Multiplicity of nonlinear thermal convection in a spherical shell.
Multiplicity of nonlinear thermal convection in a spherical shell.
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球壳内的多重非线性热对流。
DOI：
10.1103/physreve.71.016301
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
Keke Zhang
中科院分区：
文献类型：
--
作者：
Ligang Li;Pu Zhang;X. Liao;Keke Zhang
通过全三维数值模拟，系统地研究了球对称重力作用下中薄球壳在球对称边界条件下的线性和弱非线性热对流。对流问题是自伴的，并且线性对流稳定性的特征在于l，球谐函数Yml（theta，phi）的次数。线性对流的径向结构由稳定性分析确定，而球形对流的水平结构存在（2l + 1）重简并。当l = O（10），即，在中等薄的球壳中，简并的去除或部分去除代表数学上困难的、物理上不好理解的问题。通过精心选择的初始条件，我们能够获得各种非线性对流在完全相同的参数附近的对流，包括稳定的轴对称对流，稳定的方位角周期对流，稳定的方位角非周期对流，赤道非对称对流，以及覆盖整个球壳的单个巨型螺旋卷形式的稳定对流，其在很宽的普朗特数范围内是稳定的和鲁棒的。
Linear and weakly nonlinear thermal convection in a moderately thin spherical shell in the presence of a spherically symmetric gravity subject to a spherically symmetric boundary condition is systematically investigated through fully three-dimensional numerical simulations. The convection problem is self-adjoint and the linear convective stability is characterized by l, the degree of a spherical harmonics Yml (theta,phi). While the radial structure of the linear convection is determined by the stability analysis, there exists a (2l + 1)-fold degeneracy in the horizontal structure of the spherical convection. When l = O(10) , i.e., in a moderately thin spherical shell, the removal or partial removal of the degeneracy represents a mathematically difficult, physically not well-understood problem. By starting with carefully chosen initial conditions, we are able to obtain a variety of nonlinear convective flows at exactly the same parameters near the onset of convection, including steady axisymmetric convection, steady azimuthally periodic convection, steady azimuthally nonperiodic convection, equatorially asymmetric convection, and steady convection in the form of a single giant spiral roll covering the whole spherical shell which is stable and robust for a wide range of the Prandtl number.