Scale of plume clustering in large-Prandtl-number convection

Clustering of plumes in turbulent Rayleigh-B\'enard convection has been numerically observed in low-Prandtl-number fluids. In this framework, turbulent plumes undergo a phase-separation process leading to large-scale clusters and circulations, sometimes called plume superstructures and reminiscent of solar granulation and supergranulation. On the other hand, the possible presence of large-scale plume aggregates has not been explored in the case of large values of the Prandtl number, Pr, relevant to geological settings such as convection in planetary interiors. Here we address this problem and numerically explore the behavior of plume ensembles in turbulent convection at very high Prandtl number values, including the case $\text{Pr}\ensuremath{\rightarrow}\ensuremath{\infty}$. The results indicate the presence of plume clustering, albeit at smaller scale, also for large Pr number fluids, suggesting interesting consequences for mantle convection processes.