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Water wave interaction with a partially immersed rectangular block over an infinite step.

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Title: Water wave interaction with a partially immersed rectangular block over an infinite step.
Authors: Majhi, Mampi1 (AUTHOR), Chakraborty, Rumpa2 (AUTHOR) chak.rumpa@gmail.com, Mandal, B. N.3 (AUTHOR)
Source: Zeitschrift für Angewandte Mathematik und Physik (ZAMP). Jun2026, Vol. 77 Issue 6, p1-26. 26p.
Subjects: Water waves, Harbor design & construction, Hydrodynamics, Integral equations, Scattering (Mathematics), Oceanographic maps, Galerkin methods
Abstract: Water wave interaction with a partially immersed rectangular block of two different geometrical configurations in the presence of an infinite step-type bottom is studied here. It is formulated in terms of coupled first-kind integral equations involving horizontal components of velocity below the two corners of the block and above the step. The integral equations are solved by employing Galerkin approximation in terms of simple polynomials multiplied by an exponential decay function and appropriate weight functions whose forms are dictated by the edge conditions at the corner of the step and at the submerged ends of the block. The reflection and transmission coefficients and hydrodynamic forces are then computed and depicted graphically against the wave number. The numerical results are validated by comparing them with the existing results graphically. The present study is likely to be important in the design of a breakwater in the presence of an infinite step. [ABSTRACT FROM AUTHOR]
Copyright of Zeitschrift für Angewandte Mathematik und Physik (ZAMP) is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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  Data: <searchLink fieldCode="DE" term="%22Water+waves%22">Water waves</searchLink><br /><searchLink fieldCode="DE" term="%22Harbor+design+%26+construction%22">Harbor design & construction</searchLink><br /><searchLink fieldCode="DE" term="%22Hydrodynamics%22">Hydrodynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+equations%22">Integral equations</searchLink><br /><searchLink fieldCode="DE" term="%22Scattering+%28Mathematics%29%22">Scattering (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Oceanographic+maps%22">Oceanographic maps</searchLink><br /><searchLink fieldCode="DE" term="%22Galerkin+methods%22">Galerkin methods</searchLink>
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  Data: Water wave interaction with a partially immersed rectangular block of two different geometrical configurations in the presence of an infinite step-type bottom is studied here. It is formulated in terms of coupled first-kind integral equations involving horizontal components of velocity below the two corners of the block and above the step. The integral equations are solved by employing Galerkin approximation in terms of simple polynomials multiplied by an exponential decay function and appropriate weight functions whose forms are dictated by the edge conditions at the corner of the step and at the submerged ends of the block. The reflection and transmission coefficients and hydrodynamic forces are then computed and depicted graphically against the wave number. The numerical results are validated by comparing them with the existing results graphically. The present study is likely to be important in the design of a breakwater in the presence of an infinite step. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Zeitschrift für Angewandte Mathematik und Physik (ZAMP) is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00033-026-02821-w
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        Text: English
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        Type: general
      – SubjectFull: Harbor design & construction
        Type: general
      – SubjectFull: Hydrodynamics
        Type: general
      – SubjectFull: Integral equations
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      – SubjectFull: Scattering (Mathematics)
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      – SubjectFull: Oceanographic maps
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      – SubjectFull: Galerkin methods
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      – TitleFull: Water wave interaction with a partially immersed rectangular block over an infinite step.
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              M: 06
              Text: Jun2026
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              Y: 2026
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