Resolving bedload flux variability

Bedload transport plays a vital role in shaping Earth’s environment by promoting the formation and growth of geological features of various scales, including ripples and dunes, deltas and fans, and laminations and cross-bedding. A key problem hampering our understanding of bedload-induced landscape evolution is the notoriously large variability commonly associated with measurements of bedload flux, even under controlled and highly idealized conditions in the laboratory, such as fully-developed, unidirectional open-channel flows over flat beds composed of grains of nearly uniform sizes. For example, two recent experimental studies report a nearly sixfold different nondimensionalized bedload flux at a comparable Shields number for spherical grains [1, 2]. The likely culprit is the immense difficulty experimentalists face in estimating the transport-driving bed shear stress. There is currently no universally accepted method of even determining the bed surface elevation in the presence of bedload transport, which is particularly problematic for shallow flows where small changes have a large effect. Neither is there agreement on how to account for the effects of sidewall friction, which become the stronger the smaller the width-to-depth ratio b/h of the open-channel flow. Standardly employed empirical sidewall corrections have arguably a greater resemblance to cooking recipes than to formal physically-derived methods. In addition to such experimental difficulties, there is the physical question of how grain shape, which usually is not controlled for in laboratory experiments, affects bedload flux. A recent prominently published study argued that grain shape is the predominant reason for bedload flux variability and put forward a semi-empirical, analytical bedload transport model to account for it [1].

Here, we compile data from existing experiments and existing and new DNS-DEM, LES-DEM, and RANS-DEM numerical simulations of turbulent bedload transport of shape-controlled grains, in which b/h varies between 0.1 and infinity (periodic boundary conditions in simulations). After employing a non-empirical sidewall correction, which we derived from the phenomenological theory of turbulence, and a granular-physics-based method to determine the bed surface elevation, all data for spherical grains of sufficient size collapse onto a single curve, resolving the experimental problem of bed shear stress determination. Furthermore, the combined data for spherical and non-spherical grains are in strong disagreement with the model of Ref. [1] but support our alternative analytical bedload model across grain shapes, bed slopes, flow strengths, and channel widths.

[1] Deal et al., Nature 613, 298 (2023). https://doi.org/10.1038/s41586-022-05564-6

[2] Ni & Capart, Geophysical Research Letters 45, 7000 (2018). https://doi.org/10.1029/2018GL077571