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Wave Radiation From a Truncated Cylinder of Arbitrary Cross Sections
(01. Izmir Institute of Technology, 2021) Korkmaz, Ece Hazal; Yılmaz, Oğuz
Wave radiation problem in heaving motion from a vertical cylinder of circular cross-section and truncated cylinder of an arbitrary cross-section in the water of finite depth is studied. First, wave radiation from the circular cylinder is summarized which was solved analytically by Yeung (1981). The water domain is divided into two regions: the interior region below the cylinder and the exterior region outside the cylinder. The interior and exterior solutions are matched by the continuity of pressure and normal velocity in both cases. The vertical cylinder of a circular cross-section is solved by using the separation of variables method in cylindrical coordinates. The coefficients of interior and exterior solutions are related by the matching conditions. The system of equations formed by these unknown coefficients has been solved. Then, the non-dimensional z component of force is calculated by integrated pressure on the floating body. The real part and imaginary parts of this force give added mass and damping coefficients in heaving motion, respectively. These numerical results are used for the verification of asymptotic solutions of the present thesis. In the second case of this thesis, we treat wave radiation problems in heaving motion from the non-circular cylinder by using an asymptotic method. The asymptotic method of this thesis was suggested by Dişibüyük et al. (2017). Dişibüyük et al. (2017) suggested the non-dimensional maximum deviation of the cylinder cross-section from a circular one plays the role of a small parameter of the problem. The third-order asymptotic solution is used. Unknown coefficients of interior and exterior potentials are solved by using Fourier coefficients at each order of approximation. The advantage of the method is that the boundary conditions can be solved for different cross-sections by using the Fourier coefficients. The results are compared with other numerical results.
Solution of Dam Break Problem by Using Complex Analysis
(Izmir Institute of Technology, 2014) Çaylıoğlu, Özge; Yılmaz, Oğuz
In 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.
Hydrodynamic Interaction in Rotational Flow
(Izmir Institute of Technology, 2007) Çağatay, Filiz; Yılmaz, Oğuz
The 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.
The Initial Stages of Gravity Driven Flows
(Izmir Institute of Technology, 2011) Isıdıcı Demirel, Damla; Yılmaz, Oğuz
During 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.

Master Degree / Yüksek Lisans Tezleri

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