# Nonlinear evolution of linear optimal perturbations of strongly stratified shear layers

dc.creator | Taylor, John Ryan | |

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

dc.creator | Kaminski, AK | |

dc.date.accessioned | 2017-06-02 | |

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

dc.date.available | 2017-08-01T10:18:30Z | |

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

dc.date.issued | 2017-08-25 | |

dc.identifier | https://www.repository.cam.ac.uk/handle/1810/265816 | |

dc.identifier.uri | http://repository.aust.edu.ng/xmlui/handle/123456789/3563 | |

dc.description.abstract | The Miles-Howard theorem states that a necessary condition for normal-mode instability in parallel, inviscid, steady stratified shear flows is that the minimum gradient Richardson number, $Ri_{g,min}$, is less than 1/4 somewhere in the flow. However, the non-normality of the Navier-Stokes and buoyancy equations may allow for substantial perturbation energy growth at finite times. We calculate numerically the linear optimal perturbations which maximize the perturbation energy gain for a stably stratified shear layer consisting of a hyperbolic tangent velocity distribution with characteristic velocity $U_{0}^{*}$ and a uniform stratification with constant buoyancy frequency $N_{0}^{*}$. We vary the bulk Richardson number $Ri_b$=$N_{0}^{*}$$^2$$h^{*2}$/$U_{0}^{*}$$^2$ (corresponding to $Ri_{g,min}$) between 0.20 and 0.50 and the Reynolds numbers $Re$=$U_{0}^{*}$$h^{*}$/$v^{*}$ between 1000 and 8000, with the Prandtl number held fixed at $Pr$=1. We find the transient growth of non-normal perturbations may be sufficient to trigger strongly nonlinear effects and breakdown into small-scale structures, thereby leading to enhanced dissipation and non-trivial modification of the background flow even in flows where $Ri_{g,min}$>1/4. We show that the effects of nonlinearity are more significant for flows with higher $Re$, lower $Ri_b$ and higher initial perturbation amplitude $E_0$. Enhanced kinetic energy dissipation is observed for higher-$Re$ and lower-$Ri_b$ flows, and the mixing efficiency, quantified here by $\epsilon_p$/($\epsilon_p$+$\epsilon_k$) where $\epsilon_p$ is the dissipation rate of density variance and $\epsilon_k$is the dissipation rate of kinetic energy, is found to be approximately 0.35 for the most strongly nonlinear cases. | |

dc.language | en | |

dc.publisher | Cambridge University Press | |

dc.publisher | Journal of Fluid Mechanics | |

dc.subject | instability | |

dc.subject | stratified flows | |

dc.subject | transition to turbulence | |

dc.title | Nonlinear evolution of linear optimal perturbations of strongly stratified shear layers | |

dc.type | Article |

## Files in this item

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