Memory of particle clusters in decaying isotropic urbulence

Inertial particles with a density different from that of the fluid are known to cluster in response to turbulent fluctuations. Although particles of different densities are known to show variations in acceleration statistics and preferential concentrations in statistically stationary turbulence, there is a limited understanding of whether a universal clustering response is available for decaying isotropic turbulence. Here we perform direct numerical simulations of {\it decaying} isotropic turbulence Re$_\lambda \in [65,180]$, with inertial particles of Stokes number St$_{\eta0} \sim 10^{\text{-}1} - 10^1$, and density ratio covering light and heavy particles. Turbulence decay drives a decrease in the acceleration variance of particles.

However, the decay can drive an increase in the clustering exceeding even the clustering possible in stationary turbulence. Standard deviation of cluster volumes show non-monotonic trends depending on the particle inertia and density ratio, although the mean cluster size does grow in decaying turbulence. The fractal dimension of clusters for particles of wide-ranging densities may be collapsed using a revised effective evolving Stokes built on an intermediate sized eddy.