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Streamline Topologies in Stokes Flow Within Lid-Driven Cavities

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Abstract

Stokes flow in a rectangular cavity with two moving lids (with equal speed but in opposite directions) and aspect ratio A (height to width) is considered. An analytic solution for the streamfunction, ψ, expressed as an infinite series of Papkovich–Fadle eigenfunctions is used to reveal changes in flow structures as A is varied. Reducing A from A=0.9 produces a sequence of flow transformations at which a saddle stagnation point changes to a centre (or vice versa) with the generation of two additional stagnation points. To obtain the local flow topology as A→0, we expand the velocity field about the centre of the cavity and then use topological methods. Expansion coefficients depend on the cavity aspect ratio which is considered as a separation parameter. The normal-form transformations result in a much simplified system of differential equations for the streamlines encapsulating all features of the original system. Using the simplified system, streamline patterns and their bifurcations are obtained, as A→0.

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Correspondence to Fuat Gürcan.

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Communicated by

O.E. Jensen

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Gürcan, F. Streamline Topologies in Stokes Flow Within Lid-Driven Cavities. Theoret Comput Fluid Dynamics 17, 19–30 (2003). https://doi.org/10.1007/s00162-003-0095-z

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Keywords

  • Aspect Ratio
  • Velocity Field
  • Flow Structure
  • Point Change
  • Original System