# Self-similar mixing in stratified plane Couette flow for varying Prandtl number

dc.creator | Zhou, Qi | |

dc.creator | Taylor, John Ryan | |

dc.creator | Caulfield, Colm-cille Patrick | |

dc.date.accessioned | 2017-03-26 | |

dc.date.accessioned | 2018-11-24T23:20:09Z | |

dc.date.available | 2017-06-27T08:43:30Z | |

dc.date.available | 2018-11-24T23:20:09Z | |

dc.date.issued | 2017-06-10 | |

dc.identifier | https://www.repository.cam.ac.uk/handle/1810/265010 | |

dc.identifier.uri | http://repository.aust.edu.ng/xmlui/handle/123456789/3555 | |

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.language | en | |

dc.publisher | Cambridge University Press | |

dc.publisher | Journal of Fluid Mechanics | |

dc.subject | geophysical and geological flows | |

dc.subject | mixing | |

dc.subject | stratified turbulence | |

dc.title | Self-similar mixing in stratified plane Couette flow for varying Prandtl number | |

dc.type | Article |

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