Non-Mean Field Approach to Self-Organization of Landforms Via Stochastic Merger

Abstract

The stochastic merging model of Werner et al. (1993) for self-organization in landforms such as wind ripples is extended to the fully-statistical, non-mean field case, using functional methods recently developed for the closure of turbulence, kinetic equation and nonlinear two-timescale problems. The role of fluctuations and spatial correlations in the dynamics is clarified and the regime of validity of the mean-field, single-particle distribution function approximation is determined. This approach lends new support to the notion that growth and stabilization of macroscopic geophysical structures may be understood on a deeper level via a fundamentally probabilistic model.