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arXiv 0809.1625astro-ph
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恒星内部的湍流对流。II。速度场

Turbulent Convection in Stellar Interiors. II. The Velocity Field

David Arnett, Casey Meakin, P. A. Young

摘要:

我们分析恒星对流的三维流体动力学模拟的帮助下,引入湍流级联到我们的理论分析。我们设计封闭的Elbolds分解的平均场方程的模拟(我们涉及温度和密度波动通过系数)的简单物理建模;的程序(CABS,对流算法基于模拟)是terrestrially可测试的,是适合系统的改进。我们开发了一个湍流动能方程,其中包含非本地和时间相关的条款,是适当的,如果对流过境时间短于演变的时间尺度。天体物理学中通常使用的混合长度理论(MLT)的解释是不正确的; MLT迫使混合长度是一个强加的常数。直接试验表明,与流动有关的阻尼是Kolmogorov提出的。涡的大小近似为对流区的深度,而这个耗散长度对应于“混合长度”。在恒星演化方程中应该出现湍流耗散引起的局部加热的新项。焓通量(对流光度)直接与浮力加速度有关,因此也与速度尺度有关。MLT倾向于系统性地低估这个速度尺度。与各种3D模拟的定量比较揭示了先前公认的一致性。应用于恒星演化的例子将在本系列的后续论文中介绍。

英文摘要:

We analyze stellar convection with the aid of 3D hydrodynamic simulations, introducing the turbulent cascade into our theoretical analysis. We devise closures of the Reynolds-decomposed mean field equations by simple physical modeling of the simulations (we relate temperature and density fluctuations via coefficients); the procedure (CABS, Convection Algorithms Based on Simulations) is terrestrially testable and is amenable to systematic improvement. We develop a turbulent kinetic energy equation which contains both nonlocal and time dependent terms, and is appropriate if the convective transit time is shorter than the evolutionary time scale. The interpretation of mixing-length theory (MLT) as generally used in astrophysics is incorrect; MLT forces the mixing length to be an imposed constant. Direct tests show that the damping associated with the flow is that suggested by Kolmogorov. The eddy size is approximately the depth of the convection zone, and this dissipation length corresponds to the "mixing length". New terms involving local heating by turbulent dissipation should appear in the stellar evolution equations. The enthalpy flux ("convective luminosity") is directly connected to the buoyant acceleration, and hence the velocity scale. MLT tends to systematically underestimate this velocity scale. Quantitative comparison with a variety of 3D simulations reveals a previously recognized consistency. Examples of application to stellar evolution will be presented in subsequent papers in this series.

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