Forced wave induced by an atmospheric pressure disturbance moving towards shore

Atmospheric pressure disturbances moving over a vast expanse of water can induce different wave patterns, which can be determined by the Froude number Fr. Generally, Fr = 1 is a critical value for the transformation of the wave pattern and the well-known Proudman resonance happens when Fr = 1. In this study, the forced wave induced by an atmospheric pressure disturbance moving over a constant slope from deep sea to shore is numerically investigated. The wave pattern evolves from a concentric-circle type into a triangular type with the increase of the Froude number, as the local water depth decreases, which is in accord with the analysis in the unbounded flat-bottom cases. However, a hysteresis effect has been observed, which implies the obvious amplification of the forced wave induced by a pressure disturbance can not be simply predicted by Fr = 1. The effects of the characteristic parameters of pressure disturbances and slope gradient have been discussed. The results show that it is not always possible to observe significant peak of the maximum water elevation before the landing of pressure disturbances, and a significant peak can be generated by a pressure disturbance with small spatial scale and fast moving velocity over a milder slope. Besides, an extremely high run-up occurs when the forced wave hits the shore, which is an essential threat to coastal security. The results also show that the maximum run-up is not monotonously varying with the increase of disturbance moving speed and spatial scale. There exists a most dangerous speed and scale which may cause disastrous nearshore surge.