Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
Browse
3 results
Search Results
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; Yılmaz, Oğuz; Yılmaz, Oğuz; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyThe 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 LtdArticle Citation - WoS: 9Citation - Scopus: 10The Initial Stage of Dam-Break Flow of Two Immiscible Fluids. Linear Analysis of Global Flow(Elsevier Ltd., 2013) Yılmaz, Oğuz; Yılmaz, Oğuz; Iafrati, Alessandro; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyTwo-dimensional impulsive flow of two immiscible fluids is studied within the potential flow theory. Initially the fluids of different depths and different densities are at rest and separated with a thin vertical plate. The plate is withdrawn suddenly and gravity-driven flow of the fluids starts. During the early stage the flow is described by the linear potential theory. Attention is paid to the motion of the interface between the fluids and the singular behaviour of the velocity field at the triple point, where the free surfaces of the fluids and the interface meet each other. The linear problem is solved by the Fourier series method. Local analysis of the flow field close to the triple point reveals that the singularity of the flow depends on the ratio of the fluid densities with a coefficient dependent on both the density ratio and the shape of the flow region. The flow velocity is also log-singular at the point where the interface meets the bottom. The intensity of this singularity depends on the density ratio. The latter singularity disappears when the densities of the fluids are equal. The Fourier series solution supplemented by the singularity analysis at the corner points resolves these initial singularities. Comparisons with solutions obtained through the boundary element method are established for validation purposes. The numerical analysis of the problem by the boundary element method is carried out and it compares quite well with the Fourier series solution. The singular flow field which leads to the jet formation at the initial instant has been observed by both methods. The problem of dam-break flow for the wet-bed case corresponds to the present problem with equal densities of the fluids. Comparisons with data available in literature are established in the case of fluids with the same density.Article Citation - WoS: 6Citation - Scopus: 5Asymptotic Behavior of Linear Impulsive Integro-Differential Equations(Elsevier Ltd., 2008) Akhmet, Marat; Yılmaz, Oğuz; Yılmaz, Oğuz; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyAsymptotic equilibria of linear integro-differential equations and asymptotic relations between solutions of linear homogeneous impulsive differential equations and those of linear integro-differential equations are established. A new Gronwall-Bellman type lemma for integro-differential inequalities is proved. An example is given to demonstrate the validity of one of the results. © 2008 Elsevier Ltd. All rights reserved.