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    Mean dynamics of transitional channel flow

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    Mean dynamics of transitional channel flow (1.035Mb)

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    18
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    Author
    Elsnab, J; Klewicki, J; Maynes, D; Ameel, T
    Date
    2011-07-01
    Source Title
    JOURNAL OF FLUID MECHANICS
    Publisher
    CAMBRIDGE UNIV PRESS
    University of Melbourne Author/s
    Klewicki, Joseph; Elsnab, John
    Affiliation
    Department of Mechanical Engineering, Melbourne School of Engineering
    Metadata
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    Document Type
    Journal Article
    Citations
    Elsnab, J., Klewicki, J., Maynes, D. & Ameel, T. (2011). Mean dynamics of transitional channel flow. JOURNAL OF FLUID MECHANICS, 678, pp.451-481. https://doi.org/10.1017/jfm.2011.120.
    Access Status
    Open Access
    URI
    http://hdl.handle.net/11343/33013
    DOI
    10.1017/jfm.2011.120
    Description

    © 2011 Cambridge University Press. Online edition of the journal is available at http://journals.cambridge.org/action/displayJournal?jid=FLM

    Abstract
    <jats:p>The redistribution of mean momentum and vorticity, along with the mechanisms underlying these redistribution processes, is explored for post-laminar flow in fully developed, pressure driven, channel flow. These flows, generically referred to as transitional, include an instability stage and a nonlinear development stage. The central focus is on the nonlinear development stage. The present analyses use existing direct numerical simulation data sets, as well as recently reported high-resolution molecular tagging velocimetry measurements. Primary considerations stem from the emergence of the effects of turbulent inertia as represented by the Reynolds stress gradient in the mean differential statement of dynamics. The results describe the flow evolution following the formation of a non-zero Reynolds stress peak that is known to first arise near the critical layer of the most unstable disturbance. The positive and negative peaks in the Reynolds stress gradient profile are observed to undergo a relative movement toward both the wall and centreline for subsequent increases in Reynolds number. The Reynolds stress profiles are shown to almost immediately exhibit the same sequence of curvatures that exists in the fully turbulent regime. In the transitional regime, the outer inflection point in this profile physically indicates a localized zone within which the mean dynamics are dominated by inertia. These observations connect to recent theoretical findings for the fully turbulent regime, e.g. as described by Fife, Klewicki &amp; Wei (<jats:italic>J. Discrete Continuous Dyn. Syst.</jats:italic>, vol. 24, 2009, p. 781) and Klewicki, Fife &amp; Wei (<jats:italic>J. Fluid Mech.</jats:italic>, vol. 638, 2009, p. 73). In accord with momentum equation analyses at higher Reynolds number, the present observations provide evidence that a logarithmic mean velocity profile is most rapidly approximated on a sub-domain located between the zero in the Reynolds stress gradient (maximum in the Reynolds stress) and the outer region location of the maximal Reynolds stress gradient (inflection point in the Reynolds stress profile). Overall, the present findings provide evidence that the dynamical processes during the post-laminar regime and those operative in the high Reynolds number regime are connected and describable within a single theoretical framework.</jats:p>
    Keywords
    boundary layer structure; turbulent boundary layers; turbulent transition

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