Relevance of the Basset history term for Lagrangian particle dynamics

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 cause 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 when ignoring the Basset history term can be significant, in particular, if the underlying flow is turbulent.