Scattering of Water Waves by a Submerged Nearly Vertical Plate

Mandal, B. N.; Kundu, Prabir Kumar

doi:10.1137/0150074

Cited by 17 publications

(24 citation statements)

References 8 publications

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“…[17][18][19] It is to be noted that in the numerator of A0 in (4.6), after 91 (u) is substituted from (5.1), the limit can be taken inside the k-integral so as to produce (5.6) ultimately. Again, it may be noted that for a = 0, olo --/30…”

Section: Functions Gl(y) Andfl(y)mentioning

confidence: 99%

Oblique diffraction of surface waves by a submerged vertical plate

Das

1996

J Eng Math

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A train of small-amplitude surface waves is obliquely incident on a fixed, thin, vertical plate submerged in deep water. The plate is infinitely long in the horizontal direction. An appropriate one-term Galerldn approximation is employed to calculate very accurate upper and lower bounds for the reflection and transmission coefficients for any angle of incidence and any wave number thereby producing very accurate numerical results.

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Section: Functions Gl(y) Andfl(y)mentioning

confidence: 99%

Oblique diffraction of surface waves by a submerged vertical plate

Das

1996

J Eng Math

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“…https://doi.org/10.1017/S0334270000010481 Also, it is observed from (3.20) that \T\ for these cylinders is independent of A. More generally if c(6) = £ £ 1 , s p s m P#> t n e n fr°m (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) and (3.20) it is found that R\ = 0, T x = 0 (of course R o = 0). This implies that for the nearly circular cylinders with the shape function c{6) mentioned above, the transmissivity is totally unaffected by its noncircularity.…”

Section: Jo Da Oumentioning

confidence: 99%

“…For an obstacle in the form of a nearly circular cylinder, a simplified perturbation analysis can be utilized to handle the problem. A somewhat similar idea of perturbation analysis was used in some recent works involving scattering or radiation of water waves by nearly vertical barrier or plates (see Mandal and Chakrabarti [6], Mandal and Kundu [7] and Mandal and Banerjea [5]). …”

Section: Introductionmentioning

confidence: 99%

Scattering of water waves by a submerged nearly circular cylinder

Mandal

Banerjea

1995

J. Aust. Math. Soc. Series B, Appl. Math

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The problem of scattering of surface water waves by a horizontal circular cylinder totally submerged in deep water is well studied in the literature within the framework of linearised theory with the remarkable conclusion that a normally incident wave train experiences no reflection. However, if the cross-section of the cylinder is not circular then it experiences reflection in general. The present paper studies the case when the cylinder is not quite circular and derives expressions for reflection and transmission coefficients correct to order e, where e is a measure of small departure of the cylinder cross-section from circularity. A simplified perturbation analysis is employed to derive two independent boundary value problems (BVP) up to first order in e. The first BVP corresponds to the problem of water wave scattering by a submerged circular cylinder. The reflection coefficient up to first order and the first order correction to the transmission coefficient arise in the second BVP in a natural way and are obtained by a suitable use of Green's integral theorem without solving the second BVP. Assuming a Fourier expansion of the shape function, these are evaluated approximately. It is noticed that for some particular shapes of the cylinder, these vanish. Also, the numerical results for the transmission coefficients up to first order for a nearly circular cylinder for which the reflection coefficients up to first order vanish, are given in tabular form. It is observed that for many other smooth cylinders, the result for a circular cylinder that the reflection coefficient vanishes, is also approximately valid.

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“…He used a perturbation analysis that involved solution of singular integral equation. Later Mandal and Chakrabarti (1989) and Mandal and Kundu (1990) considered the problems of water waves scattering by a nearly vertical barrier and utilized a perturbation analysis different from Shaw (1985) to handle the problems. The problem of water wave diffraction by a symmetric two dimensional thin slender was plate mentioned briefly by Shaw (1985) although the first order correction to reflection and transmission coefficients are not given there explicitly.…”

Section: Introductionmentioning

confidence: 99%

Scattering of Fexural Gravity Waves by a Two-Dimensional Thin Plate

Banerjee

Maiti

Mondal³

2017

JAFM

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An approximate analysis based on standard perturbation technique together with an application of Green's integral theorem is used in this paper to study the problem of scattering of water waves by a two dimensional thin plate submerged in deep ocean with ice cover. The reflection and transmission coefficients upto first order are obtained in terms of the shape function describing the plate and are studied graphically for different shapes of the plate.

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Scattering of Water Waves by a Submerged Nearly Vertical Plate

Cited by 17 publications

References 8 publications

Oblique diffraction of surface waves by a submerged vertical plate

Oblique diffraction of surface waves by a submerged vertical plate

Scattering of water waves by a submerged nearly circular cylinder

Scattering of Fexural Gravity Waves by a Two-Dimensional Thin Plate

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