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2 results

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

  • A. DELİCEOĞLU
  • Journal:
    European Journal of Applied Mathematics / Volume 24 / Issue 1 / February 2013
    Published online by Cambridge University Press:
    25 September 2012, pp. 77-101

  • 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.