Yılmaz, Oğuz
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Yılmaz, O
Yılmaz, O.
Yilmaz, O
Yilmaz, O.
Yilmaz, Oguz
Yılmaz, O.
Yilmaz, O
Yilmaz, O.
Yilmaz, Oguz
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oguzyilmaz@iyte.edu.tr
Main Affiliation
04.02. Department of Mathematics
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Current Staff
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Sustainable Development Goals
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Documents
35
Citations
353
h-index
11
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Scholarly Output
29
Articles
20
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70400/11785
Supervised MSc Theses
4
Supervised PhD Theses
5
WoS Citation Count
117
Scopus Citation Count
125
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0
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4
WoS Citations per Publication
4.03
Scopus Citations per Publication
4.31
Open Access Source
24
Supervised Theses
9
| Journal | Count |
|---|---|
| Applied Ocean Research | 4 |
| Journal of Physics A: Mathematical and Theoretical | 2 |
| Journal of Engineering Mathematics | 2 |
| Ocean Engineering | 2 |
| Journal of Computational Technologies | 1 |
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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 LtdArticle Citation - WoS: 1Citation - Scopus: 1Initial Stages of Gravity-Driven Flow of Two Fluids of Equal Depth(American Institute of Physics, 2023) Korobkin, Alexander; Yılmaz, OğuzShort-time behavior of gravity-driven free surface flow of two fluids of equal depth and different densities is studied. Initially, the fluids are at rest and separated with a vertical rigid plate of negligible thickness. Then, the plate disappears suddenly and a gravity-driven flow of the fluids starts. The flow in an early stage is described by the potential theory. The initial flow in the leading order is described by a linear problem, which is solved by the Fourier series method. The motions of the interface between the fluids and their free surfaces are investigated. The singular behaviors of the velocity field at the bottom point, where the interface meets the rigid bottom, and the top point, where the interface meets both free surfaces, are analyzed in detail. The flow velocity is shown to be log-singular at the bottom point. The leading-order inner asymptotic solution is constructed in a small vicinity of this point. It is shown that the flow close to the bottom point is self-similar. The motion of the interface is independent of any parameters, including the density ratio, of the problem in specially stretched variables. In the limiting case of negligible density of one of the fluids, the results of the classical dam break problem are recovered. The Lagrangian representation is employed to capture the behavior of the interface and the free surfaces at the top, where the fluid interface meets the free surfaces. The shapes of the free surfaces and the interface in the leading order computed by using the Lagrangian variables show a jump discontinuity of the free surface near the top point where the free surfaces and the interface meet. Inner region formulation is derived near the top point.Article Asymptotic Behaviour of Dam Break Flow for Small Times(Institute of Computational Technologies SB RAS, 2019) Isıdıcı Demirel, Damla; Iafrati, Alessandro; Korobkin, Alexander A.; Yılmaz, OğuzTwo dimensional impulsive flow of a fluid is studied within the potential flow theory. Initially the fluid is at rest and is held on one side of a vertical plate. The plate is withdrawn suddenly and gravity driven flow of the fluid starts. Attention is paid to the singular behaviour of the velocity field at the bottom point, where the vertical free surface meets the rigid bottom. The linear problem is solved by the Fourier series method. An inner region solution is found using Mellin transform at the bottom point. The jet formation is observed at the bottom point. Also the discontinuity at the upper corner point is dealt with Lagrangian variables. For the second order outer problem, domain decomposition method is used. Comparison of the shapes of the free surfaces near the upper corner point with leading and second order solutions shows that the second order outer solution outer makes a larger difference in the vertical free surface than in the horizontal portion, compared with leading order solution.The complete picture of the shapes of the free surfaces using Lagrangian description for the upper part and Eulerian description for the bottom part at the second order is obtained. © ICT SB RAS, 2019Article Citation - WoS: 4Citation - Scopus: 4Power-Series Solution for the Two-Dimensional Inviscid Flow With a Vortex and Multiple Cylinders(Springer Verlag, 2009) Pashaev, Oktay; Yılmaz, OğuzThe problem of a point vortex and N fixed cylinders in a two-dimensional inviscid fluid is studied and an analytical-numerical solution in the form of an infinite power series for the velocity field is obtained using complex analysis. The velocity distribution for the case of two cylinders is compared with the existing results of the problem of a vortex in an annular region which is conformally mapped onto the exterior of two cylinders. Limiting cases of N cylinders and the vortex, being far away from each other are studied. In these cases, "the dipole approximation" or "the point-island approximation" is derived, and its region of validity is established by numerical tests. The velocity distribution for a geometry of four cylinders placed at the vertices of a square and a vortex is presented. The problem of vortex motion with N cylinders addressed in the paper attracted attention recently owing to its importance in many applications. However, existing solutions using Abelian function theory are sophisticated and the theory is not one of the standard techniques used by applied mathematicians and engineers. Moreover, in the N ≥ 3 cylinder problem, the infinite product involved in the presentation of the Schottky-Klein prime function must also be truncated. So, the approach used in the paper is simple and an alternative to existing methods. This is the main motivation for this study.Doctoral Thesis Short Time Behaviour of Dam Break Flow Involving Two Liquids(Izmir Institute of Technology, 2018) Isıdıcı Demirel, Damla; Yılmaz, OğuzThe two dimensional dam break problem for wet bed case is investigated. The leading order and the second order problem are stated in nondimensional form. Solution to the leading order problem by using three different methods is given and explained in detail. Both Fourier series method and Galerkin method have difficulties on its own because of the singularity at the triple point. Although the singularity is ignored in Galerkin method, the method does not work except for the interface. Thus conformal mapping techniques is preferred because of the convenience and the strength of the complex analysis. The velocity profiles at whole boundary are obtained by using this conformal mapping. The second order solution of velocities are also obtained by using the same conformal mapping. On the other hand, the domain decomposition method (DDM) is applied for the second order dam break problem of dry bed case. The leading order solution helped to determine the suitable parameters for DDM. The leading order and second order solution of the free surfaces give a more realistic shape using the Lagrangian solution at the upper corner point. We assume this work contains useful and applicable methods in it for gravity driven flows and it will wake up different perspectives in readers mind.Doctoral Thesis Solution of Maxwell Equations on Deformed Spherical Domains: Applications To the Scattering Problems(Izmir Institute of Technology, 2015) Ateş, Barış; Yılmaz, OğuzIn the present work, firstly we consider analytic solution of the Maxwell’s Equations in the vacuum in the presence of conducting deformed spherical body. Deformation is made in the normal direction of sphere with a small perturbation parameter and arbitrarily chosen smooth deformation function f ( ; φ). The azimuthal and polar angle dependence of the function is preserved till the end. Using the Debye Potentials the solution in the exterior domain of deformed conducting spherical body is given. In addition to this, scattering of electromagnetic plane waves from non-spherical dielectric and conducting objects are considered. In order to find scattered and transmitted fields, in contrast to common use of vector wave functions and their orthogonality properties, the scalar functions and orthogonalities of Associated Legendre Polynomials are used. All the surface integrals are evaluated analytically. The corrections to the coefficients of scattered and transmitted fields up to the second order are obtained and expressed in terms of the Clebsch-Gordon coefficients.Master Thesis The Initial Stages of Gravity Driven Flows(Izmir Institute of Technology, 2011) Isıdıcı Demirel, Damla; Yılmaz, OğuzDuring 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.Doctoral Thesis Asymptotic Behaviour of Gravity Driven Free Surface Flows Resulting From Cavity Collapse(Izmir Institute of Technology, 2020) Fetahu, Elona; Yılmaz, OğuzIn this thesis, the gravity driven potential flows that result from cavity collapse are studied. Initially, the collapse of a vertical cylindrical cavity of circular cross sections surrounded by a liquid region is examined for two different situations. In the first one the cavity has same depth as the fluid and in the second one the cavity starts from the free surface and has less depth than the fluid. The problem is formulated by using a small parameter that represents the short duration of the stage. The first problem, as the radius and the centre of the cavity approach infinity, reduces to the classical two-dimensional dam break problem solved by Korobkin and Yilmaz (2009). The singularity of the radial velocity at the bottom circle is shown to be of logarithmic type. In the second problem, where the cavity is less deep than the fluid, the flow region is separated into two regions: the interior one, which is underneath the cylindrical cavity and above the rigid bottom, and the exterior one, which is the rest of the flow. The corresponding new problems are solved separately and then the coefficients are found by applying the matching conditions at the interface, where the fluid radial velocities and pressures coincide. On the limiting case, the problem reduces to the two-dimensional dam break flow of two immiscible fluids by Yilmaz et al. (2013a). Singularity at the bottom circle of the cavity is observed, which is of the same type as in the latter paper. Next, a third problem studies the gravity driven flow caused by the collapse of a rectangular section of a vertical plate. During the early stage, the flow is described by the velocity potential. Attention is paid to determining the velocity potential and free surface shapes. The solution follows the Fourier series method in Renzi and Dias (2013) and the boundary element method in Yilmaz et al. (2013a). Singularity is observed at the side edges and lower edge of the rectangular section. The horizontal velocity of the initially vertical free surface along the vertical line of symmetry of the rectangle is the same to the one in the two-dimensional problem Korobkin and Yilmaz (2009). The singularities observed in these problems lead to the jet formation for the initial stage. The methods applied in these computations are expected to be helpful in the analysis of gravity-driven flow free surface shapes. This thesis is a contribution towards the 3-D generalizations of dam break problems.Article Second Order Diffraction of Water Waves by a Bottom Mounted Vertical Circular Cylinder and Some Related Numerical Problems(The American Society of Mechanical Engineers(ASME), 2007) Yılmaz, OğuzA Hankel transformation is used to obtain the second order diffraction solution of vertical cylinder of circular cross section. The improper integral over the free surface is tackled carefully. The singularity at the free surface is overcome effectively using a third order nonlinear transformation. Numerical results for free surface elevations compare well with the published data.Article Citation - WoS: 30Citation - Scopus: 33The Initial Stage of Dam-Break Flow(Springer Verlag, 2009) Korobkin, Alexandre; Yılmaz, OğuzThe liquid flow and the free surface shape during the initial stage of dam breaking are investigated. The method of matched asymptotic expansions is used to derive the leading-order uniform solution of the classical dam-break problem. The asymptotic analysis is performed with respect to a small parameter which characterizes the short duration of the stage under consideration. The second-order outer solution is obtained in the main flow region. This solution is not valid in a small vicinity of 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 outer solution close to the intersection point. Stretched 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. It is shown that the inner solution is self-similar and the corresponding boundary-value problem can be reduced to the well-known Cauchy-Poisson problem for water waves generated by a given pressure distribution along the free surface. An analysis of the inner solution reveals the complex shape of the jet head, which would be difficult to simulate numerically. The asymptotic solution obtained is expected to be helpful in the analysis of developed gravity-driven flows.
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