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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]
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Database: Engineering Source
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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]
ISSN:09977546
DOI:10.1016/j.euromechflu.2021.01.012