Streamline topologies near a non-simple degenerate critical point close to a stationary wall using normal forms


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Gurcan F. , Deliceoglu A. , Bakker P. G.

JOURNAL OF FLUID MECHANICS, cilt.539, ss.299-311, 2005 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 539
  • Basım Tarihi: 2005
  • Doi Numarası: 10.1017/s0022112005005689
  • Dergi Adı: JOURNAL OF FLUID MECHANICS
  • Sayfa Sayıları: ss.299-311

Özet

Streamline patterns and their bifurcations in two-dimensional Navier-Stokes flow of an incompressible fluid near a non-simple degenerate critical point close to a stationary wall are investigated from the topological point of view by considering a Taylor expansion of the velocity field. Using a five-order normal form approach we obtain a much simplified system of differential equations for the streamlines. Careful analysis of the simplified system gives possible bifurcations for non-simple degeneracies of codimension three. Three heteroclinic connections from three on-wall separation points merge at an in-flow saddle point to produce two separation bubbles with opposite rotations which occur only near a non-simple degenerate critical point. The theory is applied to the patterns and bifurcations found numerically in the studies of Stokes flow in a double-lid-driven rectangular cavity.