Subcritical convection of liquid metals in a rotating sphere using a quasi-geostrophic model
Subcritical convection of liquid metals in a rotating sphere using a quasi-geostrophic model
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DOI：
10.1017/jfm.2016.631
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发表时间：
2016-05
影响因子：
3.7
通讯作者：
C. Guervilly;P. Cardin
中科院分区：
文献类型：
--
作者：
C. Guervilly;P. Cardin
本文研究了具有内部加热的快速旋转球体中的非线性对流，其普朗特数与液态金属有关（$Pr\in [10^{-2}，10 ^{-1}]$）。我们使用的数值模式的准地转近似的基础上，其中的轴向涡度的变化沿着旋转轴被忽略，而温度场是完全三维的。我们确定了两个独立的分支的对流接近发病：（i）一个众所周知的弱分支埃克曼数大于10 ^{-6}$，这是连续的开始（超临界分岔），并由热Rossby波和（ii）一个新的强分支在较低的埃克曼数，这是不连续的开始。强分支对于10 ^{-8}$量级的Ekman数成为次临界的。在强分支上，流动的雷诺数大于$10^{3}$，并且发展出具有多股射流的强带状流动，甚至接近于非线性对流的开始。我们发现，次临界放大减少普朗特数。对于中间的埃克曼数，这两个分支可以共存，导致滞后（$Ek=10^{-6}$，$Pr=10^{-2}$）。当Ek=10^{-7}$和Pr=10^{-1}$时，在对流开始附近观察到非线性振荡。
We study nonlinear convection in a rapidly rotating sphere with internal heating for values of the Prandtl number relevant for liquid metals ( $Pr\in [10^{-2},10^{-1}]$ ). We use a numerical model based on the quasi-geostrophic approximation, in which variations of the axial vorticity along the rotation axis are neglected, whereas the temperature field is fully three-dimensional. We identify two separate branches of convection close to onset: (i) a well-known weak branch for Ekman numbers greater than $10^{-6}$ , which is continuous at the onset (supercritical bifurcation) and consists of thermal Rossby waves and (ii) a novel strong branch at lower Ekman numbers, which is discontinuous at the onset. The strong branch becomes subcritical for Ekman numbers of the order of $10^{-8}$ . On the strong branch, the Reynolds number of the flow is greater than $10^{3}$ , and a strong zonal flow with multiple jets develops, even close to the nonlinear onset of convection. We find that the subcriticality is amplified by decreasing the Prandtl number. The two branches can co-exist for intermediate Ekman numbers, leading to hysteresis ( $Ek=10^{-6}$ , $Pr=10^{-2}$ ). Nonlinear oscillations are observed near the onset of convection for $Ek=10^{-7}$ and $Pr=10^{-1}$ .