title: How river rocks round: resolving the shape-size paradox.
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.
authors.affiliation: Department of Mechanics, Materials and Structures, Budapest University of Technology and Economics, Budapest, Hungary.
authors.forename: Gabor
authors.initials: G
authors.lastname: Domokos
authors.affiliation: Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America.
authors.forename: Douglas J
authors.initials: DJ
authors.lastname: Jerolmack
authors.affiliation: Department of Mechanics, Materials and Structures, Budapest University of Technology and Economics, Budapest, Hungary.
authors.forename: Andras Á
authors.initials: AÁ
authors.lastname: Sipos
authors.affiliation: Department of Construction Materials and Engineering Geology, Budapest University of Technology and Economics, Budapest, Hungary.
authors.forename: Akos
authors.initials: A
authors.lastname: Török
mesh_terms: D000465:Algorithms; D019015:Geologic Sediments; D005844:Geology / Q000379:methods*; D021621:Imaging, Three-Dimensional; D008903:Minerals / Q000737:chemistry*; D008962:Models, Theoretical; D016011:Normal Distribution; D011336:Probability; D045483:Rivers
chemical_list: D008903:Minerals