Published online by Cambridge University Press: 10 November 1998
Viscous flow about a circular cylinder that is submerged beneath free-surface travelling waves is considered. The wave amplitude is assumed small and results are presented for a wide range of Reynolds number. Particular attention is focused on the second-order time-averaged flow that manifests itself as a circulatory motion about the cylinder. The paper complements earlier work on this problem by Yan & Riley (1996) in the large Reynolds number, boundary-layer, regime and Riley & Yan (1996) in the inviscid flow limit, and makes a comparison with experimental work by Chaplin (1984) possible.