A simplified Python-based kinematic model of particle transport in rivers

Abstract

We present results from a particle-scale numerical model inspired by the idea that a majority of the time during transport capable floods, bedload transport in rivers is rarefied, and a stochastic process. Physical experiments conducted by others to explore this idea suggest that the time varying particle activity N measured within a control area A above the bed surface is described by a Poisson probability mass function (pmf), assuming an absence of collective entrainment. This implies that particles are sporadically entrained from the bed surface at rate λ with no “memory” of prior entrainment events, when and where local flow conditions favor particle lift or dislodgement. In this context we developed a new open source kinematic particle-scale model written in Python (Zwiep and Chartrand, 2022). Notably, the model includes no information related to the bed surface shear stress or Shields conditions, and no sediment transport functions are used to drive the model. The model domain measures a use specified length nD of the particle diameter D, with a width of 1D. At present we have tested the model with 30 simulations using a uniform particle diameter. Each simulation was run for 1 million iterations to explore the governing model parameters: SRe is the number of subregions within the domain length nD; En is the particle entrainment rate per iteration, which we randomly sample from a Poisson pmf for a specified value of λ; lt is the particle travel distance which we randomly sample from either a lognormal distribution or a truncated normal distribution for specified values of the distribution expected value and standard deviation; and Sh is the vertical particle stacking height ranging from 1-3D. The model produces a time varying signal of particle flux counted at downstream points of internal subregion domains, and at the downstream end of the model domain. The simplified particle bed changes “relative” elevation distributions through particle stacking and downstream motions of travel distance. An implication of particle stacking within the context of a stochastic model framework is a time varying signal of the average “particle age” defined as the number of iterations since last entrainment, as well as the average “particle age range” defined as the difference of the maximum and minimum particle ages, both metrics calculated at each iteration and across all subregions. The age dynamics correlate with the magnitude of N following an initial period of particle bed organization. Our initial tests suggest that the relatively simple model logic captures the essence of rarefied particle transport. We believe the model can be used to ask basic science questions, and as a classroom tool to introduce students to bedload transport in a straightforward and illustrative manner.