Linear stability analysis of purely elastic travelling wave solutions in pressure driven channel flows

Martin Lellep; Moritz Linkmann; Alexander Morozov

doi:10.1017/jfm.2023.100

Linear stability analysis of purely elastic travelling wave solutions in pressure driven channel flows

Martin Lellep, Moritz Linkmann, Alexander Morozov

Research output: Contribution to journal › Article › peer-review

Abstract

Recent studies of pressure-driven flows of dilute polymer solutions in straight channels demonstrated the existence of two-dimensional coherent structures that are disconnected from the laminar state and appear through a subcritical bifurcation from infinity. These travelling-wave solutions were suggested to organise the phase-space dynamics of purely elastic and elasto-inertial chaotic channel flows. Here, we consider a wide range of parameters, covering the purely elastic and elasto-inertial cases, and demonstrate that the two-dimensional travelling-wave solutions are unstable when embedded in sufficiently wide three-dimensional domains. Our work demonstrates that studies of purely elastic and elasto-inertial turbulence in straight channels require three-dimensional simulations, and no reliable conclusions can be drawn from studying strictly two-dimensional channel flows.

Original language	English
Article number	R1
Pages (from-to)	1-10
Number of pages	10
Journal	Journal of Fluid Mechanics
Volume	959
DOIs	https://doi.org/10.1017/jfm.2023.100
Publication status	Published - 15 Mar 2023

Keywords / Materials (for Non-textual outputs)

polymers
shear-flow instability
bifurcation

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10.1017/jfm.2023.100Licence: Creative Commons: Attribution (CC-BY)

https://arxiv.org/abs/2211.09063Licence: Creative Commons: Attribution (CC-BY)

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title = "Linear stability analysis of purely elastic travelling wave solutions in pressure driven channel flows",

abstract = "Recent studies of pressure-driven flows of dilute polymer solutions in straight channels demonstrated the existence of two-dimensional coherent structures that are disconnected from the laminar state and appear through a subcritical bifurcation from infinity. These travelling-wave solutions were suggested to organise the phase-space dynamics of purely elastic and elasto-inertial chaotic channel flows. Here, we consider a wide range of parameters, covering the purely elastic and elasto-inertial cases, and demonstrate that the two-dimensional travelling-wave solutions are unstable when embedded in sufficiently wide three-dimensional domains. Our work demonstrates that studies of purely elastic and elasto-inertial turbulence in straight channels require three-dimensional simulations, and no reliable conclusions can be drawn from studying strictly two-dimensional channel flows.",

keywords = "polymers, shear-flow instability, bifurcation",

author = "Martin Lellep and Moritz Linkmann and Alexander Morozov",

note = "10 pages, 5 pages Funding Information: Computational resources on ARCHER2 ( www.archer2.ac.uk ) were provided by the UK Turbulence Consortium ( https://www.ukturbulence.co.uk/ , EPSRC grant number EP/R029326/1). We acknowledge financial support from the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and this work received funding from Priority Programme SPP 1881 {\textquoteleft}Turbulent Superstructures{\textquoteright} of the Deutsche Forschungsgemeinschaft (DFG, grant number Li3694/1). For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising from this submission. Publisher Copyright: {\textcopyright} The Author(s), 2023. Published by Cambridge University Press.",

year = "2023",

month = mar,

day = "15",

doi = "10.1017/jfm.2023.100",

language = "English",

volume = "959",

pages = "1--10",

journal = "Journal of Fluid Mechanics",

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publisher = "Cambridge University Press",

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TY - JOUR

T1 - Linear stability analysis of purely elastic travelling wave solutions in pressure driven channel flows

AU - Lellep, Martin

AU - Linkmann, Moritz

AU - Morozov, Alexander

N1 - 10 pages, 5 pages Funding Information: Computational resources on ARCHER2 ( www.archer2.ac.uk ) were provided by the UK Turbulence Consortium ( https://www.ukturbulence.co.uk/ , EPSRC grant number EP/R029326/1). We acknowledge financial support from the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and this work received funding from Priority Programme SPP 1881 ‘Turbulent Superstructures’ of the Deutsche Forschungsgemeinschaft (DFG, grant number Li3694/1). For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising from this submission. Publisher Copyright: © The Author(s), 2023. Published by Cambridge University Press.

PY - 2023/3/15

Y1 - 2023/3/15

N2 - Recent studies of pressure-driven flows of dilute polymer solutions in straight channels demonstrated the existence of two-dimensional coherent structures that are disconnected from the laminar state and appear through a subcritical bifurcation from infinity. These travelling-wave solutions were suggested to organise the phase-space dynamics of purely elastic and elasto-inertial chaotic channel flows. Here, we consider a wide range of parameters, covering the purely elastic and elasto-inertial cases, and demonstrate that the two-dimensional travelling-wave solutions are unstable when embedded in sufficiently wide three-dimensional domains. Our work demonstrates that studies of purely elastic and elasto-inertial turbulence in straight channels require three-dimensional simulations, and no reliable conclusions can be drawn from studying strictly two-dimensional channel flows.

AB - Recent studies of pressure-driven flows of dilute polymer solutions in straight channels demonstrated the existence of two-dimensional coherent structures that are disconnected from the laminar state and appear through a subcritical bifurcation from infinity. These travelling-wave solutions were suggested to organise the phase-space dynamics of purely elastic and elasto-inertial chaotic channel flows. Here, we consider a wide range of parameters, covering the purely elastic and elasto-inertial cases, and demonstrate that the two-dimensional travelling-wave solutions are unstable when embedded in sufficiently wide three-dimensional domains. Our work demonstrates that studies of purely elastic and elasto-inertial turbulence in straight channels require three-dimensional simulations, and no reliable conclusions can be drawn from studying strictly two-dimensional channel flows.

KW - polymers

KW - shear-flow instability

KW - bifurcation

U2 - 10.1017/jfm.2023.100

DO - 10.1017/jfm.2023.100

M3 - Article

SN - 0022-1120

VL - 959

SP - 1

EP - 10

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

M1 - R1

ER -

Linear stability analysis of purely elastic travelling wave solutions in pressure driven channel flows

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Keywords / Materials (for Non-textual outputs)

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