The triple decomposition of a velocity gradient tensor is studied with direct numerical simulations of homogeneous isotropic turbulence, where the velocity gradient tensor is decomposed into three components representing an irrotational straining motion. Strength of these motions can be quantified with the decomposed components. A procedure of the triple decomposition is proposed for three-dimensional flows, where the decomposition is applied in a basic reference frame identified by examining a finite number of reference frames obtained by three sequential rotational transformations of a Cartesian coordinate. Even though more than one basic reference frame may be available for the triple decomposition, the results of the decomposition depend little on the choice of basic reference frame. In homogeneous isotropic turbulence, regions with strong rigid-body rotations or straining motions are highly intermittent in space, while most flow regions exhibit moderately strong shearing motions in the absence of straining motions and rigid-body rotations. The shear tensor is also used for detecting intense shear layers.

中文翻译：

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均匀各向同性湍流中速度梯度张量的三次分解

通过均匀各向同性湍流的直接数值模拟研究速度梯度张量的三重分解，其中速度梯度张量被分解为三个分量，代表无旋应变运动。这些运动的强度可以用分解的分量来量化。提出了一种用于三维流的三重分解过程，其中分解应用于通过检查由笛卡尔坐标的三个连续旋转变换获得的有限数量的参考帧来识别的基本参考帧。尽管三重分解可能有多个基本参考系可用，但分解结果几乎不依赖于基本参考系的选择。在均匀各向同性湍流中，具有强刚体旋转或应变运动的区域在空间中高度间歇，而大多数流动区域在没有应变运动和刚体旋转的情况下表现出中等强度的剪切运动。剪切张量也用于检测强剪切层。