Codimension three bifurcation of streamline patterns close to a no-slip wall: A topological description of boundary layer eruption

Adnan Balci, Morten Andersen, M. C. Thompson, Morten Brøns

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Abstract

A vortex close to a no-slip wall gives rise to the creation of new vorticity at the wall. This vorticity may organize itself into vortices that erupt from the separated boundary layer. We study how the eruption process in terms of the streamline topology is initiated and varies in dependence of the Reynolds number Re. We show that vortex structures are created in the boundary layer for Re around 600, but that these disappear again without eruption unless Re > 1000. The eruption process is topologically unaltered for Re up to 5000. Using bifurcation theory, we obtain a topological phase space for the eruption process, which can account for all observed changes in the Reynolds number range we consider. The bifurcation diagram complements previously analyzes such that the classification of topological bifurcations of flows close to no-slip walls with up to three parameters is now complete.
Original languageEnglish
Article number053603
JournalPhysics of Fluids
Volume27
Issue number5
Number of pages14
ISSN1070-6631
DOIs
Publication statusPublished - 2015

Keywords

  • Bifurcation (mathematics)
  • Phase space methods
  • Reynolds number
  • Topology
  • Vortex flow
  • Vorticity
  • Bifurcation diagram
  • Bifurcation theory
  • Separated boundary layers
  • Streamline pattern
  • Streamline topology
  • Topological description
  • Topological phase
  • Vortex structures
  • Boundary layers

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