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dc.contributor.authorCaulfield, Colm-cilleen
dc.contributor.authorVermach, Lukasen
dc.date.accessioned2018-09-05T12:44:27Z
dc.date.available2018-09-05T12:44:27Z
dc.date.issued2018-09-10en
dc.identifier.issn0022-1120
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/279455
dc.description.abstractWe consider a passive zero-mean scalar field organised into two layers of different concentrations in a three-dimensional plane channel flow subjected to a constant along-stream pressure gradient. We employ a nonlinear direct-adjoint-looping method to identify the optimal initial perturbation of the velocity field with given initial energy which yields `maximal' mixing by a target time horizon, where maximal mixing is defined here as the minimisation of the spatially-integrated variance of the concentration field. We verify in three-dimensional flows the conjecture by Foures et al. (J. Fluid Mech., vol. 748, 2014, pp. 241-277) that the initial perturbation which maximizes the time-averaged energy gain of the flow leads to relatively weak mixing, and is qualitatively different from the optimal initial `mixing' perturbation which exploits classical Taylor dispersion. We carry out the analysis for two different Reynolds numbers ($Re=U_m h/\nu= 500$, and $Re = 3000$, where $U_m$ is the maximum flow speed of the unperturbed flow, $h$ is the channel half-depth and $\nu$ is the kinematic viscosity of the fluid) demonstrating that this key finding is robust with respect to the transition to turbulence. We also identify the initial perturbations that minimise, at chosen target times, the `mix-norm' of the concentration eld, i.e. a Sobolev norm of negative index in the class introduced by Mathew et al. (Physica D, vol. 211, pp. 23-46, 2005). We show that the `true' variance-based mixing strategy can be successfully and practically approximated by the mix-norm minimisation since we f ind that the mix-norm optimal initial perturbations are far less sensitive to changes in the target time horizon than their optimal variance-minimising counterparts.
dc.description.sponsorshipThis work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/H023348/1 for the University of Cambridge Centre for Doctoral Training, the Cambridge Centre for Analysis. The research activity of C.P.C. is supported by EPSRC Programme Grant EP/K034529/1 entitled Mathematical Underpinnings of Strati ed Turbulence. This re- search was also supported in part by the National Science Foundation under Grant No. NSF PHY17-48958.
dc.publisherCambridge University Press
dc.titleOptimal mixing in three-dimensional plane Poiseuille flow at high Peclet numberen
dc.typeArticle
prism.endingPage923
prism.publicationDate2018en
prism.publicationNameJournal of Fluid Mechanicsen
prism.startingPage875
prism.volume850en
dc.identifier.doi10.17863/CAM.26829
dcterms.dateAccepted2018-05-03en
rioxxterms.versionofrecord10.1017/jfm.2018.388en
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2018-09-10en
dc.contributor.orcidCaulfield, Colm-cille [0000-0002-3170-9480]
dc.identifier.eissn1469-7645
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idEPSRC (EP/K034529/1)
pubs.funder-project-idEPSRC (EP/H023348/1)
cam.issuedOnline2018-07-10en
datacite.issupplementedby.doi10.17863/CAM.22239en
rioxxterms.freetoread.startdate2019-01-10


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