Comparison of the anelastic approximation with fully compressible equations for linear magnetoconvection and magnetic buoyancy
Comparison of the anelastic approximation with fully compressible equations for linear magnetoconvection and magnetic buoyancy
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DOI：
10.1080/03091929.2010.521747
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发表时间：
2010-10
影响因子：
1.3
通讯作者：
N. A. Berkoff;E. Kersalé-;S. Tobias
中科院分区：
文献类型：
--
作者：
N. A. Berkoff;E. Kersalé-;S. Tobias
在这篇文章中，我们考察了滞弹性近似的适用范围，该近似经常用于描述地球物理和天体物理流动的动力学。具体地说，我们考虑了两个线性问题：磁对流和磁浮力，并将完全可压缩解与通过求解滞弹性问题确定的解进行了比较。我们进一步比较了Lantz[分层对流流体层中磁场的动力学行为]随后提出的简化。博士论文，康奈尔大学：伊萨卡，美国，1992]与滞弹性公式。我们发现，对于磁对流问题，如果绝热偏离很小(如预期的那样)，滞弹性近似就能很好地工作，并确定近似在哪里失效。磁浮力的结果就不那么直接了，近似的精度取决于不稳定性的增长率。我们认为，这些结果使得很难先验地评估滞弹性近似是否为稳定分层问题的完全可压缩系统提供了准确的近似。因此，与磁对流问题不同，对于磁浮力，很难给出关于何时可以使用滞弹性近似的一般规则。
In this article we examine the range of applicability of the anelastic approximation, which is often used in describing the dynamics of geophysical and astrophysical flows. Specifically, we consider two linear problems: magnetoconvection and magnetic buoyancy, and compare the fully compressible solutions with those determined by solving the anelastic problem. We further compare a subsequent simplification introduced by Lantz [Dynamical behavior of magnetic fields in a stratified, convecting fluid layer. Ph.D. Thesis, Cornell University: Ithaca, U.S.A., 1992] with the anelastic formulation. We find that for the magnetoconvection problem the anelastic approximation works well if the departure from adiabaticity is small (as expected) and determine where the approximation breaks down. The results for magnetic buoyancy are less straightforward, with the accuracy of the approximation being determined by the growth rate of the instability. We argue that these results make it difficult to assess a priori whether the anelastic approximation will provide an accurate approximation to the fully compressible system for stably stratified problems. Thus, unlike the magnetoconvection problem, for magnetic buoyancy it is difficult to provide general rules as to when the anelastic approximation can be used.