Sensitivity Analysis and Statistical Convergence of a Saltating Particle Model

TL;DR

This paper presents a simple stochastic saltation model validated against experimental data, analyzing its convergence, sensitivity to parameters, and estimating bed load transport rates with results aligning well with empirical formulas.

Contribution

It introduces a validated, efficient numerical saltation model with systematic convergence criteria and empirical formula comparisons, advancing sediment transport modeling.

Findings

At least 10^3 hops are needed for convergence; 10^4 for statistical stability.

The lift force dependent on slip velocity and flow gradient yields more stable results.

The model's bed load transport estimates agree with empirical flume data.

Abstract

Saltation models provide considerable insight into near-bed sediment transport. This paper outlines a simple, efficient numerical model of stochastic saltation, which is validated against previously published experimental data on saltation in a channel of nearly horizontal bed. Convergence tests are systematically applied to ensure the model is free from statistical errors emanating from the number of particle hops considered. Two criteria for statistical convergence are derived; according to the first criterion, at least $10^3$ hops appear to be necessary for convergent results, whereas $10^4$ saltations seem to be the minimum required in order to achieve statistical convergence in accordance with the second criterion. Two empirical formulae for lift force are considered: one dependent on the slip (relative) velocity of the particle multiplied by the vertical gradient of the horizontal flow velocity component; the other dependent on the difference between the squares of the slip velocity components at the top and bottom of the particle. The former is found to give more stable results. A parameter study indicates that the saltation length has a minimum value with increasing particle diameter (at non-dimensional $D_* \sim 12$) for a given transport stage. Variations in the friction coefficient and collision line level have negligible effect on the saltation statistics within the ranges considered. Regression equations are obtained for each of the saltation characteristics. Finally, the model is used to evaluate the bed load transport rate, which is in satisfactory agreement with common formulae based on flume data, especially when compared against other saltation-derived expressions.