dc.contributor.author Buza, G dc.contributor.author Page, J dc.contributor.author Kerswell, Richard dc.date.accessioned 2022-03-10T00:30:06Z dc.date.available 2022-03-10T00:30:06Z dc.date.issued 2022-04-08 dc.identifier.issn 0022-1120 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/334822 dc.description.abstract The recently-discovered centre-mode instability of rectilinear viscoelastic shear flow (Garg et al. Phy. Rev. Lett. 121, 024502, 2018) has offered an explanation for the origin of elasto-inertial turbulence (EIT) which occurs at lower Weissenberg ($Wi$) numbers. In support of this, we show using weakly nonlinear analysis that the subcriticality found in Page et al. (Phys. Rev. Lett. 125, 154501, 2020) is generic across the neutral curve with the instability only becoming supercritical at low Reynolds ($Re$) numbers and high $Wi$. We demonstrate that the instability can be viewed as purely elastic in origin even for $Re=O(10^3)$, rather than `elasto-inertial', as the underlying shear does not energise the instability. It is also found that the introduction of a realistic maximum polymer extension length, $L_{max}$, in the FENE-P model moves the neutral curve closer to the inertialess $Re=0$ limit at a fixed ratio of solvent-to-solution viscosities, $\beta$. In the dilute limit ($\beta \rightarrow 1$) with $L_{max} =O(100)$, the linear instability can brought down to more physically-relevant $Wi\gtrsim 110$ at $\beta=0.98$, compared with the threshold $Wi=O(10^3)$ at $\beta=0.994$ reported recently by Khalid et al. (arXiv: 2103.06794) for an Oldroyd-B fluid. Again the instability is subcritical implying that inertialess rectilinear viscoelastic shear flow is nonlinearly unstable - i.e. unstable to finite amplitude disturbances - for even lower $Wi$. dc.publisher Cambridge University Press (CUP) dc.rights Attribution-NonCommercial-NoDerivatives 4.0 International dc.rights.uri https://creativecommons.org/licenses/by-nc-nd/4.0/ dc.subject physics.flu-dyn dc.subject physics.flu-dyn dc.title Weakly nonlinear analysis of the viscoelastic instability in channel flow for finite and vanishing Reynolds numbers dc.type Article dc.publisher.department Department of Applied Mathematics And Theoretical Physics dc.date.updated 2022-03-08T09:06:29Z prism.publicationName Journal of Fluid Mechanics dc.identifier.doi 10.17863/CAM.82256 dcterms.dateAccepted 2022-03-07 rioxxterms.versionofrecord 10.1017/jfm.2022.222 rioxxterms.version AM dc.contributor.orcid Buza, G [0000-0003-2009-705X] dc.contributor.orcid Kerswell, Richard [0000-0001-5460-5337] dc.identifier.eissn 1469-7645 dc.publisher.url http://dx.doi.org/10.1017/jfm.2022.222 rioxxterms.type Journal Article/Review cam.issuedOnline 2022-04-08 cam.orpheus.success Wed May 25 11:13:20 BST 2022 - Embargo updated cam.orpheus.counter 4 cam.depositDate 2022-03-08 pubs.licence-identifier apollo-deposit-licence-2-1 pubs.licence-display-name Apollo Repository Deposit Licence Agreement rioxxterms.freetoread.startdate 2022-10-08
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