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<p>The article is concerned with oblique scattering by a step, infinite or finite. The waves can be obliquely incident from either higher depth region to lower depth region or lower depth region to higher depth region in both the cases. The problem is formulated in terms of solving first-kind integral equation on the unknown horizontal component of velocity above the step. The unknown is approximated via multi-term Galerkin technique in terms of product of simple polynomials and exponential decay function multiplied by a suitable weight functions whose form is determined by the edge condition at the step’s corner. This reduces the integral equation to a system of linear equations which are solved numerically. Reflection and transmission coefficients are computed using the numerical solution of the integral equation. The numerical results are validated by comparing with known results available in the literature. It is found that increasing the angle of incidence increases the reflection of the wave incident from either direction for both positions of step. The critical values of depth ratios are also observed corresponding to angle of incidence and frequencies for finite step for which maximum reflection occurs. Additionally, for lower frequencies which are less than or equals to <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10665_2025_10436_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">\(10^{-1},\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> there occurs critical angle of incidence for which reflection is minimum for both positions of step. This study will provide enough information about the wave behavior in the oceanic areas where these step kind of bottoms are present and is helpful for the ocean engineers before building any infrastructure in these regions.</p>

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Oblique water wave scattering by a step

  • 期刊论文

  • 发表日期：

    2025年3月14日

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  • Deepali Goyal,
  • S. C. Martha,
  • B. N. Mandal

摘要

The article is concerned with oblique scattering by a step, infinite or finite. The waves can be obliquely incident from either higher depth region to lower depth region or lower depth region to higher depth region in both the cases. The problem is formulated in terms of solving first-kind integral equation on the unknown horizontal component of velocity above the step. The unknown is approximated via multi-term Galerkin technique in terms of product of simple polynomials and exponential decay function multiplied by a suitable weight functions whose form is determined by the edge condition at the step’s corner. This reduces the integral equation to a system of linear equations which are solved numerically. Reflection and transmission coefficients are computed using the numerical solution of the integral equation. The numerical results are validated by comparing with known results available in the literature. It is found that increasing the angle of incidence increases the reflection of the wave incident from either direction for both positions of step. The critical values of depth ratios are also observed corresponding to angle of incidence and frequencies for finite step for which maximum reflection occurs. Additionally, for lower frequencies which are less than or equals to \(10^{-1},\) 10 - 1 , there occurs critical angle of incidence for which reflection is minimum for both positions of step. This study will provide enough information about the wave behavior in the oceanic areas where these step kind of bottoms are present and is helpful for the ocean engineers before building any infrastructure in these regions.