Rarefied particle motions on hillslopes – Part 1: Theory

Abstract. We describe the probabilistic physics of rarefied particle motions and deposition on rough hillslope surfaces. The energy balance involves gravitational heating with conversion potential to kinetic energy, frictional cooling associated particle–surface collisions, an apparent preferential low-energy particles. Deposition probabilistically occurs in relation distribution states whose spatial evolution is described by a Fokker–Planck equation. Kirkby number Ki – defined as ratio sets basic behavior form probability fr(r) travel distances r, generalized Pareto distribution. shape scale parameters are well-defined mechanically. For isothermal conditions where matches plus due deposition, exponential. With non-isothermal small this bounded represents rapid thermal collapse. increasing becomes heavy-tailed net heating. It may possess finite mean variance, or variance be undefined sufficiently large Ki. formulation provides key elements entrainment forms flux Exner equation, it clarifies mechanisms particle-size sorting talus scree slopes. Namely, translational rotational spinning particles less likely stopped collisional friction than angular for same surface roughness.