Role of Third-Order Structure Function in Studying Two-Dimensionalisation of Turbulence
Role of Third-Order Structure Function in Studying Two-Dimensionalisation of Turbulence
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三阶结构函数在二维湍流研究中的作用
DOI：
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发表时间：
2008
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通讯作者：
S. Chakraborty
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作者：
S. Chakraborty
我们研究了二维各向同性均匀非受迫湍流中的各种关联函数，其中包括速度场和涡量场的关联函数。由于Kolmogorov(随后，Landau在他的流体力学文本中)，我们采用了更直观的方法，并展示了如何以更简单的方式建立2D湍流的结果，使用其他方法可以获得。用同样的方法计算了准地转湍流中赝势拟能正级联和能量逆级联的准地转湍流的三阶结构函数。这些结果促使我们在二维化效应的背景下研究两点三阶结构函数。随后的研究使我们能够给出二维快速旋转三维不可压缩湍流中逆能量级联的原因。对于这样的系统，文献表明能谱关系中的波数指数有可能介于-2和-3之间。我们论证了在快速旋转湍流的情况下，指数存在-2到-7/3的更严格的范围，这与最近的实验一致。此外，还提供了两点三阶结构函数的推导，这有助于人们论证，即使在缓慢旋转的情况下，一个人也可以得到指数为-2.87的谱，从而暗示了旋转的二维化效应的开始。此外，利用经旋转修正的Gledzer-Ohkitani-Yamada(GOY)壳模型，验证了这些二维化效应的特征。
We look at various correlation functions, which include those that involve both the velocity and the vorticity fields, in two-dimensional (2D) isotropic homogeneous unforced turbulence. We adopt the more intuitive approach due to Kolmogorov (and subsequently, Landau in his text on fluid dynamics) and show that how the 2D turbulence's results, obtainable using other methods, may be established in a simpler way. Same method is used to calculate some third-order structure functions for quasi-geostrophic (QG) turbulence for the forward cascade of pseudo-potential enstrophy and the inverse energy cascade in quasi-geostrophic turbulence. These results motivate us to study the two-point third order structure function in the context of the two-dimensionalisation effect. Consequent studies enable us to give a reason for the inverse energy cascade in the two-dimensionalised rapidly rotating three dimensional (3D) incompressible turbulence. For such a system, literature shows a possibility of the exponent of wavenumber in the energy spectrum's relation to lie between -2 and -3. We argue the existence of a stricter range of -2 to -7/3 for the exponent in the case of rapidly rotating turbulence which is in accordance with the recent experiments. Also, a derivation for the two point third order structure function has been provided helping one to argue that even with slow rotation one gets, although dominated, a spectrum with the exponent -2.87, thereby hinting at the initiation of the two-dimensionalisation effect with rotation. Moreover, using the Gledzer-Ohkitani-Yamada (GOY) shell model, modified for rotation, these signatures of two-dimensionalisation effect have been verified.