The wave energy scattering by interaction with the refracted breakwater and varying trench depth

Kim, Sung-Duk; Jun, Kye-Won; Lee, Ho-Jin

doi:10.1177/1687814015585430

Cited by 7 publications

(3 citation statements)

References 15 publications

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“…The normal and oblique incidence by the two-dimensional wave scattering by a rectangular submarine trench was considered by Mandal (2014, 2015) reducing the problem to solving appropriate integral equation which is solved by multi-term Galerkin approximation involving ultraspherical Gegenbauer polynomials. Kim et al (2015) investigated the effects of scattered wave fields around a breakwater when a dredging trench exists at the offshore seabed using Green's function based on the boundary integral technique. Later, Roy et al (2017) considered the problem of water wave scattering by an asymmetric rectangular trench using an approach similar to Mandal (2014, 2015).…”

Section: Introductionmentioning

confidence: 99%

Wave propagation over a rectangular trench in the presence of a partially immersed barrier

Ray

Mandal

2021

Fluid Dyn. Res.

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The problem of water wave propagation over a rectangular submarine trench in the presence of a thin vertical partially immersed barrier for its three different positions are investigated here assuming linear theory. For each position of the barrier, the problem is reduced to solving three weakly singular integral equations of first kind involving horizontal component of velocity above the two edges of the trench and below the barrier. The integral equations are solved employing Galerkin approximation in terms of simple polynomials multiplied by appropriate weight functions whose forms are dictated by the edge conditions at the corners of the trench and at the submerged end of the barrier. The numerical estimates for reflection and transmission coefficients are depicted graphically against the wave number for different lengths and positions of the barrier.

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Section: Introductionmentioning

confidence: 99%

Wave propagation over a rectangular trench in the presence of a partially immersed barrier

Ray

Mandal

2021

Fluid Dyn. Res.

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“…S. Lee 2004; H. S. Lee and Kim 2004;H. S. Lee et al 2009;Kim et al 2015). Another issue related with such types of bathymetries is that the trenches (cavities) usually act as sediment pockets or traps, resulting in a strong density stratification and the development of internal waves within them (Lassiter 1972;Ting 1994).…”

Section: Introductionmentioning

confidence: 99%

“…It has also been recognized that a single trench or a system of multiple trenches modify the local wave climate and may function as a submerged breakwater, called pit breakwater or multiple-pit breakwater, respectively; see e.g. (McDougal et al 1996; H. S. Lee 2004; H. S. Lee and Kim 2004; H. S. Lee et al 2009;Kim et al 2015). Another issue related with such types of bathymetries is that the trenches (cavities) usually act as sediment pockets or traps, resulting in a strong density stratification and the development of internal waves within them (Lassiter 1972;Ting 1994).…”

Section: Introductionmentioning

confidence: 99%

A numerical study of the run-up and the force exerted on a vertical wall by a solitary wave propagating over two tandem trenches

Athanassoulis

Mavroeidis

Koutsogiannakis

et al. 2019

J. Ocean Eng. Mar. Energy

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1. Introduction 2. An overview of the fully non-linear Hamiltonian Coupled-Mode Theory 2.1. Classical differential and variational formulation 2.2. The Hamiltonian Coupled-Mode Theory 3. A concise description of the numerical implementation 3.1. Numerical solution of the kinematical substrate problem 3.2. Numerical solution of the Hamiltonian evolution equations 4. Propagation of a solitary wave over some typical bathymetries. Validation and limitations of the present method 4.1. Propagation over a shelf 4.2. Propagation over a step 4.3. Comparison and assessment of the findings of Sec. 4.1 and 4.2 4.4. Propagation over a trench 5. Propagation of a solitary wave over two trenches and reflection at a vertical wall 5.1. Propagation over the trenches 5.2. Run-up on the wall 5.3. Maximum force exerted on the vertical wall Conclusions A numerical study of the run-up and the force exerted on a vertical wall by a solitary wave propagating over two tandem trenches and impinging on the wall AbstractThe propagation and transformation of water waves over varying bathymetries is a subject of fundamental interest to ocean, coastal and harbor engineers. The specific bathymetry considered in this paper consists of one or two, naturally formed or man-made, trenches. The problem we focus on is the transformation of an incoming solitary wave by the trench(es), and the impact of the resulting wave system on a vertical wall located after the trench(es). The maximum run-up and the maximum force exerted on the wall are calculated for various lengths and heights of the trench(es), and are compared with the corresponding quantities in the absence of them. The calculations have been performed by using the fully nonlinear water-wave equations, in the form of the Hamiltonian coupled-mode theory, recently developed in Papoutsellis et al (Eur. J. Mech. B/Fluids, Vol. 72, 2018, pp. 199-224). Comparisons of the calculated free-surface elevation with existing experimental results indicate that the effect of the vortical flow, inevitably developed within and near the trench(es) but not captured by any potential theory, is not important concerning the frontal wave flow regime. This suggests that the predictions of the run-up and the force on the wall by nonlinear potential theory are expected to be nearly realistic.The main conclusion of our investigation is that the presence of two tandem trenches in front of the wall may reduce the run-up from (about) 20% to 45% and the force from 15% to 38%., depending on the trench dimensions and the wave amplitude. The percentage reduction is greater for higher waves. The presence of only one trench leads to reductions 1.4 -1.7 times smaller.Keywords: nonlinear water waves; wave-trench interaction; solitary wave over varying bathymetry; run-up on vertical wall; force on vertical wall; submerged breakwater

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Oblique wave interaction with an infinite trench in presence of a bottom-standing thick rectangular barrier

Ray¹,

Sarkar²,

De³

2023

J Eng Math

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The wave energy scattering by interaction with the refracted breakwater and varying trench depth

Cited by 7 publications

References 15 publications

Wave propagation over a rectangular trench in the presence of a partially immersed barrier

Wave propagation over a rectangular trench in the presence of a partially immersed barrier

A numerical study of the run-up and the force exerted on a vertical wall by a solitary wave propagating over two tandem trenches

Oblique wave interaction with an infinite trench in presence of a bottom-standing thick rectangular barrier

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