Turbulent fluid flows exhibit a complex small-scale structure with frequently occurring extreme velocity gradients. Particles probing such swirling and straining regions respond with an intricate shape-dependent orientational dynamics, which sensitively depends on the particle history. Here, we systematically develop a reduced-order model for the small-scale dynamics of turbulence, which captures the velocity gradient statistics along particle paths. An analysis of the resulting stochastic dynamical system allows pinpointing the emergence of non-Gaussian statistics and nontrivial temporal correlations of vorticity and strain, as previously reported from experiments and simulations. Based on these insights, we use our model to predict the orientational statistics of anisotropic particles in turbulence, enabling a host of modeling applications for complex particulate flows.

中文翻译：

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捕获湍流中的速度梯度和粒子旋转速率

湍流呈现出复杂的小规模结构，并经常出现极端的速度梯度。探测这种涡旋和应变区域的粒子以复杂的形状相关的取向动力学响应，该动力学依赖于粒子的历史。在这里，我们系统地为湍流的小尺度动力学开发了降阶模型，该模型捕获了沿粒子路径的速度梯度统计信息。如先前从实验和模拟中报告的那样，对所得的随机动力系统进行分析后，可以查明非高斯​​统计量以及涡度和应变的非平凡时间相关性的出现。基于这些见解，我们使用我们的模型预测湍流中各向异性颗粒的方向统计数据，