Harbour resonance due to set-down beneath wave groups

Natural modes of water oscillation inside harbours are known to occur with periods of the order of minutes. It seems likely that these oscillations are excited by water fluctuations of similar period outside the harbour and an often quoted cause of such fluctuations is the phenomenon of surf beats. These are thought to be long waves which are reflected back out to sea when a primary wave system breaks upon a beach. In this paper it is shown theoretically that the natural oscillations of a harbour can be excited directly, without breaking of the primary wave system, by set-down beneath wave groups, which is a long-period disturbance travelling towards the shore line at the group velocity. This theory is in agreement with model experimental results which show that, when the group period is close to a natural period of the harbour, resonance will occur with the set-down behaving as if it were a real long wave.