Water wave scattering by thick rectangular slotted barriers

Kanoria, M.

doi:10.1016/s0141-1187(01)00018-9

Cited by 26 publications

(28 citation statements)

References 19 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%

“…Exploiting the geometrical symmetry of the rectangular trench about its center line taken as the y-axis, the problem is split into two separate problems involving the symmetric and antisymmetric potential functions describing the resultant motion in the fluid region, as was done by Kanoria et al [5] for the problem of water wave scattering by a thick vertical barrier of rectangular cross section having four different geometrical shapes. The use of eigenfunction expansions of the potential functions, along with the Havelock inversion formula followed by a matching process, produces integral equations for the corresponding unknown horizontal velocity components across the vertical line through the corner point of the trench.…”

Section: Introductionmentioning

confidence: 99%

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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%

Section: Introductionmentioning

confidence: 99%

Water wave scattering by a rectangular trench

Chakraborty

Mandal

2014

J Eng Math

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“…The boundary conditions at the discontinuity surface are the following: the continuity of the pressure and axial particle velocity on the aperture p A ðr; 0ÀÞ ¼ p C ðr; 0þÞ; 0 r < b; (15) t A ðr; 0ÀÞ ¼ t C ðr; 0þÞ; 0 r < b:…”

Section: Theoretical Analysismentioning

confidence: 99%

“…The analysis by Evans and Fernyough, 13 Kanoria, 15 and Homentcovschi and Miles 1 show that in the case of a step discontinuity the axial velocity has around the point r ¼ b a singular behavior of the typet…”

Section: Theoretical Analysismentioning

confidence: 99%

Re-expansion method for circular waveguide discontinuities: Application to concentric expansion chambers

Homentcovschi

Miles

2012

The Journal of the Acoustical Society of America

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The paper applies the re-expansion method for analyzing planar discontinuities at the junction of two axi-symmetrical circular waveguides. The normal modes in the two waveguides are expanded at the junction plane into a system of functions accounting for velocity singularities at the corner points. As the new expansion has a high convergence order, only a few terms have to be considered for obtaining the solution of most practical problems. This paper gives the equivalent impedance accounting for nonplanar waves into a plane-wave analysis and also the scattering matrix describing the coupling of arbitrary modes at each side of the discontinuity valid in the case of many propagating modes in both sides of the duct. The last section applies the re-expansion technique to some concentric expansion chambers providing an explicit formula for the transmission loss coefficient.

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“…Let a progressive wave train represented by the velocity potential Ref/ 0 ðx; yÞ e Àirt g, where / 0 ðx; yÞ is given by (4) and corresponds to the solution for an ocean of uniform finite depth h given in the Introduction, be incident from the direction of x ¼ À1 upon the bottom elevation of an ice-covered ocean occupying the region 0 y h þ cðxÞ. It will be partially reflected by and partially transmitted over the elevation of the ocean bottom.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Wave diffraction by a small elevation of the bottom of an ocean with an ice-cover

Basu

2004

Archive of Applied Mechanics (Ingenieur Archiv)

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Diffraction of water waves by a small cylindrical elevation of the bottom of a laterally unbounded ocean covered by an ice sheet is investigated by the perturbation analysis. The ice sheet is modelled as a thin elastic plate. The reflection and transmission coefficients are evaluated up to the first order in terms of integrals involving the shape function representing the bottom elevation. Three particular forms of the shape function are considered for which explicit expressions for these coefficients are obtained. For the particular case of a patch of sinusoidal undulations at the bottom, the reflection coefficient up to first order is found to be an oscillatory function of the ratio of the wavelength of the bottom undulations and that of the incident wave train. When this ratio approaches 0.5, the reflection coefficient becomes a multiple of the number of undulations and high reflection of the incident wave energy occurs if this number is large. Reflection coefficient is depicted graphically to visualize the effect of the presence of ice-cover and the number of undulations. IntroductionProblems of water wave diffraction by obstacles situated at the bottom of water basins of finite depth having a free surface at the top, have been investigated assuming linear theory in the literature of the last few decades. The earliest work in this area involves propagation of long waves over an abrupt change in the depth of the basin, which was briefly discussed in the treatise of Lamb [1, Art 176]. Conformal transformations were used in [2] to investigate the reflection of water waves by obstacles of arbitrary shape at the bottom. For rectangular obstacles situated at the bottom of basins of uniform finite depth, a variational formulation was used in [3], and more recently [4] and [5] presented multi-term Galerkin approximations in the papers' analysis, to obtain accurate numerical estimates for the reflection coefficient. In [6], water-wave reflection by a patch of sinusoidal undulations at the bottom was considered. The problem was solved by using the Fourier transform, after introducing a linear friction term in the free surface condition for the purpose of ensuring

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Water wave scattering by thick rectangular slotted barriers

Cited by 26 publications

References 19 publications

Water wave scattering by a rectangular trench

Water wave scattering by a rectangular trench

Re-expansion method for circular waveguide discontinuities: Application to concentric expansion chambers

Wave diffraction by a small elevation of the bottom of an ocean with an ice-cover

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