Waves incident on a circular harbour
The wave amplitude inside a harbour that is subject to incident waves is greatly affected by the frequency of the incident waves. If the harbour entrance is small it is expected that the internal resonances of the harbour will be excited at the appropriate incident frequencies. Published arguments concerning the magnitude of the resonances are, however, not conclusive. In this paper a circular harbour with a small entrance is studied with the use of a rigorous mathematical treatment. It is found that as the harbour entrance decreases in size the magnitude of resonance owing to a single frequency increases slowly (logarithmically). However, this increase is too slow to make a significant difference. The magnitude of resonance in relation to a continuous spectrum input increases, but for the Helmholtz mode only. Again the increase is slow (logarithmic). These results are found to be in agreement with the work of J. Miles ( J. Fluid Mech. 46, 241-265 (1971)). In many approximate calculations it is assumed that the total flow through the gap will effectively determine the flow near a resonant frequency. This is correct near the Helmholtz resonance, but incorrect near the higher resonances where the through-flow is small.