Clustering of advected passive sliders on a fluctuating surface

TL;DR

This paper investigates the clustering behavior of passive particles advected by a fluctuating surface, revealing strong clustering and similar statistical properties in both nonequilibrium and equilibrium conditions.

Contribution

It provides a comparative analysis of particle clustering in nonequilibrium Burgers flow and equilibrium random landscapes, with analytical and numerical results.

Findings

Density correlations scale with system size

Mass distribution exhibits divergence at small scales

Clustering is strong and statistically similar in equilibrium and nonequilibrium cases

Abstract

We study the clustering properties of advected, non-interacting,passive scalar particles in a Burgers fluid with noise, a problem which maps to that of passive sliding particles moving under gravity on a surface evolving through the Kardar-Parisi-Zhang equation. Numerical simulations show that both the density-density correlation function and the single-site mass distribution scale with system size. The scaling functions diverge at small argument, indicating strong clustering of particles. We analytically evaluate the scaling functions for the two-point correlation and mass distribution of noninteracting particles in thermal equilibrium in a random landscape, and find that the results are remarkably similar to those for nonequilibrium advection.