A mathematical study of a two-layer fluid flow system in the presence of a floating breakwater in front of VLFS

Barman, Koushik Kanti; Chanda, Ayan; Tsai, Chia‐Cheng

doi:10.1016/j.apm.2023.06.017

Cited by 13 publications

(16 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where 𝑏 0 (1) (𝜈 1 ) and 𝑏 0 (2) (𝜈 2 ) represents the amplitudes of the surface and internal wave modes, respectively.…”

Section: Formulationmentioning

confidence: 99%

“…The kinematic and dynamic conditions on the upper surface and the interface satisfied by 𝜉 (1) and 𝜉 (2) , are as follows:…”

Section: Of 15mentioning

confidence: 99%

“…The eigenfunctions 𝑊 (1) (𝜈 𝑛 , 𝑧) and 𝑊 (2) (𝜈 𝑛 , 𝑧) are given by ( 3) and ( 4), respectively and 𝜈 𝑗 (1) and 𝜈 𝑗 (2) are roots of the dispersion relations given by:…”

Section: Radiated Potentialmentioning

confidence: 99%

“…𝛹 2 (𝑠) (𝑟, 𝑧) = 𝐷 0 (1) 𝑉 1 (𝜂 0 (1) , 𝑟) 𝑌 (𝑠) (𝜂 0 (1) , 𝑧) + 𝐷 0 (2) 𝑉 1 (𝜂 0 (2) , 𝑟) 𝑌 (𝑠) (𝜂 0 (2) , 𝑧) + { ∑ 𝐷 𝑘 (1) 𝑉 1 (𝜂 𝑘 (1) , 𝑟) 𝑌 (𝑠) (𝜂 𝑘 (1) , 𝑧) + ∞ 𝑘=1 ∑ 𝐷 𝑘 (2) 𝑉 1 (𝜂 𝑘 (2) , 𝑟) 𝑌 (𝑠) (𝜂 𝑘 (2) , 𝑧) where 𝑉 1 (𝜂 0 (1) , 𝑟), 𝑉 1 (𝜂 0 (2) , 𝑟), 𝑉 1 (𝜂 𝑘 (1) , 𝑟) and 𝑉 1 (𝜂 𝑘 (2) , 𝑟) are the radial eigenfunctions given respectively by: 𝑉 1 (𝜂 0 (1) , 𝑟)…”

Section: Radiated Potentialmentioning

confidence: 99%

“…The various concept of the interaction of water waves with geometrical structure have been covered [1]. The study on the effect of interaction of waves with floating structures like porous breakwater, very large floating structures (VLFS), have gained popularity [2,3]. Further the installation of wave energy devices on breakwater have gained popularity due to its cost savings and space [4].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Analysis of Hydrodynamic Loads by a Vertical Hollow Cylindrical Structure in A Two-Layer Fluid of Finite Depth

Tashi,

Hassan

2024

Trends Sci

View full text Add to dashboard Cite

This paper aims to study the effect of surge radiation by a vertically hollow cylinder floating in a two-layer fluid of finite depth. Since most of the important characteristics of the oscillating water column are preserved by the hollow cylindrical structure, so the proposed device can be considered as an oscillating water column (OWC) which is one of the important wave energy device. In this two-layer fluid system, the upper layer is bounded above by a free surface and the lower layer is bounded below by a solid impermeable bottom, and the submerged hollow cylindrical structure allows it to oscillate in a surge mode of motion in the upper layer. On the assumption that wave amplitudes are small in comparison to wavelengths, hence the linear water wave theory is applied to formulate boundary value problems by dividing whole domain into 2 sub-domains. The formulated boundary value problems for surge radiated potentials in each sub-domain; we execute to obtain solutions in each sub-domain by using variable separation and matched eigenfunction expansion methods. With the help of obtained surge radiated potentials, we derive the radiation forces by the device in terms of added mass and damping coefficients. A set of influences of different parameters of the device on the added mass and damping coefficients are demonstrated in both surface and internal wave modes of motion. Hydrodynamic coefficients oscillate highly near a particular frequency, which leads to the resonance phenomena. In addition to that, the 3D plots of the free surface elevation in surface and internal wave modes are presented. A density ratio γ = 0.97 has a higher oscillation than a density ratio γ = 0.93, 0.95. High oscillations occur around a particular frequency ω = 3.83 due to the resonance phenomenon in which the waves incoming match with the natural motion of the object. HIGHLIGHTS A floating hollow vertical cylindrical structure is considered in a two-layer fluid system having finite depth The separation of variables and matched eigenfunction expansion methods are utilized to obtain the solutions to the boundary-value problems The diffracted velocity potentials under the surge mode of motion are evaluated in the identified regions The added mass, damping coefficients, free surface and interface elevations in surface and internal wave modes are evaluated with different set of parameters of the device A number of results are presented regarding the effect of parameters of the device on the added mass, damping coefficients, free surface and interface elevations It is observed that the density ratio of the two-layer fluid has significant effect on the added mass, damping coefficient and the elevations GRAPHICAL ABSTRACT

show abstract

“…where 𝑏 0 (1) (𝜈 1 ) and 𝑏 0 (2) (𝜈 2 ) represents the amplitudes of the surface and internal wave modes, respectively.…”

Section: Formulationmentioning

confidence: 99%

“…The kinematic and dynamic conditions on the upper surface and the interface satisfied by 𝜉 (1) and 𝜉 (2) , are as follows:…”

Section: Of 15mentioning

confidence: 99%