TRAPPED MODES ABOUT MULTIPLE CYLINDERS IN A CHANNEL

The trapped modes which can occur in a long narrow wave channel contai ning any number of different-sized bottom-mounted circular cylinders a rbitrarily spaced along the centreline of the channel are considered. The modes, all of which are antisymmetric with respect to the centrepl ane of the channel are of two types: Neumann modes, in which the fluid has normal velocity zero on the channel walls corresponding to a loca lized sloshing near the cylinders, and Dirichlet modes, in which the d ynamic 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 b oundary conditions apply. It is shown that in general there are less t han or equal to N trapped modes for any configuration of N cylinders, the precise number depending critically on the geometry of the configu ration. Both types are of importance in predicting the exciting forces on individual cylinders within a large but finite periodic arrangemen t of cylinders.