Particle size dynamics in abrading pebble populations

Abstract. Abrasion of sedimentary particles in fluvial and aeolian environments is widely associated with collisions encountered by the particle. Although the physics of abrasion is complex, purely geometric models recover the course of mass and shape evolution of individual particles in low and middle energy environments (in the absence of fragmentation) remarkably well. In this paper, utilizing results of this individual, geometric abrasion theory as a collision kernel, following techniques adopted in the statistical theory of coagulation and fragmentation, we construct the corresponding Fokker-Planck equation as the first model for the collision-driven collective mass evolution of sedimentary particles. Our model uncovers a startling fundamental feature of collective particle size dynamics: collisional abrasion may, depending on the energy level, either focus size distributions, thus enhancing the effects of size selective transport or it may act in the opposite direction by dispersing the distribution. This complex behaviour fits geological observations on mass distributions.