Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Citation - WoS: 1Citation - Scopus: 1A Three Dimensional Dam Break Flow: Small Time Behavior(Elsevier, 2021) Fetahu, Elona; Yılmaz, OğuzSmall time behavior of gravity driven free surface flows resulting from the collapse of a cavity is studied. Initially there is a rigid vertical cylinder of circular cross section starting from the free surface of a liquid and ending at the rigid bottom. The cylinder disappears suddenly and gravity driven flow of the fluid starts. The flow in early stage is described by the potential theory. Attention is paid to the singular behavior of the velocity field at the intersection line between the bottom and the free surface of the cavity. The leading order linear problem is solved by the Fourier series method. The flow velocity is log-singular at the intersection line. In the limiting case where the radius and the center of the cavity approach infinity, the problem is reduced to the classical two dimensional dam break problem where the fluid is initially on one side of a vertical wall (dry bed case). The flow resulting from cavity collapse is a three dimensional dam break flow. It is concluded that the three dimensional effects are important when the radius of the cavity is small compared with its depth and that the local flow near the intersection line of the cavity is governed only by the hydrostatic pressure.Article Citation - WoS: 7Citation - Scopus: 8Diffraction of Flexural-Gravity Waves by a Vertical Cylinder of Non-Circular Cross Section(Elsevier Ltd., 2020) Dişibüyük, Nazile Buğurcan; Korobkin, A. A.; Yılmaz, OğuzThe 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. © 2020 Elsevier Ltd