Phase Transitions in Geomorphology

Abstract:

Landscapes are patterns in a dynamic steady-state, due to competing processes that smooth or sharpen features over large distances and times. Geomorphic transport laws have been developed to model the mass-flux due to different processes, but are unreasonably effective at recovering the scaling relations of landscape features. Using a continuum approximation to compare experimental landscapes and the observed landscapes of the earth, one finds they share similar morphodynamics despite a breakdown of classical dynamical similarity between the two. We propose the origin of this effectiveness is a different kind of dynamic similarity in the statistics of initiation and cessation of motion of groups of grains, which is common to disordered systems of grains under external driving. We will show how the existing data of sediment transport points to common signatures with dynamical phase transitions between “mobile” and “immobile” phases in other disordered systems, particularly granular materials, colloids, and foams. Viewing landscape evolution from the lens of non-equilibrium statistical physics of disordered systems leads to predictions that the transition of bulk measurements such as particle flux is continuous from one phase to another, that the collective nature of the particle dynamics leads to very slow aging of bulk properties, and that the dynamics are history-dependent. Recent results from sediment transport experiments support these predictions, suggesting that existing geomorphic transport laws may need to be replaced by a new generation of stochastic models with ingredients based on the physics of disordered phase transitions. We discuss possible strategies for extracting the necessary information to develop these models from measurements of geomorphic transport noise by connecting particle-scale collective dynamics and space-time fluctuations over landscape features.