Rotations of spheroidal particles immersed in turbulent flows reflect the combined effects of fluid strain and vorticity, as well as the time history of these quantities along the particle's trajectory. Conversely, particle rotation statistics in turbulence provide a way to characterise the Lagrangian properties of velocity gradients. Particle rotations are also important for a range of environmental and industrial processes where particles of various shapes and sizes are immersed in a turbulent flow. In this study, we investigate the rotations of inertialess spheroidal particles that follow Lagrangian fluid trajectories. We perform direct numerical simulations (DNS) of homogeneous isotropic turbulence and investigate the dynamics of different particle shapes at different scales in turbulence using a filtering approach. We find that the mean-square particle angular velocity is nearly independent of particle shape across all scales from the Kolmogorov scale to the integral scale. The particle shape does determine the relative split between different modes of rotation (spinning vs tumbling), but this split is also almost independent of the filter scale suggesting a Lagrangian scale-invariance in velocity gradients. We show how the split between spinning and tumbling can be quantitatively related to the particle's alignment with respect to the fluid vorticity.

中文翻译：

---

湍流中球体与速度梯度之间的形状和尺度相关耦合

浸入湍流中的球形粒子的旋转反映了流体应变和涡量的综合影响，以及这些量沿粒子轨迹的时间历程。相反，湍流中的粒子旋转统计提供了一种表征速度梯度的拉格朗日特性的方法。粒子旋转对于各种形状和大小的粒子浸入湍流中的一系列环境和工业过程也很重要。在这项研究中，我们研究了遵循拉格朗日流体轨迹的无惯性球形粒子的旋转。我们对均匀各向同性湍流进行直接数值模拟 (DNS)，并使用过滤方法研究湍流中不同尺度的不同粒子形状的动力学。我们发现，从 Kolmogorov 尺度到积分尺度的所有尺度，均方粒子角速度几乎与粒子形状无关。粒子形状确实决定了不同旋转模式（旋转与翻滚）之间的相对分裂，但这种分裂也几乎与滤波器尺度无关，表明速度梯度具有拉格朗日尺度不变性。我们展示了旋转和翻滚之间的分裂如何与粒子相对于流体涡度的排列在数量上相关。但这种分裂也几乎与滤波器尺度无关，表明速度梯度具有拉格朗日尺度不变性。我们展示了旋转和翻滚之间的分裂如何与粒子相对于流体涡度的排列在数量上相关。但这种分裂也几乎与滤波器尺度无关，表明速度梯度具有拉格朗日尺度不变性。我们展示了旋转和翻滚之间的分裂如何与粒子相对于流体涡度的排列在数量上相关。