Generalization of Hop Distance‐Time Scaling and Particle Velocity Distributions via a Two‐Regime Formalism of Bedload Particle Motions

Abstract

AbstractTo date, there is no consensus on the probability distribution of particle velocities during bedload transport, with some studies suggesting an exponential‐like distribution while others a Gaussian‐like distribution. Yet, the form of this distribution is key for the determination of sediment flux and the dispersion characteristics of tracers in rivers. Combining theoretical analysis of the Fokker‐Planck equation for particle motions, numerical simulations of the corresponding Langevin equation, and measurements of motion in high‐speed imagery from particle‐tracking experiments, we examine the statistics of bedload particle trajectories, revealing a two‐regime distance‐time (L‐Tp) scaling for the particle hops (measured from start to stop). We show that particles of short hop distances scale as L ~ giving rise to the Weibull‐like front of the hop distance distribution, while particles of long hop distances transition to a different scaling regime of L ~ Tp leading to the exponential‐like tail of the hop distance distribution. By demonstrating that the predominance of mostly long hop particles results in a Gaussian‐like velocity distribution, while a mixture of both short and long hop distance particles leads to an exponential‐like velocity distribution, we argue that the form of the probability distribution of particle velocities can depend on the physical environment within which particle transport occurs, explaining and unifying disparate views on particle velocity statistics reported in the literature.