Passive Sliders on Growing Surfaces and (anti-)Advection in Burger's Flows

TL;DR

This paper investigates particle fluctuations on growing surfaces, revealing complex behaviors like clustering and variable diffusion depending on particle advection direction, using renormalization, simulations, and scaling in one dimension.

Contribution

It introduces a novel mapping of particle sliding on growing surfaces to passive scalar advection in Burger's flows, uncovering new phenomena and variable exponents.

Findings

Particles advected with the surface tend to cluster.

Anti-advection results in slower diffusion and complex density fluctuations.

The study suggests a rich set of phenomena with possible continuously varying exponents.

Abstract

We study the fluctuations of particles sliding on a stochastically growing surface. This problem can be mapped to motion of passive scalars in a randomly stirred Burger's flow. Renormalization group studies, simulations, and scaling arguments in one dimension, suggest a rich set of phenomena: If particles slide with the avalanche of growth sites (advection with the fluid), they tend to cluster and follow the surface dynamics. However, for particles sliding against the avalanche (anti-advection), we find slower diffusion dynamics, and density fluctuations with no simple relation to the underlying fluid, possibly with continuously varying exponents.