Vorticity topology of vortex pair interactions at low Reynolds numbers

Research output: Contribution to journalJournal article – Annual report year: 2019Researchpeer-review

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Vorticity topology of vortex pair interactions at low Reynolds numbers. / Andersen, Morten; Schreck, Cédric; Hansen, Jesper Schmidt; Brøns, Morten.

In: European Journal of Mechanics, B/Fluids, Vol. 74, 01.03.2019, p. 58-67.

Research output: Contribution to journalJournal article – Annual report year: 2019Researchpeer-review

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Andersen, Morten ; Schreck, Cédric ; Hansen, Jesper Schmidt ; Brøns, Morten. / Vorticity topology of vortex pair interactions at low Reynolds numbers. In: European Journal of Mechanics, B/Fluids. 2019 ; Vol. 74. pp. 58-67.

Bibtex

@article{8987decc34ac4d76b3c27891a5378498,
title = "Vorticity topology of vortex pair interactions at low Reynolds numbers",
abstract = "We investigate vortex merging at low Reynolds numbers from a topological point of view. We identify vortices as local extremal points of vorticity and follow the motion and bifurcation of these points as time progresses. We consider both two-dimensional simulations of the vorticity transport equation and an analytical study of the core growth model. The merging process of identical vortices is shown to occur through a pitchfork bifurcation and for asymmetric vortices one vortex merges with a saddle through a cusp (perturbed pitchfork) bifurcation. Excellent agreement between the core growth model and the numerical simulations is observed. For higher Reynolds numbers, filamentation becomes dominant hence limiting the predictive value of the core growth model. A complete investigation of merging in the core growth model is conducted for all possible vortex strengths. Simple, analytical expressions are derived for bifurcation curves, merging time, and vortex positions depending on systems parameters.",
keywords = "Bifurcations, Topology of fluid flow, Vortex dynamics, Vortex merging",
author = "Morten Andersen and C{\'e}dric Schreck and Hansen, {Jesper Schmidt} and Morten Br{\o}ns",
year = "2019",
month = "3",
day = "1",
doi = "10.1016/j.euromechflu.2018.10.022",
language = "English",
volume = "74",
pages = "58--67",
journal = "European Journal of Mechanics B - Fluids",
issn = "0997-7546",
publisher = "Elsevier Masson",

}

RIS

TY - JOUR

T1 - Vorticity topology of vortex pair interactions at low Reynolds numbers

AU - Andersen, Morten

AU - Schreck, Cédric

AU - Hansen, Jesper Schmidt

AU - Brøns, Morten

PY - 2019/3/1

Y1 - 2019/3/1

N2 - We investigate vortex merging at low Reynolds numbers from a topological point of view. We identify vortices as local extremal points of vorticity and follow the motion and bifurcation of these points as time progresses. We consider both two-dimensional simulations of the vorticity transport equation and an analytical study of the core growth model. The merging process of identical vortices is shown to occur through a pitchfork bifurcation and for asymmetric vortices one vortex merges with a saddle through a cusp (perturbed pitchfork) bifurcation. Excellent agreement between the core growth model and the numerical simulations is observed. For higher Reynolds numbers, filamentation becomes dominant hence limiting the predictive value of the core growth model. A complete investigation of merging in the core growth model is conducted for all possible vortex strengths. Simple, analytical expressions are derived for bifurcation curves, merging time, and vortex positions depending on systems parameters.

AB - We investigate vortex merging at low Reynolds numbers from a topological point of view. We identify vortices as local extremal points of vorticity and follow the motion and bifurcation of these points as time progresses. We consider both two-dimensional simulations of the vorticity transport equation and an analytical study of the core growth model. The merging process of identical vortices is shown to occur through a pitchfork bifurcation and for asymmetric vortices one vortex merges with a saddle through a cusp (perturbed pitchfork) bifurcation. Excellent agreement between the core growth model and the numerical simulations is observed. For higher Reynolds numbers, filamentation becomes dominant hence limiting the predictive value of the core growth model. A complete investigation of merging in the core growth model is conducted for all possible vortex strengths. Simple, analytical expressions are derived for bifurcation curves, merging time, and vortex positions depending on systems parameters.

KW - Bifurcations

KW - Topology of fluid flow

KW - Vortex dynamics

KW - Vortex merging

U2 - 10.1016/j.euromechflu.2018.10.022

DO - 10.1016/j.euromechflu.2018.10.022

M3 - Journal article

VL - 74

SP - 58

EP - 67

JO - European Journal of Mechanics B - Fluids

JF - European Journal of Mechanics B - Fluids

SN - 0997-7546

ER -