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How river rocks round: Resolving the shape-size paradox:

Domokos, G., Jerolmack, D.J., Sipos, A.A, and Torok, A.
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River-bed sediments display two universal downstream trends: fining, in which particlensize 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.
EES Authors: 
Douglas J. Jerolmack

Department of Earth and Environmental Science / University of Pennsylvania, 251 Hayden Hall, 240 South 33rd Street, Philadelphia, PA 19104-6316