Abstract
River-bed sediments display two universal downstream trends: fining, in which particle size decreases; and rounding, where pebble shapes evolve toward ellipsoids. Rounding is known to result from transport-induced abrasion; however many researchers argue that the contribution of abrasion to downstream fining is negligible. This presents a paradox: downstream shape change indicates substantial abrasion, while size change apparently rules it out. Here we use laboratory experiments and numerical modeling to show quantitatively that pebble abrasion is a curvature-driven flow problem. As a consequence, abrasion occurs in two well-separated phases: first, pebble edges rapidly round without any change in axis dimensions until the shape becomes entirely convex; and second, axis dimensions are then slowly reduced while the particle remains convex. Explicit study of pebble shape evolution helps resolve the shape-size paradox by reconciling discrepancies between laboratory and field studies, and enhances our ability to decipher the transport history of a river rock.
Highlights
Transport of pebbles in a stream causes them to collide and rub against one another and the stream bed, and the resulting abrasion produces the familiar smooth and rounded shape of river rocks
Controversy has ensued regarding the importance of abrasion versus size-selective sorting in diminution of particle size [5]
The emerging consensus has been that abrasion rates reported from laboratory experiments [3,4,5,9,10,11] are too low to account for the downstream fining observed in natural rivers [12,13,14]; the few studies conducted with more energetic collisions – representative of steep river environments – reported significantly higher abrasion rates [3,11]
Summary
Transport of pebbles in a stream causes them to collide and rub against one another and the stream bed, and the resulting abrasion produces the familiar smooth and rounded shape of river rocks. As pointed out by several researchers [4,5], rounding of a cube to an inscribed sphere would reduce mass to p/6 of its original value while producing no change in measured axis lengths. These authors concluded that the importance of abrasion may be significantly underestimated by field studies. Experiments show unequivocally that abrasion occurs in two phases depending on particle shape This two-phase behavior emerges spontaneously from the both the continuous-Firey and discrete-chopping models
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