| Wave propagation in the coastal zone can induce both scattering andcapturing of wave energy. The latter phenomenon is of great interestdue to the weak attenuation of waves over long distances. Trappedwaves are an important component of sea disturbances produced bycyclones moving along coastlines and their existence explains the non-uniform character of tsunami height along the coastline. Edge wavesmay be generated from normally incident wind waves due to the strongnonlinearity of wind waves and many field observations demonstrate theoccurrence of these edge waves in coastal environments. Edge waves areoften considered as the major factor in the long-term evolution ofirregular coastal morphology, forming rhythmical crescentic bars.There is good agreement between the characteristic scales of thesemorphological features when measured in laboratory experiments and thenatural environment. However, the energetics of the wave processes ispoorly understood and the sediment transport rates associated with theedge wave field has neither been estimated nor measured. The main goalof this paper is to study the unsteady dynamics of the progressive andstanding edge wave propagation above a sloping beach. In particular,the mechanism of the spatial–temporal focusing (dispersionenhancement) of multi-modal edge waves in the shelf zone isinvestigated in the framework of shallow water theory bothanalytically and numerically. The asymptotic solution is derived forthe wave evolution above a sloping beach smoothly varied in along-shore direction. The unusual appearance of the coastal flood tongue isdemonstrated in the framework of developed theory. |
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