Oblique diffraction of surface waves by a submerged vertical plate

De, Soumen; Das, Pulak

doi:10.1007/bf00049246

Cited by 21 publications

(3 citation statements)

References 17 publications

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“…Their averages give actual values of reflection coefficients for all practical purposes. The present method produces numerical results which are in good agreement with the earlier results obtained by [22].…”

Section: Oblique Scattering By a Thin Vertical Platesupporting

confidence: 89%

“…6 and 7 of [22]. Further it is also observed that for most of the cases the results displayed in Table 5 coincide upto 3 to 4 decimal places with the results in Table 1 of [22]. These provide another check on the correctness of the results obtained using the present method.…”

Section: Oblique Scattering By a Thin Vertical Platesupporting

confidence: 74%

“…From these figures it is seen that the curve of |R| almost coincides with the curve of |R| in Figs. 6 and 7 of [22]. Further it is also observed that for most of the cases the results displayed in Table 5 coincide upto 3 to 4 decimal places with the results in Table 1 of [22].…”

Section: Oblique Scattering By a Thin Vertical Platesupporting

confidence: 72%

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Use of Galerkin Technique in Some Water Wave Scattering Problems Involving Plane Vertical Barriers

2019

Applied Mathematical Analysis: Theory, Methods, and Applications

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The explicit solutions exist for normal incidence of the surface wave train or a single thin plane vertical barrier partially immersed or completely submerged in deep water. However, for oblique incidence of the wave train and/or for finite depth water, no such explicit solution is possible to obtain. Some approximate mathematical techniques are generally employed to solve them approximately in the sense that quantities of physical interest associated with each problem, namely the reflection and transmission coefficients, can be obtained approximately either analytically or numerically. The method of Galerkin approximations has been widely used to investigate such water wave scattering problems involving thin vertical barriers. Use of Galerkin method with basis functions involving somewhat complicated functions in solving these problems has been carried out in the literature. Choice of basis functions as simple polynomials multiplied by appropriate weights dictated by the edge conditions at the submerged end points of the barrier providing fairly good numerical estimates for the reflection and transmission coefficients have been demonstrated in this article.

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Section: Oblique Scattering By a Thin Vertical Platesupporting

confidence: 89%

Section: Oblique Scattering By a Thin Vertical Platesupporting

confidence: 74%

See 1 more Smart Citation

Use of Galerkin Technique in Some Water Wave Scattering Problems Involving Plane Vertical Barriers

2019

Applied Mathematical Analysis: Theory, Methods, and Applications

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The Problem of Oblique Scattering by a Thin Vertical Submerged Plate in Deep Water Revisited

Das

2018

Springer Proceedings in Mathematics &Amp; Statistics

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Water-wave scattering by two submerged thin vertical unequal plates

2016

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The problem of water-wave scattering by two thin vertical plates of unequal lengths submerged beneath the free surface of an infinitely deep water is studied here assuming linear theory. The problem is reduced to a pair of vector integral equations of first kind which are solved approximately by using single-term Galerkin approximation. Very accurate numerical estimates for the reflection and transmission coefficients for different values of the wave number and other parameters are obtained. The numerical results for the reflection coefficient are plotted against the wave number in a number of figures for different configurations of the two plates. It is observed from these figures that the reflection coefficient vanishes for a sequence of values of the wave number only for two identical submerged plates. However, for two non-identical plates, the reflection coefficient never becomes zero, although there exists a few wave numbers at which this becomes small for some particular configurations of the plates. When the two plates become very close to each other, known numerical results for a single plate are deduced.

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Oblique diffraction of surface waves by a submerged vertical plate

Cited by 21 publications

References 17 publications

Use of Galerkin Technique in Some Water Wave Scattering Problems Involving Plane Vertical Barriers

Use of Galerkin Technique in Some Water Wave Scattering Problems Involving Plane Vertical Barriers

The Problem of Oblique Scattering by a Thin Vertical Submerged Plate in Deep Water Revisited

Water-wave scattering by two submerged thin vertical unequal plates

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