Abstract
The dynamics of the shallow-water linear edge waves above an inclined bottom slowly varied in an along-shore direction is studied. By using the asymptotic method, the offshore structure of the edge waves and their dispersion relation are determined in the leading order, and the wave amplitude – in next order. The asymptotic theory confirms the “energetic” approach that the wave amplitude can be derived from the energy flux conservation in the leading order. Three different offshore bottom profiles are considered: the beach of constant slope, exponential shelf, and step-shelf. The variations of the wave amplitude and along-shore wave number are calculated in details for the cases when the parameters of the shelf zone are changed slowly in the along-shore direction.
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