On freely decaying, anisotropic, axisymmetric Saffman turbulence
On freely decaying, anisotropic, axisymmetric Saffman turbulence
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关于自由衰变、各向异性、轴对称萨夫曼湍流
DOI：
10.1017/jfm.2012.242
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发表时间：
2012
影响因子：
3.7
通讯作者：
Okamoto N. and Kaneda Y.
中科院分区：
文献类型：
--
作者：
Davidson P.A.;Okamoto N. and Kaneda Y.
我们考虑自由衰减、各向异性、统计轴对称的Saffman湍流，其中，是能谱和波数。我们注意到，这样的湍流具有两个统计不变量，这是有关的频谱张量在小的形式。它们是和，其中下标和表示平行于和垂直于对称轴的量。由于和和是整数标度，大标度的自相似性（当它适用时）要求和。这反过来又要求它是恒定的，这与自由衰减的湍流应该表现出“回归各向同性”的流行观点相反。在大型周期域进行的数值模拟，具有不同类型和水平的初始各向异性，证实，和确实是不变的，并在充分发展的状态，。有些令人惊讶的是，同样的模拟也表明，在完全发展的状态下，它或多或少是恒定的。简单的理论论据表明，当和都是常数，积分尺度应演变为和，而不管各向异性的水平和螺旋度的存在。这些衰减规律，首先提出的Saffman（物理流体，第10卷，1967年，第1349页），通过数值模拟验证。
We consider freely decaying, anisotropic, statistically axisymmetric, Saffman turbulence in which , where is the energy spectrum and the wavenumber. We note that such turbulence possesses two statistical invariants which are related to the form of the spectral tensor at small . These are and , where the subscripts and indicate quantities parallel and perpendicular to the axis of symmetry. Since and , and being integral scales, self-similarity of the large scales (when it applies) demands and . This, in turn, requires that is constant, contrary to the popular belief that freely decaying turbulence should exhibit a ‘return to isotropy’. Numerical simulations performed in large periodic domains, with different types and levels of initial anisotropy, confirm that and are indeed invariants and that, in the fully developed state, . Somewhat surprisingly, the same simulations also show that is more or less constant in the fully developed state. Simple theoretical arguments are given which suggest that, when and are both constant, the integral scales should evolve as and , irrespective of the level of anisotropy and of the presence of helicity. These decay laws, first proposed by Saffman (Phys. Fluids, vol. 10, 1967, p. 1349), are verified by the numerical simulations.