Abstract
Abstract
Highlights
There is considerable engineering and scientific interest in the probability of large waves occurring in the ocean
This paper develops second-order theory for narrow-banded surface gravity wavepackets experiencing a sudden depth transition based on a Stokes and multiple-scales expansion
As a wavepacket travels over a sudden depth transition, additional wavepackets are generated that propagate freely obeying the linear dispersion relation and arise at both first and second order in wave steepness in a Stokes expansion
Summary
There is considerable engineering and scientific interest in the probability of large waves occurring in the ocean. In order to do so, this paper develops analytical solutions for narrow-banded wavepackets experiencing a sudden depth transition in the form of a step using a Stokes expansion up to second order in wave steepness These solutions, which extend the results of Massel (1983) for monochromatic waves to wavepackets, capture the release of both sub- and superharmonic second-order free waves at the step. We validate these solutions by comparing to a fully nonlinear potential-flow model in the present paper and to experiments in the companion paper Li et al (2021)
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