<p>This study presents an analytical investigation of the interaction between waves and a rectangular-toothed obstacle in the presence of a uniform current, oriented either in the same or opposite direction to the incident wave propagation. This analysis is based on the linearized potential theory and employs the connection technique by enforcing the continuity of the velocity potential and the horizontal velocity component at the tooth interfaces. The results indicate that the presence of a uniform current significantly influences the hydrodynamic coefficients. Specifically, the maximum reflection coefficient increases by approximately <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$19.03\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>19.03</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> when the current is co-directional with the wave propagation (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">${F}_{r}=0.04$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>F</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>0.04</mn> </mrow> </math></EquationSource> </InlineEquation>) and decreases by about <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$18.73\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>18.73</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> when the current is opposing (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">${F}_{r}=-0.04$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>F</mi> <mi>r</mi> </msub> <mo>=</mo> <mo>-</mo> <mn>0.04</mn> </mrow> </math></EquationSource> </InlineEquation>), whereas the transmission coefficient exhibits the opposite trend. Moreover, the geometry of the toothed obstacle (including its length, submergence depth, secondary inner depth, and inter-tooth spacing) has a pronounced impact on the hydrodynamic performance. Increasing the obstacle length, secondary depth, and inter-tooth spacing enhances reflection and reduces transmission, whereas greater submergence depth leads to lower reflection and higher transmission. The validity and reliability of the proposed model are confirmed through comparisons with experimental and numerical results reported in the literature.</p>

Analytical study of wave interaction with a rectangular-toothed obstacle in the presence of current

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发表日期：

2026年1月29日

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

摘要

This study presents an analytical investigation of the interaction between waves and a rectangular-toothed obstacle in the presence of a uniform current, oriented either in the same or opposite direction to the incident wave propagation. This analysis is based on the linearized potential theory and employs the connection technique by enforcing the continuity of the velocity potential and the horizontal velocity component at the tooth interfaces. The results indicate that the presence of a uniform current significantly influences the hydrodynamic coefficients. Specifically, the maximum reflection coefficient increases by approximately $19.03\%$ $19.03 %$ when the current is co-directional with the wave propagation ( ${F}_{r}=0.04$ $F_{r} = 0.04$ ) and decreases by about $18.73\%$ $18.73 %$ when the current is opposing ( ${F}_{r}=-0.04$ $F_{r} = - 0.04$ ), whereas the transmission coefficient exhibits the opposite trend. Moreover, the geometry of the toothed obstacle (including its length, submergence depth, secondary inner depth, and inter-tooth spacing) has a pronounced impact on the hydrodynamic performance. Increasing the obstacle length, secondary depth, and inter-tooth spacing enhances reflection and reduces transmission, whereas greater submergence depth leads to lower reflection and higher transmission. The validity and reliability of the proposed model are confirmed through comparisons with experimental and numerical results reported in the literature.