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The Green function for diffraction and radiation of regular waves by two-dimensional structures.

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Title: The Green function for diffraction and radiation of regular waves by two-dimensional structures.
Authors: Mackay, Ed1 (AUTHOR) e.mackay@exeter.ac.uk
Source: European Journal of Mechanics B: Fluids. May2021, Vol. 87, p151-160. 10p.
Subjects: Wave diffraction, Bodies of water, Radiation, Boundary element methods
Abstract: New expressions are derived for the Green function (GF) for diffraction and radiation of waves by a two-dimensional (2D) body in finite water depth. The finite depth GF is expressed as a sum of singularities, the infinite depth GF and smoothly-varying integrals that are convergent for all parameter values. The infinite depth component is given explicitly, making it very fast to compute. Explicit expressions are derived for the limiting cases of zero and infinite frequency, for both finite and infinite water depth. The low frequency limit of the 2D GF is inconsistent with the zero-frequency 2D GF, with the real part tending to infinity when the water depth is infinite and the imaginary part tending to infinity in finite water depth. The inconsistencies with the zero frequency GF differ between the 2D and 3D cases. These inconsistencies lead to differences between the low-frequency behaviour of the added mass and damping of an oscillating body and the values at zero frequency. It is shown that these differences can be inferred directly from the behaviour of the GF at low frequencies. • Finite depth Green function (GF) expressed as infinite depth GF plus perturbations. • Explicit expression derived for infinite depth Green function. • Explicit expressions derived for zero and infinite frequency GF in finite depth. • Inconsistencies in low frequency added mass and damping related to behaviour of GF. [ABSTRACT FROM AUTHOR]
Copyright of European Journal of Mechanics B: Fluids is the property of Elsevier B.V. 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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Header DbId: egs
DbLabel: Engineering Source
An: 149014465
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: The Green function for diffraction and radiation of regular waves by two-dimensional structures.
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  Data: <searchLink fieldCode="AR" term="%22Mackay%2C+Ed%22">Mackay, Ed</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> e.mackay@exeter.ac.uk</i>
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  Data: <searchLink fieldCode="JN" term="%22European+Journal+of+Mechanics+B%3A+Fluids%22">European Journal of Mechanics B: Fluids</searchLink>. May2021, Vol. 87, p151-160. 10p.
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  Data: <searchLink fieldCode="DE" term="%22Wave+diffraction%22">Wave diffraction</searchLink><br /><searchLink fieldCode="DE" term="%22Bodies+of+water%22">Bodies of water</searchLink><br /><searchLink fieldCode="DE" term="%22Radiation%22">Radiation</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+element+methods%22">Boundary element methods</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: New expressions are derived for the Green function (GF) for diffraction and radiation of waves by a two-dimensional (2D) body in finite water depth. The finite depth GF is expressed as a sum of singularities, the infinite depth GF and smoothly-varying integrals that are convergent for all parameter values. The infinite depth component is given explicitly, making it very fast to compute. Explicit expressions are derived for the limiting cases of zero and infinite frequency, for both finite and infinite water depth. The low frequency limit of the 2D GF is inconsistent with the zero-frequency 2D GF, with the real part tending to infinity when the water depth is infinite and the imaginary part tending to infinity in finite water depth. The inconsistencies with the zero frequency GF differ between the 2D and 3D cases. These inconsistencies lead to differences between the low-frequency behaviour of the added mass and damping of an oscillating body and the values at zero frequency. It is shown that these differences can be inferred directly from the behaviour of the GF at low frequencies. • Finite depth Green function (GF) expressed as infinite depth GF plus perturbations. • Explicit expression derived for infinite depth Green function. • Explicit expressions derived for zero and infinite frequency GF in finite depth. • Inconsistencies in low frequency added mass and damping related to behaviour of GF. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of European Journal of Mechanics B: Fluids is the property of Elsevier B.V. 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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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.euromechflu.2021.01.012
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      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 10
        StartPage: 151
    Subjects:
      – SubjectFull: Wave diffraction
        Type: general
      – SubjectFull: Bodies of water
        Type: general
      – SubjectFull: Radiation
        Type: general
      – SubjectFull: Boundary element methods
        Type: general
    Titles:
      – TitleFull: The Green function for diffraction and radiation of regular waves by two-dimensional structures.
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            NameFull: Mackay, Ed
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            – D: 01
              M: 05
              Text: May2021
              Type: published
              Y: 2021
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              Value: 87
          Titles:
            – TitleFull: European Journal of Mechanics B: Fluids
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