Master Degree / Yüksek Lisans Tezleri
Permanent URI for this collectionhttps://hdl.handle.net/11147/3008
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Master Thesis Solution of Dam Break Problem by Using Complex Analysis(Izmir Institute of Technology, 2014) Çaylıoğlu, Özge; Yılmaz, Oğuz; Yılmaz, Oğuz; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyIn this thesis, we examine the liquid flow and the free surface shape by using some methods of complex analysis during the early stage of dam breaking. In order to obtain the leading-order uniform solution, we use the asymptotic expansions with respect to a small parameter. The small parameter describe the initial duration of the stage. However, this solution which calls outer solution is not valid in a small vicinity of the intersection point between the vertical free surface and the horizontal rigid bottom. A local analysis of the outer solution helps to estimate the dimension of this vicinity. In the vicinity of the intersection point, local coordinates are stretched to solve the flow singularity and with the aid of these coordinates the leading order inner solution is obtained which describes the formation of the jet flow along the bottom.Master Thesis Hydrodynamic Interaction in Rotational Flow(Izmir Institute of Technology, 2007) Çağatay, Filiz; Yılmaz, Oğuz; Yılmaz, Oğuz; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyThe interaction of water waves with arrays of vertical cylinders problem is studied using diffraction of water waves and addition theorem for bessel functions. The linear boundary value problem which is derived from physical assumptions is used as the approximate mathematical model for time-harmonic waves. Linearization procedure is described for the nonlinear boundary conditions on the free surface. The problem is solved by using Addition theorem for Bessel functions. Limiting case, k 0, known as long wave approximation, is analysed using limiting forms of Bessel functions. Vortex-cylinder interaction is analyzed using a similar technique involving Laurent series expansions of complex velocity and the Circle Theorem. But this method failed to work. Further analysis is necessary. Vortex dynamics is analysed in annular domains, which can conformally be mapped into infinite domain with two cylinders, using the terminology of q-calculus. Finally, the result of vortex-cylinder interaction in annular domain is transformed into the infinite domain with two cylinders using conformal mapping. Image representation clearly shows the mechanism of inverse images which accumulate at zero and infinity in the w-plane and a and 1/a in the z-plane.Master Thesis The Initial Stages of Gravity Driven Flows(Izmir Institute of Technology, 2011) Isıdıcı Demirel, Damla; Yılmaz, Oğuz; Yılmaz, Oğuz; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyDuring the initial stage of dam breaking; the liquid flow and the free surface shape are investigated. We used small-time approximation for this investigation and derived the leading order solution of classical dam-break problem. But this solution is not valid in a small vicinity of the corner point (the intersection point between the initially vertical free surface and the horizontal rigid bottom). The dimension of this vicinity is estimated with the help of a local analysis of the this outer solution close to the corner point. Streched local coordinates are used in this vicinity to resolve the flow singularity and to derive the leading order inner solution (which describes the formation of the jet flow along the bottom) and the correction to the leading order. This asymptotic solution obtained is expected to be helpful in the analysis of developed gravity driven flows.