Oblique wave scattering by submerged thin wall with gap in finite-depth water

Banerjea, Sudeshna; Kanoria, M.; Dolai, D. P.; Mandal, B. N.

doi:10.1016/s0141-1187(97)00002-3

Cited by 31 publications

(9 citation statements)

References 9 publications

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“…The method of Galerkin approximations has been widely used to investigate water wave scattering problems involving thin vertical barriers (cf. Porter and Evans [1], Evans and Fernyhough [2], Banerjea et al [3], Das et al [4]) or thick vertical barriers with rectangular cross sections [5,6]. There is another important class of wave scattering problems involving water of variable depth in which the depth is constant except for variations over a finite interval.…”

Section: Introductionmentioning

confidence: 99%

Water wave scattering by a rectangular trench

Chakraborty

Mandal

2014

J Eng Math

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Assuming linear theory, the two-dimensional problem of water wave scattering by a rectangular submarine trench is reinvestigated here employing the multiterm Galerkin approximations involving ultraspherical Gegenbauer polynomials for solving the integral equations arising in the mathematical analysis. Because of the geometrical symmetry of the rectangular trench about the y-axis, the problem is split into two separate problems involving symmetric and antisymmetric potential functions. Very accurate numerical estimates for the reflection and transmission coefficients for various values of different parameters are obtained, and these are seen to satisfy the energy identity. These coefficients are computed numerically and depicted graphically against the wave number in a number of figures. Some figures available in the literature drawn using different mathematical methods and laboratory experiments are also recovered following the present analysis, thereby confirming the correctness of the results presented here. It is also observed that the reflection and transmission coefficients depend significantly on the width of the trench.

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Section: Introductionmentioning

confidence: 99%

Water wave scattering by a rectangular trench

Chakraborty

Mandal

2014

J Eng Math

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“…A multi-term Galerkin approximation techniques are used to solve these problem. This technique applied to the oblique wave scattering problems involving vertical barriers with gap in uniform depth water analysed by Kanoria and Mandal [11]; Banerjea et al [12]. It is observed that the numerical results for reflection coefficients in these problems are accurate mostly, depends on the wave number of incident wave field and geometry of barriers.…”

Section: Introductionmentioning

confidence: 99%

Effect of Inertial Surface on Surface Gravity Wave Propagation by Thick Rectangular Barrier

Chakraborty¹,

Majhi²

2021

International Journal of Lakes and Rivers

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In presence of an inertial surface, this paper develops new analytical solutions of two-dimensional water wave scattering problem of thick vertical barrier of rectangular cross section of uniform depth, considering the linear theory. Four types of barrier, surface-piercing or bottom standing or fully submerged in water or in the form of a thick vertical rectangular wall with submerged gap in water are examined. The problem is formulated in terms of integral equation by assuming symmetric and anti-symmetric parts of velocity potential. The analytical solutions make use of the multi-term Galerkin method which involves ultra-spherical Gegenbauer polynomials as its basis function. The reflection coefficients are obtained for different parametric values, which are depicted graphically against the wave number using very accurate numerical estimation. It is remarkable that the reflection coefficients depend significantly on the width of the barrier.

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“…Mandal and Dolai (1994) and Porter and Evans (1995) derived the solution of the problem involving scattering of water waves by vertical barrier by using the Galerkin approximation method. Banerjea et al (1996) utilized the one-term and multi-term Galerkin approximation to evaluate the reflection coefficient for the problem handled by Porter (1972). Mandal and Chakrabarti (1999) obtained the approximate solutions of a number of water wave scattering problems involving thin vertical barriers by utilizing the Galerkin's method.…”

Section: Introductionmentioning

confidence: 99%