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


Deliceoglu A.

EUROPEAN JOURNAL OF APPLIED MATHEMATICS, vol.24, pp.77-101, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24
  • Publication Date: 2013
  • Doi Number: 10.1017/s0956792512000319
  • Title of Journal : EUROPEAN JOURNAL OF APPLIED MATHEMATICS
  • Page Numbers: pp.77-101

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 Brons (Brons, M. (1994) Topological fluid dynamics of interfacial flows. Phys. Fluids 6, 2730-2736). Brons'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.