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Streamline Topology of Axisymmetric Flow Near Non-Simple Singular Point

Yıl 2018, Cilt 39, Sayı 3, 557 - 564, 30.09.2018
https://doi.org/10.17776/csj.431321

Öz

The aim of this paper is to obtain streamline patterns of axisymmetric flow and their bifurcations for 2-D incompressible flows close to non-simple singular point. The streamlines of a Hamiltonian vector field system are simplified by using the homotopy invariance of the index theory. Using a homotopy invariance of the index, we develop a theory for the sufficient and necessary conditions for structural bifurcation of axisymmetric flow near non-simple degenerate critical points. The variation of parameters in the flow field can cause structural bifurcations. The bifurcation of the degenerate flow structure is obtained when it is perturbed slightly.

Kaynakça

  • [1]. Brøns, M., Voigt, L.K. and Sørensen, J.N., Topology of vortex breakdown bubbles in a cylinder with a rotating bottom and a free surface, J. Fluid Mech. 428 (2001) 133-148.
  • [2]. Brøns, M., Voigt, L.K. and Sørensen, J.N., Streamline topology of steady axisymmetric vortex breakdown in a cylinder with co- and counter-rotating end-covers, J. Fluid Mech., 401 (1999) 275-292.
  • [3]. Bisgaard, A.V., Brøns, M. and Sørensen, J.N., Vortex breakdown generated by off-axis bifurcation in a cylinder with rotating covers, Acta Mech. 187 (2006) 75-83.
  • [4]. Brøns M., Topologic al fluid mechanics of axisymmetric flows, In simulation and identification of organized structures in flows, (ed. J. N. Sørensen et al.), Kluwer Academic Publishers, Dordrecht, (1999) 213-222.
  • [5]. Brøns M., Streamline patterns and their bifurcations using methods from dynamical systems, In: Ricca R.L. (eds), An introduction to the geometry and topology of fluid flows, NATO Science Series (Series II: Mathematics, Physics and Chemistry), Springer, Dordrecht, 47 (2001) 167-182.
  • [6]. Bisgaard, A. V., Structures and bifurcations in fluid flows with applications to vortex breakdown and wakes, PhD thesis, Department of Mathematics, Technical University of Denmark, (2005).
  • [7]. Bakker, P.G., Bifurcation in flow patterns, vol. 2: Nonlinear topics in the mathematical sciences, Dordrecht: Klüver, (1991).
  • [8]. Brøns, M. and Hartnack, J.N., Streamline topologies near simple-degenerate critical points in two-dimensional flow away from boundaries, Phys. Fluids, 11(1999) 314-324.
  • [9]. Hartnack, J.N., Streamlines topologies near a fixed wall using normal form, Acta Mech., 136 (1999) 55-75.
  • [10]. Deliceouğlu, A. and Gürcan, F., Streamline topology near non-simple degenerate critical points in two-dimensional flow with symmetry about an axis, J. Fluid Mech., 606 (2008) 417-432.
  • [11]. Gürcan F. and Deliceoğlu, A., Streamline topologies near non-simple degenerate points in two dimensional flows with double symmetry away from boundaries and an application, Phys. Fluids, 17 (2005) 093116.
  • [12]. Deliceoğlu, A., Dinamik sistemler ve basit olmayan dejenere nokta civarındaki sıkıştırılamaz akışların topolojik çatallanmaları, Ph.D Thesis, University of Erciyes, (2004).
  • [13]. Ma, T. and Wang, S., Interior structural bifurcation and seperation of 2D incompressible flows, J. Math. Phys., 45 (2004) 1762-1776.
  • [14]. Ma, T. and Wang, S., Geometric theory of incompressible flows with applications to fluid dynamics (Mathematical Surveys and Monographs, American Mathematical Society), (2005).
  • [15]. Ma, T. and Wang, S., Structural classification and stability of divergence-free vector fields, Physica D, 171 (2002) 107-126.

Basit Olmayan Dejenere Nokta Civarındaki Eksenel Simetrik Akış Topolojisi

Yıl 2018, Cilt 39, Sayı 3, 557 - 564, 30.09.2018
https://doi.org/10.17776/csj.431321

Öz

Bu makalenin amacı basit olmayan tekil nokta civarındaki 2-Boyutlu sıkıştırılamaz akışlar için eksenel simetrik akışların akış çizgi modellerini ve onların çatallanmalarını elde etmektir. Hamiltoniyen vektör alan sisteminin akış çizgileri, indeks teorisinin homotopi değişmezliği kullanılarak basitleştirildi. İndeksin homotopi değişmezliği kullanılarak, basit olmayan dejenere nokta civarında, eksenel simetrik akışın yapısal çatallanması için yeterli ve gerekli koşullar için bir teori geliştirildi.  Akış alanındaki parametrelerin değişimi yapısal çatallanmalara neden olabilir. Dejenere akış yapısının çatallanması, bu parametrelerin hafifçe değiştirilmesiyle elde edildi.

Kaynakça

  • [1]. Brøns, M., Voigt, L.K. and Sørensen, J.N., Topology of vortex breakdown bubbles in a cylinder with a rotating bottom and a free surface, J. Fluid Mech. 428 (2001) 133-148.
  • [2]. Brøns, M., Voigt, L.K. and Sørensen, J.N., Streamline topology of steady axisymmetric vortex breakdown in a cylinder with co- and counter-rotating end-covers, J. Fluid Mech., 401 (1999) 275-292.
  • [3]. Bisgaard, A.V., Brøns, M. and Sørensen, J.N., Vortex breakdown generated by off-axis bifurcation in a cylinder with rotating covers, Acta Mech. 187 (2006) 75-83.
  • [4]. Brøns M., Topologic al fluid mechanics of axisymmetric flows, In simulation and identification of organized structures in flows, (ed. J. N. Sørensen et al.), Kluwer Academic Publishers, Dordrecht, (1999) 213-222.
  • [5]. Brøns M., Streamline patterns and their bifurcations using methods from dynamical systems, In: Ricca R.L. (eds), An introduction to the geometry and topology of fluid flows, NATO Science Series (Series II: Mathematics, Physics and Chemistry), Springer, Dordrecht, 47 (2001) 167-182.
  • [6]. Bisgaard, A. V., Structures and bifurcations in fluid flows with applications to vortex breakdown and wakes, PhD thesis, Department of Mathematics, Technical University of Denmark, (2005).
  • [7]. Bakker, P.G., Bifurcation in flow patterns, vol. 2: Nonlinear topics in the mathematical sciences, Dordrecht: Klüver, (1991).
  • [8]. Brøns, M. and Hartnack, J.N., Streamline topologies near simple-degenerate critical points in two-dimensional flow away from boundaries, Phys. Fluids, 11(1999) 314-324.
  • [9]. Hartnack, J.N., Streamlines topologies near a fixed wall using normal form, Acta Mech., 136 (1999) 55-75.
  • [10]. Deliceouğlu, A. and Gürcan, F., Streamline topology near non-simple degenerate critical points in two-dimensional flow with symmetry about an axis, J. Fluid Mech., 606 (2008) 417-432.
  • [11]. Gürcan F. and Deliceoğlu, A., Streamline topologies near non-simple degenerate points in two dimensional flows with double symmetry away from boundaries and an application, Phys. Fluids, 17 (2005) 093116.
  • [12]. Deliceoğlu, A., Dinamik sistemler ve basit olmayan dejenere nokta civarındaki sıkıştırılamaz akışların topolojik çatallanmaları, Ph.D Thesis, University of Erciyes, (2004).
  • [13]. Ma, T. and Wang, S., Interior structural bifurcation and seperation of 2D incompressible flows, J. Math. Phys., 45 (2004) 1762-1776.
  • [14]. Ma, T. and Wang, S., Geometric theory of incompressible flows with applications to fluid dynamics (Mathematical Surveys and Monographs, American Mathematical Society), (2005).
  • [15]. Ma, T. and Wang, S., Structural classification and stability of divergence-free vector fields, Physica D, 171 (2002) 107-126.

Ayrıntılar

Birincil Dil İngilizce
Konular Temel Bilimler
Bölüm Natural Sciences
Yazarlar

Ali DELİCEOĞLU (Sorumlu Yazar)
Erciyes University
Türkiye


Deniz BOZKURT Bu kişi benim

Yayımlanma Tarihi 30 Eylül 2018
Başvuru Tarihi 6 Haziran 2018
Kabul Tarihi 24 Temmuz 2018
Yayınlandığı Sayı Yıl 2018, Cilt 39, Sayı 3

Kaynak Göster

APA Deliceoğlu, A. & Bozkurt, D. (2018). Streamline Topology of Axisymmetric Flow Near Non-Simple Singular Point . Cumhuriyet Science Journal , 39 (3) , 557-564 . DOI: 10.17776/csj.431321