Effect of the Reynolds number on flow bifurcations and eddy genesis in a lid-driven sectorial cavity

  • Halis BilgilEmail author
  • Fuat Gürcan
Original Paper Area 1


This paper presents the two-dimensional (2D) steady incompressible flow in a lid-driven sectorial cavity. In order to analyze the flow structures, the 2D Navier–Stokes equations are solved by using the finite element method. Different cases of the cavity aspect ratio A and three cases of the speed ratios \((S=-1,0,1)\) of the upper and the lower lids are considered. The finite element formulation for the governing equations is adopted via the velocity-pressure formulation. By varying A for each S, the effect of the Reynolds number on the streamline patterns and their bifurcations are investigated in range \(Re\in [0,200]\). A comparison between the obtained results and some earlier studies is presented.


Bifurcation Eddy Finite element Flow structure Stagnation point Streamline 

List of symbols


radius of the inner and outer circles respectively


cavity aspect ratio = \(r_{2}/r_{1}\)

\(2{\alpha }\)

angle of the sector


dimensionless fluid velocity


speed of the upper and lower lids respectively


speed ratio of the moving lids = \(U_{2}/U_{1}\)

\(\psi \)



Reynolds number

Mathematics Subject Classification

35Q35 74S05 00A69 


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Copyright information

© The JJIAM Publishing Committee and Springer Japan 2016

Authors and Affiliations

  1. 1.Department of MathematicsAksaray UniversityAksarayTurkey
  2. 2.Faculty of Engineering and Natural SciencesInternational University of SarajevoSarajevoBosnia and Herzegovina

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