Radiation, trapping and near-trapping in arrays of floating truncated cylinders

Circular arrays of fixed truncated vertical cylinders are known to support so-called sloshing near-trapped modes when subjected to incident water waves of the appropriate frequency and direction. In this paper waves radiated from circular arrays of truncated cylinders oscillating independently in still water are considered. For a square array of four cylinders, peaks in the condition number of the radiation damping matrix are used to identify body motion modes of interest. Body motions which excite the same free surface motion local to the array as the sloshing near-trapped mode are associated with enhanced radiation from the array. In contrast, at lower frequencies oscillations with low wave radiation to infinity are found when the cylinders oscillate in phase, in either heave or surge. For an array with eight cylinders this almost wave-free behaviour is dramatically enhanced, and a very simple arrangement which represents an extremely close approximation to a ‘motion-trapping structure’ may be constructed.