Wave transformation due to multiple bottom-standing porous barriers

Karmakar, D.; Soares, C. Guedes

doi:10.1016/j.oceaneng.2014.01.012

Cited by 66 publications

(13 citation statements)

References 39 publications

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“…[1] are also added in these tables. For solid barriers, the fluid velocity at the gap Λ can also be expanded using a similar method to that in (21). The two approaches based on expanding the pressure jump at D and the fluid velocity at Λ for solid barrier can give the lower and upper bounds of hydrodynamic quantities, respectively.…”

Section: Resultsmentioning

confidence: 99%

“…Substituting the expressions for the velocity potentials in (11) into (21) and multiplying both sides of the obtained new equation by ( ) and then integrating with respect to over [− , 0] and using (14) and (15), we have…”

Section: Multi-term Galerkin Methods Following Porter Andmentioning

confidence: 99%

“…Sahoo et al [20] generalized the solution of Lee and Chwang [19] to obliquely incident waves. Recently, Karmakar and Guedes Soares [21] developed analytical solution for wave transformation due to multiple bottom-standing flexible porous barriers using eigenfunction expansion method. Gayen and Mondal [22] studied normally incident wave reflection and transmission by a submerged inclined porous barrier by solving a second kind hypersingular integral equation.…”

Section: Introductionmentioning

confidence: 99%

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Accurate Solutions to Water Wave Scattering by Vertical Thin Porous Barriers

Liu

2015

Mathematical Problems in Engineering

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The water wave scattering by vertical thin porous barriers is accurately solved in this study. Two typical structures of a surface-piercing barrier and a submerged bottom-standing barrier are considered. The solution procedure is based on the multi-term Galerkin method, in which the pressure jump across a porous barrier is expanded in a set of basis functions involving the Chebychev polynomials. Then, the square-root singularity of fluid velocity at the edge of the porous barrier is correctly modeled. The present solutions have the merits of very rapid convergence. Accurate results for both the reflection and the transmission coefficients and wave forces are presented. This study not only gives a promising procedure to tackle wave interaction with vertical thin porous barriers but also provides a reliable benchmark for complicated numerical solutions.

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Section: Resultsmentioning

confidence: 99%

Section: Multi-term Galerkin Methods Following Porter Andmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Accurate Solutions to Water Wave Scattering by Vertical Thin Porous Barriers

Liu

2015

Mathematical Problems in Engineering

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“…Karmakar et al [17] developed a model for wave scattering by multiple bottom-standing flexible porous barriers using the methods of least squares and wide-spacing approximation. Several aspects of wave scattering by multiple surface-piercing floating membrane were studied by Karmakar and Soares [18], who reported that the number of barriers and the barrier spacing can play a central role in controlling wave transmission. Apart from wave interaction with vertical structures, there has been significant progress on wave past horizontal structures of different configurations.…”

Section: Introductionmentioning

confidence: 99%

Interaction between oblique waves and multiple bottom-standing flexible porous barriers near a rigid wall

Behera

2017

Meccanica

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The interaction between oblique surface waves and multiple bottom-standing flexible porous barriers under the combined effects of a neighboring rigid vertical wall and a step of arbitrary profile on the bottom is investigated. The problem is analyzed under the assumptions of small-amplitude water waves and structural response. The solutions are found using the methods of least-squares approximation, eigenfunction expansion and multi-mode approximation associated with the modified mild-slope equation. To keep the barriers at a desired position of interest, clamped-free or clamped-moored edge conditions are considered. Effects of various wave and structural parameters are studied for single, double and multiple barriers by looking into the reflection coefficient, wave force exerted on the rigid wall, free-surface elevations, and plate deflection of the barriers. The model is validated by comparing with results available in the literature for the special case of wave interaction with single and double rigid porous barriers near a rigid wall in the presence of a vertical step. The study reveals that the presence of multiple flexible porous barriers may effectively reduce the wave reflection and wave force exerted on the rigid wall. Further, full and nearly zero wave reflection can be found in the case of single and/or multiple barriers.

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“…Feng and Lu (2011) investigated the problem of interaction of water waves with floating structures of arbitrary shapes with the aid of an eigenfunction expansion method. Karmakar and Soares (2014) Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/oceaneng investigated the linear water wave propagation of oblique surface waves through multiple bottom standing flexible porous barriers.…”

Section: Introductionmentioning

confidence: 99%