The movement of small but finite spherical particles in a fluid can be described by the Maxey-Riley equation (MRE) if they are too large to be considered passive tracers. The MRE contains an integral "history term" modeling wake effects, which causes the force acting on a particle at some given time to depend on its full past trajectory. The history term causes complications in the numerical solution of the MRE and is therefore often neglected, despite both numerical and experimental evidence that its effects are generally not negligible. By numerically computing trajectories with and without the history term of a large number of particles in different flow fields, we investigate its impact on the large-scale Lagrangian dynamics of simulated particles. We show that for moderate to large Stokes numbers, ignoring the history term leads to significant differences in clustering patterns. Furthermore, we compute finite-time Lyapunov exponents and show that, even for small particles, the differences in the resulting scalar field from ignoring the BHT can be significant, in particular if the underlying flow is turbulent.

翻译：当微小但有限尺寸的球形颗粒在流体中运动时，若其尺寸过大而不能视为被动示踪粒子，则可用Maxey-Riley方程（MRE）进行描述。MRE包含一个模拟尾流效应的积分"历史项"，该项导致作用在粒子上的力取决于其完整的过往运动轨迹。历史项使得MRE的数值求解变得复杂，因此常被忽略，尽管数值和实验证据均表明其影响通常不可忽略。通过在不同流场中对大量粒子进行含历史项与不含历史项的轨迹数值计算，我们研究了该历史项对模拟粒子大尺度拉格朗日动力学的影响。研究表明，对于中等至较大的斯托克斯数，忽略历史项会导致聚类模式出现显著差异。此外，我们计算了有限时间李雅普诺夫指数，结果表明即使对于微小粒子，忽略Basset历史项（BHT）所产生的标量场差异也可能非常显著，特别是在底层流动为湍流的情况下。