dc.contributor.author Zhou, Qi en dc.contributor.author Taylor, John en dc.contributor.author Caulfield, Colm-cille en dc.date.accessioned 2017-06-27T08:43:30Z dc.date.available 2017-06-27T08:43:30Z dc.date.issued 2017-06-10 en dc.identifier.issn 0022-1120 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/265010 dc.description.abstract We 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.sponsorship The EPSRC Programme grant EP/K034529/1 entitled ‘Mathematical Underpinnings of Stratified Turbulence’ is gratefully acknowledged for supporting the research presented here. dc.language.iso en en dc.publisher Cambridge University Press dc.subject geophysical and geological flows en dc.subject mixing en dc.subject stratified turbulence en dc.title Self-similar mixing in stratified plane Couette flow for varying Prandtl number en dc.type Article prism.endingPage 120 prism.publicationDate 2017 en prism.publicationName Journal of Fluid Mechanics en prism.startingPage 86 prism.volume 820 en dc.identifier.doi 10.17863/CAM.10380 dcterms.dateAccepted 2017-03-26 en rioxxterms.versionofrecord 10.1017/jfm.2017.200 en rioxxterms.version AM en rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved en rioxxterms.licenseref.startdate 2017-06-10 en dc.contributor.orcid Taylor, John [0000-0002-1292-3756] dc.contributor.orcid Caulfield, Colm-cille [0000-0002-3170-9480] dc.identifier.eissn 1469-7645 rioxxterms.type Journal Article/Review en pubs.funder-project-id EPSRC (EP/K034529/1) cam.issuedOnline 2017-05-04 en datacite.issupplementedby.doi 10.17863/CAM.8978 en rioxxterms.freetoread.startdate 2017-11-04
﻿