Near-trapping of waves by circular arrays of vertical cylinders

Abstract

The effect of incident waves on arrays of identical bottom-mounted circular cylinders arranged in a circle are considered. The present paper is motivated by the recent work of Maniar and Newman [Maniar, H.D. and Newman, J.N., Journal of Fluid Mechanics, 1997, 339, 309–330], who show how large forces can be generated on long linear arrays at certain frequencies corresponding to trapped modes present in an infinite periodic linear array. Their analysis for the linear array motivates the idea of ‘near trapping’ in circular arrays in which it is assumed that adjacent cylinders only differ by a change in phase characterised by an integer, p. By using the interaction theory of Linton and Evans [Linton, C.M. and Evans, D.V., Journal of Fluid Mechanics, 1990, 215, 549–569] it is shown how large peaks in the forces on circular arrays of four, five and six cylinders develop as the gap between the cylinders is reduced, and the peaks are shown to correspond to particular values of p by examining the complex roots of the near-trapping system. The largest forces appear to arise when the near-trapped mode corresponds to a standing wave motion, in agreement with the largest forces in linear arrays.