Linear Wave Interaction with a Vertical Cylinder of Arbitrary Cross Section: An Asymptotic Approach

Dişibüyük, N.B.; Korobkin, A.A.; Yılmaz, Oğuz

doi:10.1061/(asce)ww.1943-5460.0000407

Cited by 15 publications

(8 citation statements)

References 21 publications

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“…In the present paper, diffraction of hydro-elastic waves by a vertical cylinder of an arbitrary smooth cross section is investigated by using the vertical mode method (Korobkin et al [8]) and the asymptotic method of Disibuyuk et al [11]. The asymptotic solution of the problem is based on the idea that the cross section of the cylinder can be described by a perturbation series using a small parameter representing the deviation of the cross section of the cylinder from a circle.…”

Section: Introductionmentioning

confidence: 99%

Diffraction of flexural-gravity waves by a vertical cylinder of non-circular cross section

Dişibüyük

Korobkin

Yılmaz

2020

Applied Ocean Research

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The linear three-dimensional problem of flexural-gravity wave (hydro-elastic wave) diffraction by a vertical cylinder of an arbitrary smooth cross section is studied using an asymptotic approach combined with the vertical mode method for water of finite depth. The surface of the water is covered by an infinite, continuous elastic ice plate. The rigid cylinder extends from the sea bottom to the ice surface. The ice plate is frozen to the cylinder. The ice deflection is described by the equation of a thin elastic plate of constant thickness with clamped edge conditions at the cylinder. The flow under the ice is described by the linear theory of potential flows. The coupled problem of wave diffraction is solved in two steps. First, the problem is solved without evanescent waves similar to the problem of water waves diffracted by a vertical cylinder. This solution does not satisfy the edge conditions. Second, a radiation problem with a prescribed motion of the ice plate edge is solved by the vertical mode method. The sum of these two solutions solve the original problem. Both solutions are obtained by an asymptotic method with a small parameter quantifying a small deviation of the cylinder cross section from a circular one. Third-order asymptotic solutions are obtained by solving a set of two-dimensional boundary problems for Helmholtz equations in the exterior of a circle. Strains along the edge, where the ice plate is frozen to the cylinder, are investigated for nearly square and elliptic cross sections of the vertical cylinders depending on the characteristics of ice and incident wave. The strains are shown to be highest in the places of high curvatures of the cross sections. The derived asymptotic formulae can be used in design of vertical columns in ice. They directly relate the strains in ice plate to the shape of the column.

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Section: Introductionmentioning

confidence: 99%

Diffraction of flexural-gravity waves by a vertical cylinder of non-circular cross section

Dişibüyük

Korobkin

Yılmaz

2020

Applied Ocean Research

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“…Alternatively, Dişibűyűk, Korobkin and Yilmaz [26] solved wave diffraction from a uniform vertical cylinder of arbitrary cross section by using an asymptotic approach, in which a fifth-order asymptotic expansion of the velocity potential was substituted in the boundary condition. The agreement between their theoretical predictions of the hydrodynamic forces and wave run-up and those from Liu, Guo and Li [24] was shown to be fairly good.…”

Section: Introductionmentioning

confidence: 99%

Wave diffraction from multiple truncated cylinders of arbitrary cross sections

Zheng

Zhang

Liu

et al. 2020

Applied Mathematical Modelling

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Many marine structures are supported by piles or caissons which, from a mathematical point of view, can be assimilated to an array of truncated cylinders of arbitrary cross sections. The focus of this paper is such an array subjected to harmonic waves of small steepness. We develop an analytic method based on linear potential flow theory to solve the diffraction problem and evaluate the excitation forces and moments acting on each cylinder. The water domain is divided into the interior regions below each cylinder and an exterior region extending to infinity in the horizontal plane. A series of eigen-functions are applied to express the velocity potential in each region. The Fourier series method combined with the eigen-function expansion matching method is used to satisfy the wetted surface body conditions and continuity conditions between adjacent regions. The analytic model is validated by comparing its results with numerical modelling results and published data. It is then applied to two truncated cylinders with caisson cross sections, and results are given for the excitation forces and moments on each cylinder for different values of incident wave direction and spacing between the cylinders, and for different configurations.

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“…The semi-analytical results of both wave excitation forces and water elevation around the cylinder agreed rather well with the numerical ones. Additionally, the problem of wave diffraction from a bottom-mounted cylinder was also considered by Disibüyük et al (2017) with an asymptotic approach. The asymptotic solution of the wave run-up around the cylinder with cosine-type perturbation cross section provided good agreement with those by Liu et al (2016).…”

Section: Introductionmentioning

confidence: 99%

Wave radiation from a truncated cylinder of arbitrary cross section

et al. 2019

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In this paper, a semi-analytical model for solving wave radiation from a truncated cylinder of arbitrary cross section is presented based on linear potential flow theory. The water domain is divided into the interior domain beneath the cylinder and the exterior domain outside the vertical cylinder column. Radiated spatial potentials in these subdomains are expressed as a series expansion of eigen-functions using the method of separation of variables. The continuity conditions for pressure and velocity are satisfied at the interface of the two domains, where the Fourier series expansion method is employed to deal with the radius function associated terms. Therefore, the unknown coefficients in the radiated potential expressions are determined by means of the eigen-function matching method. Hydrodynamic coefficients of the truncated cylinder are evaluated directly based on the radiated spatial potentials. Case studies on wave radiation from a truncated cylinder with "cosine" and "circular" cross sections show a good agreement between the semi-analytical results of added-mass/radiation damping and numerical ones/published data. The validated semi-analytical model is then adopted to study the hydrodynamic characteristics of truncated cylinders with "circular", "cosine", "elliptical" and "quasi-elliptical" sections. For the latter case, the influence of draft on wave radiation is also investigated.

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Linear Wave Interaction with a Vertical Cylinder of Arbitrary Cross Section: An Asymptotic Approach

Cited by 15 publications

References 21 publications

Diffraction of flexural-gravity waves by a vertical cylinder of non-circular cross section

Diffraction of flexural-gravity waves by a vertical cylinder of non-circular cross section

Wave diffraction from multiple truncated cylinders of arbitrary cross sections

Wave radiation from a truncated cylinder of arbitrary cross section

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