Many rivers worldwide exhibit an abrupt downstream transition from gravel-bedded to sand-bedded reaches, and eolian sand seas show analogous abrupt downwind grain-size transitions; both are accompanied by a bimodal grain-size distribution with a near-empty 'grain-size gap' — a paucity of sediment in the 1–10 mm range in the source's own terms, commonly quoted as 1–5 mm in the later literature. Jerolmack and Brzinski (2010) hypothesized that the two settings are dynamically equivalent, governed by threshold transport conditions and inter-particle collision dynamics, and that collision-driven attrition — the spallation of small chips off coarse grains during saltation and bed-load transport — creates the fine-sediment population and hence the bimodality and abruptness of the transitions. Sixteen years of subsequent work has tested fragments of this hypothesis with mixed results: aeolian field and wind-tunnel studies support spallation in soft lithologies but measure small fines fluxes from quartz sand; morphodynamic models now reproduce bimodal grain-size distributions and abrupt transitions from sorting and suspension processes alone; and the proposed Shields–Stokes similitude scaling has never been experimentally tested. This record states the unresolved quantitative attribution question: is collision attrition necessary and quantitatively sufficient — relative to selective sorting and suspension-fallout mechanisms — to produce the observed fine-sediment flux, bimodality, and spatial abruptness of grain-size transitions in both rivers and sand seas.

Background

Rivers generally fine downstream — particle diameter decreases with distance from the sediment source, a trend known as downstream fining — but in a great many rivers this fining is not gradual: at some point the median bed grain size drops abruptly from coarse gravel (~10 mm) to medium sand (~1 mm) over a short distance. This is the gravel–sand transition (GST). Associated with it is the grain-size gap: riverbeds composed of gap-range sediment (fine gravel and coarse sand) are remarkably rare worldwide, so that bed-material grain-size distributions are commonly bimodal, with two modes (gravel and sand) separated by a near-empty interval. Jerolmack and Brzinski (2010) describe this paucity as spanning the 1–10 mm range; the later literature commonly defines the gap as 1–5 mm (e.g., Lamb and Venditti 2016; An et al. 2024). Eolian sand seas (large sand-dune fields) show a phenomenologically similar pattern, with downwind grain-size transitions and bimodal distributions. The GST is foundational for fluvial engineering, sedimentology, and geomorphology because sand-bedded and gravel-bedded channels obey different empirical relations for flow resistance, sediment transport, and channel morphology.

Before 2010, explanations for the gap fell into two families. Comminution hypotheses (Yatsu 1955; Kodama 1994) held that particles in the gap range break down rapidly into sand; weathering hypotheses (Wolcott 1988) held that hillslopes simply supply little gap-sized sediment. Sorting hypotheses, exemplified by Ferguson (2003), held that size-selective transport alone can produce an abrupt transition. Jerolmack and Brzinski (2010) proposed a mechanistic unification built on two dimensionless groups. The Shields stress is the ratio of fluid shear force to particle weight, and measures how close a grain is to entrainment; they argued both gravel rivers and sand seas organize near a threshold state where the dominant grain size moves at Shields stresses near unity (a 'threshold channel' or 'threshold sand sea'). The Stokes number of a collision is the ratio of grain inertia to viscous forces, St=ρsdus/(9μ)\mathrm{St} = \rho_s d u_s / (9\mu) for grain diameter dd, grain velocity usu_s, density ρs\rho_s, and fluid viscosity μ\mu; below St∼105\mathrm{St} \sim 10^5 collisions are viscously damped, so that impact energy is dissipated in the water or air film rather than fracturing the grain; the source argues that the reduction of collision efficiency with grain diameter sets a lower limit on gravel size, leading to the grain-size gap. Because damping suppresses effective collisions below roughly 10 mm in water — the lower limit on gravel size, at the top of the 1–10 mm paucity range — they argued, gravel cannot attrite into the gap range; instead, coarse grains undergoing saltation (hopping transport) and bed-load collisions spall off small angular chips — spallation, a low-energy chipping mode of attrition distinct from bulk fragmentation — producing a fine (sand-to-silt) population while the gap range stays empty. On this view the bimodal supply created by attrition, interacting with threshold transport, generates the abrupt transitions of both rivers and sand seas. In the source's own formulation, spallation is paired with a second process — segregation of the fine and coarse modes by suspension and saltation transport, respectively — so that attrition and segregation are complementary components of a single hypothesis.

Later work complicated this picture on three fronts. First, experiments on bedrock incision by suspended sediment (Scheingross et al. 2014) showed that collisions remain energetic well into the fine range, undermining the viscous-damping argument; Lamb and Venditti (2016) proposed instead that the gap emerges from suspension transport itself: below a bed shear velocity of about 0.1 m/s rivers lose the ability to carry sand as wash load (fine sediment that travels in suspension without depositing), forcing abrupt fallout, and the 1–5 mm gap follows from Reynolds-number dependencies of the thresholds for wash load and initial motion — with testable planetary predictions for Mars and Titan. Second, aeolian measurements (Swet et al. 2019, 2020; Huang et al. 2019) found that wind abrasion of mature quartz sand produces only minor fines, with most emitted dust derived from pre-existing clay coatings, although spallation products were directly observed in the soft gypsum sand of White Sands (Jerolmack, Reitz and Martin 2011). Third, morphodynamic modeling advanced the sorting family: Blom et al. (2017) reproduced GST migration assuming a bimodal supply; Dingle and Venditti (2023) showed in flumes that gap-sized particles are preferentially mobilized once sand deposits on the bed, explaining their scarcity on riverbeds; and An et al. (2024) demonstrated that a one-dimensional model with size-specific bed-load and suspended-load transport generates bimodal grain-size distributions and a GST autogenically from a unimodal sediment feed, with no attrition term at all. In parallel, the mechanics of attrition itself were quantified: geometric theory and field verification established two-phase pebble abrasion (Miller et al. 2014; Domokos et al. 2013), and rotating-drum experiments mapped the transition between chipping (products orders of magnitude smaller than the parent) and fragmentation as a function of material strength (Bodek and Jerolmack 2021). What no study has delivered is the quantitative attribution the 2010 hypothesis requires: field-representative attrition rates and spallation-product size distributions across lithologies, provenance evidence tying downstream or downwind fines to the upstream coarse grains that supposedly shed them, scaled experiments matching both Shields stress and Stokes number between model and target systems, and a mechanistic attrition model coupled to transport and sorting models tested against the observed abruptness and bimodality of natural transitions.

Problem Statement

Determine whether collision-driven attrition (spallation of small chips off coarse grains during bed-load and saltation transport) is necessary and quantitatively sufficient to explain the abrupt grain-size transitions of alluvial rivers and eolian sand seas, as posited by Jerolmack and Brzinski (2010) — or whether selective sorting and suspension fallout mechanisms suffice without it. The overarching objective is a validated quantitative attribution of the fine-sediment flux, the bimodal grain-size distributions, and the spatial abruptness of the transitions in both settings. In the source, spallation and the segregation of the fine and coarse modes (by suspension and saltation transport, respectively) are complementary components of a single hypothesis; the attrition-versus-sorting/suspension opposition posed above is the attribution contest as sharpened by the subsequent literature (Ferguson 2003; Lamb and Venditti 2016; An et al. 2024).

References

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