Trapped modes embedded in the continuous spectrum

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Abstract
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 Neuman and Dirichlet 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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