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arXiv 0901.4254astro-ph.SR
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Ia型超新星三维爆燃模型中的Turbulence:I.缩放属性

Turbulence in a three-dimensional deflagration model for Type Ia supernovae: I. Scaling properties

F. Ciaraldi-Schoolmann, W. Schmidt, J. C. Niemeyer, F. K. Roepke, W. Hillebrandt

摘要:

分析了Ia型超新星爆燃模型中湍流速度场的统计特性。特别是,我们考虑的问题,是否湍流是各向同性的,并符合Kolmogorov理论在小的长度尺度。利用一个热核超新星爆炸高分辨率模拟的数值数据,计算了湍流能量和速度结构函数的谱。我们表明,湍流速度场是各向同性的小长度尺度,并遵循标度律,这是一致的Kolmogorov理论,直到大部分的核燃料燃烧。当长度尺度大于某一特征尺度时,湍流变得各向异性。在这里,径向速度波动遵循瑞利-泰勒不稳定性的标度律,而角度分量仍然服从柯尔莫哥洛夫标度。在爆炸的后期阶段,这一特征尺度下降到模拟的数值分辨率以下。分析证实,一个亚网格尺度模型的未解决的湍流能量是需要一致的计算Ia型超新星的爆燃模型中的火焰速度,并在这些尺度上的各向同性的假设是适当的。

英文摘要:

We analyze the statistical properties of the turbulent velocity field in the deflagration model for Type Ia supernovae. In particular, we consider the question of whether turbulence is isotropic and consistent with the Kolmogorov theory at small length scales. Using numerical data from a high-resolution simulation of a thermonuclear supernova explosion, spectra of the turbulence energy and velocity structure functions are computed. We show that the turbulent velocity field is isotropic at small length scales and follows a scaling law that is consistent with the Kolmogorov theory until most of the nuclear fuel is burned. At length scales greater than a certain characteristic scale, turbulence becomes anisotropic. Here, the radial velocity fluctuations follow the scaling law of the Rayleigh-Taylor instability, whereas the angular component still obeys Kolmogorov scaling. In the late phase of the explosion, this characteristic scale drops below the numerical resolution of the simulation. The analysis confirms that a subgrid-scale model for the unresolved turbulence energy is required for the consistent calculation of the flame speed in deflagration models of Type Ia supernovae, and that the assumption of isotropy on these scales is appropriate.

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