<p>In this work, we focus on the analytical study of wave interaction with two spaced rectangular trenches placed on a flat seabed under a uniform current, oriented either in the same direction as or opposite to the incident wave. The analysis is based on linearized potential theory and utilizes the evanescent modes model. Ensuring the continuity of velocity potentials at the trench boundaries results in a system of singular integral equations, which are analytically solved. Particular focus is put on calculating reflection and transmission coefficients, which are subsequently illustrated graphically as a function of the dimensionless wavenumber <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40722_2025_409_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="TEX">$kH$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">kH</mi> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40722_2025_409_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$k$</EquationSource> <EquationSource Format="MATHML"><math> <mi>k</mi> </math></EquationSource> </InlineEquation> is the wavenumber and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40722_2025_409_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$H$</EquationSource> <EquationSource Format="MATHML"><math> <mi>H</mi> </math></EquationSource> </InlineEquation> is the depth of water at rest. The aim is to understand the influence of current and various geometric parameters on these coefficients. The results obtained are compared with experimental and numerical data from the literature to validate the proposed approach.</p>

Analytical study of wave-trenches interaction under the effect of current

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发表日期：

2025年6月11日

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Hamza Mabchour,
Hasna Akarni,
Abdelilah Akouibaa,
Laila El Aarabi,
Soumia Mordane

摘要

In this work, we focus on the analytical study of wave interaction with two spaced rectangular trenches placed on a flat seabed under a uniform current, oriented either in the same direction as or opposite to the incident wave. The analysis is based on linearized potential theory and utilizes the evanescent modes model. Ensuring the continuity of velocity potentials at the trench boundaries results in a system of singular integral equations, which are analytically solved. Particular focus is put on calculating reflection and transmission coefficients, which are subsequently illustrated graphically as a function of the dimensionless wavenumber $kH$ $kH$ , where $k$ $k$ is the wavenumber and $H$ $H$ is the depth of water at rest. The aim is to understand the influence of current and various geometric parameters on these coefficients. The results obtained are compared with experimental and numerical data from the literature to validate the proposed approach.