AI 中文总结
本文开发了加入有限相关切向加速度的二阶马尔可夫拉格朗日随机颗粒再悬浮模型，通过多尺度轨迹统计打破了与一阶模型的宏观简并性，揭示了脱离前的反常输运特性。
AI 中文摘要
颗粒再悬浮模型通常通过宏观再悬浮分数进行评估，尽管这种积分可观测量可能掩盖导致脱离的时间动态过程。本文开发了一种二阶马尔可夫拉格朗日随机模型，方法是在角速度状态中加入有限相关的切向加速度。该模型在雷诺数范围为$Re_\tau \in [60, 430]$的湍流通道流中进行了检验，并与已有的一阶公式进行了比较。两种模型产生的再悬浮分数几乎重叠，揭示了不同随机描述之间存在宏观简并性。多尺度轨迹统计打破了这种简并性。加入加速度的公式将短时间正则性从$S_2(\tau) \propto \tau$变为$S_2(\tau) \propto \tau^2$，维持了角速度相关性，并产生了更强的方向不对称性和更重的增量尾。条件均方位移的幸存者分析揭示了一个与雷诺数相关的反常输运窗口，其中附着颗粒集合的增长速度快于扩散参考值，在向类扩散输运过渡前，局部接近弹道和超弹道标度。这条有限时间路径记录了颗粒接近脱离的过程，且被宏观再悬浮分数所忽略。在$Re_\tau \approx 60$时，轨迹进入不同的低雷诺数统计状态，其特征是速度和加速度去相关收敛，以及接近高斯增量。这些结果确立了多尺度轨迹统计作为随机再悬浮模型间的关键判别依据，并确定有限加速度相关性是超出宏观脱离动力学的动态信息来源。
英文摘要
Particle resuspension models are commonly evaluated using the macroscopic resuspended fraction, although this integrated observable may conceal the temporal dynamics leading to detachment. Here, a second-order Markovian Lagrangian stochastic model is developed by augmenting the angular-velocity state with a finite-correlated tangential acceleration. The model is examined over turbulent channel flows with ($Re_τ\in [60, 430]$) and compared with an established first-order formulation. The two models produce nearly overlapping resuspended fractions, revealing a macroscopic degeneracy between distinct stochastic descriptions. Multiscale trajectory statistics break this degeneracy. The acceleration-augmented formulation changes the short-time regularity from $S_2(τ) \propto τ$ to $S_2(τ) \propto τ^2$, sustains angular-velocity correlation, and produces stronger directional asymmetry and heavier increment tails. The survivor-conditioned mean square displacement exposes a Reynolds-number-dependent anomalous-transport window, in which the attached-particle ensemble grows more rapidly than the diffusive reference and locally approaches ballistic and super-ballistic scaling before crossing toward diffusion-like transport. This finite-time pathway records how particles approach detachment and is compressed out of the macroscopic resuspended fraction. At $Re_τ\approx 60$, the trajectories enter a distinct low-Reynolds-number statistical state characterized by converging velocity and acceleration decorrelation and near-Gaussian increments. These results establish multiscale trajectory statistics as essential discriminants between stochastic resuspension models and identify finite acceleration correlation as a source of dynamical information beyond macroscopic detachment kinetics.
