
configurations. In this paper, we provide convincing numerical evidence
for an additional isolated trapped mode of both Neumann and Dirchlet
type embedded in the continuous spectrum (or above the channel cut-off)
in the case of a rigid circular cylinder placed on the centre-plane of
the channel. Thus, for each type of mode we give results showing that
there is just one cylinder size and wave frequency at which the trapped
mode occurs.
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