Modeling of resonance within harbors

Two numerical models have been developed to evaluate the resonance within h arbours of variable depth. The first model determines the eigenvalues of a system, corresponding to the natural mode of vibration of the water body wi thin the harbour. Although the model produced interesting frequency values for completely open harbours, the computed values exhibited discrepancies o f about 15% compared with measured frequencies. Moreover, the model is limi ted by the fact that an artificial nodal line must be set at the mouth of t he harbour and that the amplification factor cannot be interpreted without the prior knowledge of the wave amplitude affecting the water body. Hence, the model ignores influences from the water body outside the harbour, which can be considered as infinite. The second model uses the method of finite boundary elements and introduces radiation terms to account for the infinit e water body outside the harbour. This model yielded good results compared with the exact solution and the laboratory measurements by Yoshida and Ijim a (1983), who studied the behaviour of an open harbour with variable depth. Differences of up to 12% were observed for the amplification factor around certain frequencies close to the second vibration mode. A comparison with field spectral density measurements from Sainte-Therese-de-Gaspe shows a go od agreement between the modelled results and the vibratory behaviour of th is harbour, thus supporting the use of this model for case studies. Nonline ar terms, along with flow friction and separation effects near the inside e dges of the mouth of the harbour, may also be included within the model.