2D OR NOT 2D: THE EFFECT OF DIMENSIONALITY ON THE DYNAMICS OF FINGERING CONVECTION AT LOW PRANDTL NUMBER
2D OR NOT 2D: THE EFFECT OF DIMENSIONALITY ON THE DYNAMICS OF FINGERING CONVECTION AT LOW PRANDTL NUMBER
复制标题
二维或非二维：维数对低普朗特数下指指对流动力学的影响
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
N. Brummell
中科院分区：
文献类型：
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作者：
P. Garaud;N. Brummell
指指对流（也称为热盐对流）是一种不稳定的对流，发生在恒星辐射内部，存在不稳定的成分梯度。为了估计由这种不稳定性引起的混合效率，我们进行了数值模拟。然而，在适合恒星天体物理学（即低普朗特数）的参数范围内进行全三维（3D）计算是非常昂贵的。这就提出了一个问题，即二维（2D）模拟是否可以用来实现同样的目标。在这项工作中，我们通过比较低普朗特数下指指对流的二维和三维模拟结果来解决这个问题。我们发现2D模拟并不合适。然而，我们也发现所需的三维计算域不必非常宽：第三维度只需要包含至少两个波长的增长最快的线性不稳定模式，以捕获小规模指法的本质三维动力学。然而，窄域仍应谨慎使用，因为它们可能限制通常与指指对流相关的任何大规模动力学的后续发展。
Fingering convection (otherwise known as thermohaline convection) is an instability that occurs in stellar radiative interiors in the presence of unstable compositional gradients. Numerical simulations have been used in order to estimate the efficiency of mixing induced by this instability. However, fully three-dimensional (3D) computations in the parameter regime appropriate for stellar astrophysics (i.e., low Prandtl number) are prohibitively expensive. This raises the question of whether two-dimensional (2D) simulations could be used instead to achieve the same goals. In this work, we address this issue by comparing the outcome of 2D and 3D simulations of fingering convection at low Prandtl number. We find that 2D simulations are never appropriate. However, we also find that the required 3D computational domain does not have to be very wide: the third dimension only needs to contain a minimum of two wavelengths of the fastest-growing linearly unstable mode to capture the essentially 3D dynamics of small-scale fingering. Narrow domains, however, should still be used with caution since they could limit the subsequent development of any large-scale dynamics typically associated with fingering convection.