Selfsimilar mixing in stratified plane Couette flow for varying Prandtl number
dc.contributor.author  Zhou, Qi  en 
dc.contributor.author  Taylor, John  en 
dc.contributor.author  Caulfield, Colmcille  en 
dc.date.accessioned  20170627T08:43:30Z  
dc.date.available  20170627T08:43:30Z  
dc.date.issued  20170610  en 
dc.identifier.issn  00221120  
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. 298329) 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 MoninObukhov (MO) similarity theory and van Driest damping functions. We then employ MO 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 halfchannel 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$$_\nu$ is the nearwall viscous scale. The flux Richardson number $Ri_f$ $\equiv$ $B$/$P$, where $B$ is the buoyancy flux and $P$ is the shear production, is found to be proportional to $Ri_g$. This then leads to a turbulent Prandtl number $Pr_t$ $\equiv$ $\nu_t$/$\kappa_t$ of order unity, where $\nu_t$ and $\kappa_t$ are the turbulent viscosity and diffusivity respectively, which is consistent with Reynolds analogy. The turbulent Froude number $Fr_h$ $\equiv$ $\varepsilon$/($NU^\prime$$^2$), where $U^\prime$ is a turbulent horizontal velocity scale, is found to vary like $Ri_g$$^{1/2}$. All these scalings are consistent with our numerical data and appear to be independent of $Pr$. The classical Osborn model based on turbulent kinetic energy balance in statistically stationary stratified sheared turbulence (Osborn, J. Phys. Oceanogr., vol. 10, 1980, pp. 8389), together with MO scalings, results in a parameterization of $\kappa_t$/$\nu$ ~ $\nu_t$/$\nu$ ~ $Re_b$$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 MO similarity theory. These results are also discussed and rationalized with respect to other parameterizations in the literature. This paper demonstrates the role of MO similarity in setting the mixing efficiency of equilibrated constantflux layers, and the effects of Prandtl number on mixing in wallbounded 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  Selfsimilar 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  20170326  en 
rioxxterms.versionofrecord  10.1017/jfm.2017.200  en 
rioxxterms.version  AM  en 
rioxxterms.licenseref.uri  http://www.rioxx.net/licenses/allrightsreserved  en 
rioxxterms.licenseref.startdate  20170610  en 
dc.contributor.orcid  Taylor, John [0000000212923756]  
dc.contributor.orcid  Caulfield, Colmcille [0000000231709480]  
dc.identifier.eissn  14697645  
rioxxterms.type  Journal Article/Review  en 
pubs.funderprojectid  EPSRC (EP/K034529/1)  
cam.issuedOnline  20170504  en 
datacite.issupplementedby.doi  10.17863/CAM.8978  en 
rioxxterms.freetoread.startdate  20171104 
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