Analytical theories of turbulence and the ε expansion
Analytical theories of turbulence and the ε expansion
复制标题
湍流和 ε 展开的解析理论
DOI：
10.1063/1.866216
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发表时间：
1987
期刊：
影响因子：
--
通讯作者：
S. Orszag
中科院分区：
文献类型：
--
作者：
W. Dannevik;V. Yakhot;S. Orszag
利用重整化耦合常数(雷诺数)Re*∝e1/2的幂的微扰展开，分析了强湍流重整化群分析得到的流体动力学方程的不动点形式。在二阶e展开式中，导出了被动标量的能量和方差的输运方程，它们与涡阻尼准正规马尔科夫近似的惯性量程形式相同，但没有必须由实验确定的可调参数。能量谱和标量方差谱分别为Ek=1.617e2/3k−5/3和Θk=1.146N e−1/3k−5/3，其中e和N分别为能量耗散率和标量方差。过去已经证明，如果不引入必须针对不同动力场调整到不同值的参数，很难从应用于裸流体动力学方程的重整化微扰理论中获得与实验的这种程度的一致性。Pre的忠诚度...
The fixed‐point form of hydrodynamic equations emerging from renormalization group analysis of strong turbulence is analyzed using perturbation expansion in powers of the renormalized coupling constant (Reynolds number) Re*∝e1/2. In the second order of e expansion, transport equations are derived for energy and variance of a passive scalar which are identical to the inertial‐range form of the eddy‐damped quasinormal Markovian approximation (EDQNM), but without adjustable parameters which must be determined from experiment. The energy and scalar variance spectra are predicted to be Ek=1.617e2/3k−5/3, and Θk=1.146N e−1/3k−5/3, where e and N are, respectively, the dissipation rate of energy and scalar variance. This level of agreement with experiment has in the past proved difficult to obtain from renormalized perturbation theory applied to the bare hydrodynamic equations, without introduction of parameters that must be adjusted to different values for different dynamical fields. The fidelity of the pre...