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Topology of two-dimensional flow associated with degenerate dividing streamline on a free surface

Published online by Cambridge University Press:  25 September 2012

A. DELİCEOĞLU
A. DELİCEOĞLU*
Affiliation:
Department of Mathematics, Erciyes University, Kayseri 38039, Turkey email: [email protected]
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Abstract

Topology of two-dimensional flow associated with degenerate dividing streamline on a free surface is analysed from a topological point of view by considering the critical point concept. Streamline patterns and their bifurcations in the vicinity of a free surface were investigated by Brøns (Brøns, M. (1994) Topological fluid dynamics of interfacial flows. Phys. Fluids6, 2730–2736). Brøns's work is extended to the case of a stream function, including the fourth-order normal form approach. From this, a complete description of bifurcations which can occur in two-dimensional incompressible flow is obtained up to codimension three. The theory is applied to the patterns found numerically in a roll coater.

Keywords

Dynamical systems in fluid mechanics (37N10)Incompressible viscous fluids (76D99)Bifurcation problems
Type
Papers
Information
European Journal of Applied Mathematics , Volume 24 , Issue 1 , February 2013 , pp. 77 - 101
Copyright
Copyright © Cambridge University Press 2012

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