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

Research output: Contribution to journalJournal articleResearchpeer-review

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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

Cite this

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title = "Codimension three bifurcation of streamline patterns close to a no-slip wall: A topological description of boundary layer eruption",
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.",
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",
author = "Adnan Balci and Morten Andersen and Thompson, {M. C.} and Morten Br{\o}ns",
year = "2015",
doi = "10.1063/1.4921527",
language = "English",
volume = "27",
journal = "Physics of Fluids",
issn = "1070-6631",
publisher = "American Institute of Physics",
number = "5",

}

Codimension three bifurcation of streamline patterns close to a no-slip wall: A topological description of boundary layer eruption. / Balci, Adnan; Andersen, Morten; Thompson, M. C.; Brøns, Morten.

In: Physics of Fluids, Vol. 27, No. 5, 053603, 2015.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Codimension three bifurcation of streamline patterns close to a no-slip wall: A topological description of boundary layer eruption

AU - Balci, Adnan

AU - Andersen, Morten

AU - Thompson, M. C.

AU - Brøns, Morten

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - Bifurcation (mathematics)

KW - Phase space methods

KW - Reynolds number

KW - Topology

KW - Vortex flow

KW - Vorticity

KW - Bifurcation diagram

KW - Bifurcation theory

KW - Separated boundary layers

KW - Streamline pattern

KW - Streamline topology

KW - Topological description

KW - Topological phase

KW - Vortex structures

KW - Boundary layers

U2 - 10.1063/1.4921527

DO - 10.1063/1.4921527

M3 - Journal article

VL - 27

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 5

M1 - 053603

ER -