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dc.contributor.authorZhou, Qien
dc.contributor.authorTaylor, Johnen
dc.contributor.authorCaulfield, Colm-cilleen
dc.date.accessioned2017-06-27T08:43:30Z
dc.date.available2017-06-27T08:43:30Z
dc.date.issued2017-06-10en
dc.identifier.issn0022-1120
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/265010
dc.description.abstractWe investigate fully developed turbulence in stratified plane Couette flows using direct numerical simulations similar to those reported by Deusebio et al. (J. Fluid Mech., vol. 781, 2015, pp. 298-329) expanding the range of Prandtl number $Pr$ examined by two orders of magnitude from 0.7 up to 70. Significant effects of $Pr$ on the heat and momentum fluxes across the channel gap and on the mean temperature and velocity profile are observed. These effects can be described through a mixing length model coupling Monin-Obukhov (M-O) similarity theory and van Driest damping functions. We then employ M-O theory to formulate similarity scalings for various flow diagnostics for the stratified turbulence in the gap interior. The midchannel gap gradient Richardson number $Ri_g$ is determined by the length scale ratio $\textit{h/L}$, where $\textit{h}$ is the half-channel gap depth and $\textit{L}$ is the Obukhov length scale. As $\textit{h/L}$ approaches very large values, $Ri_g$ asymptotes to a maximum characteristic value of approximately 0.2. The buoyancy Reynolds number $Re_b$ $\equiv$ $\varepsilon$/($\nu$$N^2$), where $\varepsilon$ is the dissipation, $\nu$ is the kinematic viscosity and $N$ is the buoyancy frequency defined in terms of the local mean density gradient, scales linearly with the length scale ratio $L$+ $\equiv$ $L$/$\delta$$_\nu$, where $\delta$$_\nu$ is the near-wall viscous scale. The flux Richardson number $Ri_f$ $\equiv$ -$B$/$P$, where $B$ is the buoyancy flux and $P$ is the shear production, is found to be proportional to $Ri_g$. This then leads to a turbulent Prandtl number $Pr_t$ $\equiv$ $\nu_t$/$\kappa_t$ of order unity, where $\nu_t$ and $\kappa_t$ are the turbulent viscosity and diffusivity respectively, which is consistent with Reynolds analogy. The turbulent Froude number $Fr_h$ $\equiv$ $\varepsilon$/($NU^\prime$$^2$), where $U^\prime$ is a turbulent horizontal velocity scale, is found to vary like $Ri_g$$^{-1/2}$. All these scalings are consistent with our numerical data and appear to be independent of $Pr$. The classical Osborn model based on turbulent kinetic energy balance in statistically stationary stratified sheared turbulence (Osborn, J. Phys. Oceanogr., vol. 10, 1980, pp. 83-89), together with M-O scalings, results in a parameterization of $\kappa_t$/$\nu$ ~ $\nu_t$/$\nu$ ~ $Re_b$$Ri_g$/(1-$Ri_g$). With this parameterization validated through direct numerical simulation data, we provide physical interpretations of these results in the context of M-O similarity theory. These results are also discussed and rationalized with respect to other parameterizations in the literature. This paper demonstrates the role of M-O similarity in setting the mixing efficiency of equilibrated constant-flux layers, and the effects of Prandtl number on mixing in wall-bounded stratified turbulent flows.
dc.description.sponsorshipThe EPSRC Programme grant EP/K034529/1 entitled ‘Mathematical Underpinnings of Stratified Turbulence’ is gratefully acknowledged for supporting the research presented here.
dc.language.isoenen
dc.publisherCambridge University Press
dc.subjectgeophysical and geological flowsen
dc.subjectmixingen
dc.subjectstratified turbulenceen
dc.titleSelf-similar mixing in stratified plane Couette flow for varying Prandtl numberen
dc.typeArticle
prism.endingPage120
prism.publicationDate2017en
prism.publicationNameJournal of Fluid Mechanicsen
prism.startingPage86
prism.volume820en
dc.identifier.doi10.17863/CAM.10380
dcterms.dateAccepted2017-03-26en
rioxxterms.versionofrecord10.1017/jfm.2017.200en
rioxxterms.versionAMen
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2017-06-10en
dc.contributor.orcidTaylor, John [0000-0002-1292-3756]
dc.contributor.orcidCaulfield, Colm-cille [0000-0002-3170-9480]
dc.identifier.eissn1469-7645
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idEPSRC (EP/K034529/1)
cam.issuedOnline2017-05-04en
datacite.issupplementedby.doi10.17863/CAM.8978en
rioxxterms.freetoread.startdate2017-11-04


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