We investigate the properties of the velocity gradient tensor for spatially evolving turbulent flows (a near-wake, two axisymmetric jets and a planar mixing layer). Emphasis is placed on the study of the normal and non-normal parts of the tensor. Non-normality plays a greater role in the dynamics than is observed for HIT and does so for all spatial locations examined. This implies a greater role for the deviatoric part of the pressure Hessian. Results for the wake flow, where we isolate the coherent part of the dynamics using a modal decomposition, clarify how these competing effects operate. Previous studies have shown the shape of the Q–R diagram (formed by the second and third invariants of the characteristic equation for the tensor) is approximately universal at small-scales for different flows. The non-normal dynamics are neglected in the Q–R approach but appear to differ significantly between flows.

中文翻译：

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速度梯度张量动力学的非法向贡献对于空间发展的非均匀湍流的重要性

我们研究了空间演化湍流（近尾流、两个轴对称射流和平面混合层）的速度梯度张量的特性。重点放在张量的正常和非正常部分的研究上。非正态性在动态中比在 HIT 中观察到的作用更大，并且对于检查的所有空间位置也是如此。这意味着压力 Hessian 的偏斜部分的作用更大。尾流的结果，我们使用模态分解来隔离动力学的相干部分，阐明了这些竞争效应是如何运作的。先前的研究表明，Q-R 图的形状（由张量特征方程的第二个和第三个不变量形成）在不同流量的小尺度上近似通用。