Quadrupolar flows around spots in internal shear flows

Turbulent spots occur in shear flows confined between two walls and are surrounded by robust quadrupolar flows. Although the far-field decay of such large-scale flows has been reported to be exponential, we predict a different algebraic decay for the case of plane Couette flow. We address this probl...

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Main Authors: Wang, Zhe, Guet, Claude, Monchaux, Romain, Duguet, Yohann, Eckhardt, Bruno
Other Authors: School of Materials Science and Engineering
Format: Article
Language:English
Published: 2020
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Online Access:https://hdl.handle.net/10356/142313
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1423132021-01-08T01:24:47Z Quadrupolar flows around spots in internal shear flows Wang, Zhe Guet, Claude Monchaux, Romain Duguet, Yohann Eckhardt, Bruno School of Materials Science and Engineering Interdisciplinary Graduate School (IGS) Energy Research Institute @ NTU (ERI@N) Engineering::Materials Transition to Turbulence Navier-Stokes Equations Turbulent spots occur in shear flows confined between two walls and are surrounded by robust quadrupolar flows. Although the far-field decay of such large-scale flows has been reported to be exponential, we predict a different algebraic decay for the case of plane Couette flow. We address this problem theoretically, by modelling an isolated spot as an obstacle in a linear plane shear flow with free-slip boundary conditions at the walls. By seeking invariant solutions in a co-moving Lagrangian frame and using geometric scale separation, a set of differential equations governing large-scale flows is derived from the Navier–Stokes equations and solved analytically. The wall-normal velocity turns out to be exponentially localised in the plane, while the quadrupolar in-plane velocity field, after wall-normal averaging, features a superposition of algebraic and exponential decays. The algebraic decay exponent is -3. The quadrupolar angular dependence stems from (i) the shearing of the streamwise velocity and (ii) the breaking of the spanwise homogeneity. Near the spot, exponentially decaying solutions can generate reversed quadrupolar flows. Eventually, by noting that the algebraically decaying in-plane flow is two-dimensional and harmonic, we suggest a topological origin to the quadrupolar large-scale flow. Accepted version 2020-06-19T02:12:00Z 2020-06-19T02:12:00Z 2020 Journal Article Wang, Z., Guet, C., Monchaux, R., Duguet, Y., & Eckhardt, B. (2020). Quadrupolar flows around spots in internal shear flows. Journal of Fluid Mechanics, 892, A27-. doi:10.1017/jfm.2020.190 0022-1120 https://hdl.handle.net/10356/142313 10.1017/jfm.2020.190 892 en Journal of Fluid Mechanics © 2020 The Author(s). All rights reserved. This paper was published by Cambridge University Press in Journal of Fluid Mechanics and is made available with permission of The Author(s). application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Engineering::Materials
Transition to Turbulence
Navier-Stokes Equations
spellingShingle Engineering::Materials
Transition to Turbulence
Navier-Stokes Equations
Wang, Zhe
Guet, Claude
Monchaux, Romain
Duguet, Yohann
Eckhardt, Bruno
Quadrupolar flows around spots in internal shear flows
description Turbulent spots occur in shear flows confined between two walls and are surrounded by robust quadrupolar flows. Although the far-field decay of such large-scale flows has been reported to be exponential, we predict a different algebraic decay for the case of plane Couette flow. We address this problem theoretically, by modelling an isolated spot as an obstacle in a linear plane shear flow with free-slip boundary conditions at the walls. By seeking invariant solutions in a co-moving Lagrangian frame and using geometric scale separation, a set of differential equations governing large-scale flows is derived from the Navier–Stokes equations and solved analytically. The wall-normal velocity turns out to be exponentially localised in the plane, while the quadrupolar in-plane velocity field, after wall-normal averaging, features a superposition of algebraic and exponential decays. The algebraic decay exponent is -3. The quadrupolar angular dependence stems from (i) the shearing of the streamwise velocity and (ii) the breaking of the spanwise homogeneity. Near the spot, exponentially decaying solutions can generate reversed quadrupolar flows. Eventually, by noting that the algebraically decaying in-plane flow is two-dimensional and harmonic, we suggest a topological origin to the quadrupolar large-scale flow.
author2 School of Materials Science and Engineering
author_facet School of Materials Science and Engineering
Wang, Zhe
Guet, Claude
Monchaux, Romain
Duguet, Yohann
Eckhardt, Bruno
format Article
author Wang, Zhe
Guet, Claude
Monchaux, Romain
Duguet, Yohann
Eckhardt, Bruno
author_sort Wang, Zhe
title Quadrupolar flows around spots in internal shear flows
title_short Quadrupolar flows around spots in internal shear flows
title_full Quadrupolar flows around spots in internal shear flows
title_fullStr Quadrupolar flows around spots in internal shear flows
title_full_unstemmed Quadrupolar flows around spots in internal shear flows
title_sort quadrupolar flows around spots in internal shear flows
publishDate 2020
url https://hdl.handle.net/10356/142313
_version_ 1688665570197635072