Effect of stratification on dynamic characteristics of a rapidly-rotating fluid

Abstract

Rotating flows with density stratification are investigated. There are three cases in this thesis that are carefully designed to show the effects of density variation in the rotating flows. Firstly, a numerical study is made for the flow of a density-stratified fluid in a vertical cylinder with a rotating top lid. Under the Boussinesq-fluid assumption, the governing Navier-Stokes equations are numerically solved. For large rotational Reynolds number Re and the cylinder aspect ratio $Ar~O(1)$, details of flow and temperature fields are displayed. The effect of the Prandtl number on global flow patterns is scrutinized for both gravitationally-unstable and gravitationally-stable configurations. Of particular interest is the behavior of the vortex breakdown stagnation bubble under the influence of buoyancy. Plots are presented for the azimuthal vorticity fields, in line with the simple axisymmetric inviscid kinematic consideration. An explicit comparison is made for the individual terms appearing in the azimuthal vorticity equation. For both gravitationally-unstable and gravitationally-stable configurations, the argument based on the behavior of azimuthal vorticity is seen to produce predictions consistent with the numerical results. Secondly, a numerical study is made of the basic-state flow field of a fluid with a density maximum in a differentially-rotating cylinder. The fluid density reaches a maximum $ρ_m$ at temperature $T_m$, and a quadratic $(ρ-T)$ relationship is used to model the fluid behavior near $T_m$. The temperature at the bottom (top) endwall disk is $T_B$ $(T_T)$, with ΔT ≡ $T_T$ - $T_B$ ＞ 0, and $T_m$ lies between $T_B$ and $T_T$. The rotation rate of the bottom (top) endwall disk is $Ω_B$ $(Ω_T)$, with ε ≡ ($Ω_T$ - $Ω_B$)/$Ω_B$ ≪ 1. Numerical solutions were obtained of the Navier-Stokes equations for large rotational Reynolds number and large Rayleigh number. Detailed flow and density fields are portrayed to be strongly dependent on the density ...