A PHENOMENOLOGICAL TREATMENT OF ROTATING TURBULENCE
A PHENOMENOLOGICAL TREATMENT OF ROTATING TURBULENCE
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DOI：
10.1063/1.868457
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发表时间：
1995-05
影响因子：
4.6
通讯作者：
Ye Zhou
中科院分区：
文献类型：
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作者：
Ye Zhou
注意到磁流体动力学 (MHD) 湍流与旋转的初始各向同性湍流之间的高度相似性。然后我们将 Kraichnan、Matthaeus 和 Zhou 的 MHD 现象学应用于旋转湍流。当湍流受到强烈旋转时，发现能谱的比例为 E(k) = C_Omega (Omega epsilon)^1/2 k^-2，其中 Omega 是旋转速率，k 是波数，epsilon 是耗散率。这种光谱形式与泽曼最近的一封信一致。然而，这里发现常数 C_Omega 与柯尔莫哥洛夫常数有关，并且对于后者常数的典型值估计在 1.22-1.8 范围内。推导出将光谱传输时间与涡流周转时间以及三重相关性衰减的时间尺度联系起来的“规则”。三重相关衰减率的假设导致谱定律在“-5/3”（无旋转）和“-2”定律（强旋转）之间变化。对于中间旋转速率，光谱根据无量纲参数的值而变化，该参数测量相对于波数 k 的旋转波数 k_Omega =(Omega^3/epsilon)^1/2 的强度。涡流粘度的导出与旋转速率有明确的相关性。
The strong similarity between the magnetohydrodynamic (MHD) turbulence and initially isotropic turbulence subject to rotation is noted. We then apply the MHD phenomenologies of Kraichnan and Matthaeus and Zhou to rotating turbulence. When the turbulence is subject to a strong rotation, the energy spectrum is found to scale as E(k) = C_Omega (Omega epsilon)^1/2 k^-2, where Omega is the rotation rate, k is the wavenumber, and epsilon is the dissipation rate. This spectral form is consistent with a recent letter by Zeman. However, here the constant C_Omega is found to be related to the Kolmogorov constant and is estimated in the range 1.22-1.8 for the typical values of the latter constant. A `rule'' that relates spectral transfer times to the eddy turnover time and the time scale for decay of the triple correlations is deduced. A hypothesis for the triple correlation decay rate leads to the spectral law which varies between the `-5/3'' (without rotation) and `-2'' laws (with strong rotation). For intermediate rotation rates, the spectrum varies according to the value of a dimensionless parameter that measures the strength of the rotation wavenumber k_Omega =(Omega^3/epsilon)^1/2 relative to the wavenumber k. An eddy viscosity is derived with an explicit dependence on the rotation rate.