WKB theory for rapid distortion of inhomogeneous turbulence
WKB theory for rapid distortion of inhomogeneous turbulence
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非均匀湍流快速畸变的 WKB 理论
DOI：
10.1017/s0022112099005340
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发表时间：
1999
影响因子：
3.7
通讯作者：
B. Dubrulle
中科院分区：
文献类型：
--
作者：
S. Nazarenko;N. Kevlahan;B. Dubrulle
WKB 方法用于将 RDT（快速畸变理论）扩展到初始非均匀湍流和非定常平均流。 WKB 方程描述了由平均速度传输的湍流波包，并且具有因平均应变而演化的波数。湍流还改变平均流量并通过平均雷诺应力张量产生大规模涡度。该理论应用于泰勒四辊流，以解释实验观察到的平均应变的降低。由于四个滚子限制的湍流点形成了大规模的涡旋四极结构，因此发生了应变减小。湍流不均匀性和三维性对于这种效应都很重要。如果初始各向同性湍流在空间上是均匀的或二维的，则它对大尺度应变没有影响。此外，二维情况下湍流动能守恒，这对二维湍流理论具有重要意义。这里给出的分析和数值结果与实验具有良好的定性一致性。
A WKB method is used to extend RDT (rapid distortion theory) to initially inhomogeneous turbulence and unsteady mean flows. The WKB equations describe turbulence wavepackets which are transported by the mean velocity and have wavenumbers which evolve due to the mean strain. The turbulence also modifies the mean flow and generates large-scale vorticity via the averaged Reynolds stress tensor. The theory is applied to Taylor's four-roller flow in order to explain the experimentally observed reduction in the mean strain. The strain reduction occurs due to the formation of a large-scale vortex quadrupole structure from the turbulent spot confined by the four rollers. Both turbulence inhomogeneity and three-dimensionality are shown to be important for this effect. If the initially isotropic turbulence is either homogeneous in space or two-dimensional, it has no effect on the large-scale strain. Furthermore, the turbulent kinetic energy is conserved in the two-dimensional case, which has important consequences for the theory of two-dimensional turbulence. The analytical and numerical results presented here are in good qualitative agreement with experiment.