Particle size dynamics in abrading pebble populations

Abstract

Abstract. Abrasion of sedimentary particles in fluvial and eolian 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, we introduce the first model for the collision-driven collective mass evolution of sedimentary particles. The model utilizes results of the individual, geometric abrasion theory as a collision kernel; following techniques adopted in the statistical theory of coagulation and fragmentation, the corresponding Fokker–Planck equation is derived. 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.

On the Oval Shapes of Beach Stones

“…Intuitively, when the beach stone becomes extremely small, it is comparable to one of the grains of sand that make up the beach and is subject to different dynamics, such as collisional abrasion and fracturing. Moreover, (11) does not address the changing size of the abrading stone, which in some river rock models has been shown to decrease exponentially in time (e.g., see [8,43]).…”