Streamline topologies in Stokes flow within lid-driven cavities

Gurcan F.

THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS, vol.17, no.1, pp.19-30, 2003 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 1
  • Publication Date: 2003
  • Doi Number: 10.1007/s00162-003-0095-z
  • Page Numbers: pp.19-30


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.