Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Linear Wave Interaction by Multiple Vertical Cylinders of Non-Circular Smooth Cross-Section: an Iterative-Asymptotic Approach(Elsevier Ltd, 2024) Yılmaz, Oğuz; Yilmaz,O.; 01. Izmir Institute of Technology; 04.02. Department of Mathematics; 04. Faculty of ScienceThe three-dimensional problem of water wave diffraction by multiple cylinders of non-circular smooth cross-sections is studied. The rigid cylinders extend from the sea bottom to the free surface in water of finite depth. The flow is described by the linear theory of potential flow. A fourth-order asymptotic solution of the diffraction problem by a single cylinder with the asymptotic parameter being the closeness of the cross-section to a circle is combined with an iterative method to consider the effect of the wave interaction between the cylinders. The original problem for non-circular cylinders is reduced to a set of diffraction and radiation problems for circular cylinders at each asymptotic order. The velocity potentials are given by their Fourier series, and the problem solving is simplified to the algebraic operations involving the Fourier coefficients of the potentials and the shape function, which describes the cross-sectional shape of the vertical cylinder. The hydrodynamic forces and wave run-up values for geometries of two elliptical and four nearly square cylinders are presented for a range of incident wave frequencies and angles of attack. The method is validated by comparing the present hydrodynamic force results with the ones in the literature, and good agreement is reported. © 2024 Elsevier LtdArticle Citation - WoS: 17Citation - Scopus: 18Linear Wave Interaction With a Vertical Cylinder of Arbitrary Cross Section: an Asymptotic Approach(American Society of Civil Engineers (ASCE), 2017) Dişibüyük, Nazile Buğurcan; Yılmaz, Oğuz; Yılmaz, Oğuz; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyAn asymptotic approach to the linear problem of regular water waves interacting with a vertical cylinder of an arbitrary cross section is presented. The incident regular wave was one-dimensional, water was of finite depth, and the rigid cylinder extended from the bottom to the water surface. The nondimensional maximum deviation of the cylinder cross section from a circular one plays the role of a small parameter of the problem. A fifth-order asymptotic solution of the problem was obtained. The problems at each order were solved by the Fourier method. It is shown that the first-order velocity potential is a linear function of the Fourier coefficients of the shape function of the cylinder, the second-order velocity potential is a quadratic function of these coefficients, and so on. The hydrodynamic forces acting on the cylinder and the water surface elevations on the cylinder are presented. The present asymptotic results show good agreement with numerical and experimental results of previous investigations. Long-wave approximation of the hydrodynamic forces was derived and used for validation of the asymptotic solutions. The obtained values of the forces are exact in the limit of zero wave numbers within the linear wave theory. An advantage of the present approach compared with the numerical solution of the problem by an integral equation method is that it provides the forces and the diffracted wave field in terms of the coefficients of the Fourier series of the deviation of the cylinder shape from the circular one. The resulting asymptotic formula can be used for optimization of the cylinder shape in terms of the wave loads and diffracted wave fields.