天体物理Turbulence亚网格尺度模型的先验验证
A-priori Validation of Subgrid-scale Models for Astrophysical Turbulence
摘要：
我们进行先验验证测试的亚网格尺度（SGS）模型的湍流输送的动量，能量和被动标量。为此，我们进行了两套高分辨率的流体动力学模拟与拉格朗日代码：一个等温的湍流箱均方根马赫数为0.3，2和8，和经典的风洞中，冷云通过热介质逐渐溶解，由于流体不稳定性。检查两个SGS模型：天体物理模拟中广泛采用的涡动扩散率（ED）模型和Clark等人（1979）提出的“梯度模型”。我们发现，这两个模型预测的SGS项的大小同样好（相关系数> 0.8）。然而，梯度模型提供了很好的预测SGS条款的方向和形状，而ED模型预测差，这表明各向同性扩散是一个穷人的近似瞬时湍流运输。对于动量输运，梯度模型的最佳拟合系数在[0.16，0.21]范围内，湍流Schmidt数和Prandtl数都接近于1，在[0.92，1.15]范围内。
英文摘要：
We perform a-priori validation tests of subgrid-scale (SGS) models for the turbulent transport of momentum, energy and passive scalars. To this end, we conduct two sets of high-resolution hydrodynamical simulations with a Lagrangian code: an isothermal turbulent box with rms Mach number of 0.3, 2 and 8, and the classical wind tunnel where a cold cloud traveling through a hot medium gradually dissolves due to fluid instabilities. Two SGS models are examined: the eddy diffusivity (ED) model wildly adopted in astrophysical simulations and the "gradient model" due to Clark et al. (1979). We find that both models predict the magnitude of the SGS terms equally well (correlation coefficient > 0.8). However, the gradient model provides excellent predictions on the orientation and shape of the SGS terms while the ED model predicts poorly on both, indicating that isotropic diffusion is a poor approximation of the instantaneous turbulent transport. The best-fit coefficient of the gradient model is in the range of [0.16, 0.21] for the momentum transport, and the turbulent Schmidt number and Prandtl number are both close to unity, in the range of [0.92, 1.15].
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