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

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.