Abstract

<p>This work focuses on two different aspects of the effect of an abrupt depth transition on weakly nonlinear surface gravity waves: deterministic and stochastic. It is known that the kurtosis of waves can reach a maximum near the top of such abrupt depth transitions. The analysis is based on three different approaches: (1) a novel theoretical framework that allows for narrow-banded surface waves experiencing a step-type seabed, correct to the second order in wave steepness; (2) experimental observations; and (3) a numerical model based on a fully nonlinear potential flow solver. To reveal the fundamental physics, the evolution of a wave envelope that experiences an abrupt depth transition is examined in detail; (a) we show the release of free waves at second order in wave steepness both for the super-harmonic and sub-harmonic or ‘mean’ terms; (b) a local wave height peak that occurs near the top of a depth transition – whose exact position depends on several nondimensional parameters – is revealed; (c) furthermore, we examine which parameters affect this peak. The novel physics has implications for wave statistics for long-crested irregular waves experiencing an abrupt depth transition. We show the connection of the second-order physics at work in the deterministic and stochastic cases: the peak of wave kurtosis and skewness occurs in the neighborhood of the deterministic wave peak in (b) and for the same parameters set composed of a seabed topography, water depths, primary wave frequency and steepness, and bandwidth.</p>

Highlights

  • Effects of an abrupt depth change on weakly nonlinear surface gravity waves: deterministic and stochastic analysis

  • This work focuses on two different aspects of the effect of an abrupt depth transition on weakly nonlinear surface gravity waves: deterministic and stochastic

  • It is known that the kurtosis of waves can reach a maximum near the top of such abrupt depth transitions

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Summary

Introduction

Effects of an abrupt depth change on weakly nonlinear surface gravity waves: deterministic and stochastic analysis Yan Li1,3, Samuel Draycott2, Yaokun Zheng4, Thomas A.A. Adcock1, Zhiliang Lin4, and Ton S. van den Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK; Department of Mechanical, Aerospace & Civil Engineering, University of Manchester, Manchester, UK; Norwegian University of Science and Technology, Department of energy and process engineering, 7491 Trondheim, Norway

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