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.

11 pages, 5 figures

References in corpus (6)

• What is in a pebble shape?
• Formation of sharp edges and planar areas of asteroids by polyhedral abrasion
• The evolution of pebble size and shape in space and time
• Smoothing a Rock by Chipping
• Geometrical and physical models of abrasion
• Abrasion of flat rotating shapes

Cited by in corpus (7)

• Bistability in Rayleigh-Bénard convection with a melting boundary
• A boundary-integral framework to simulate viscous erosion of a porous medium
• Explaining the elongated shape of 'Oumuamua by the Eikonal abrasion model
• On the monotonicity of spatial critical points evolving under curvature-driven flows
• A genealogy of convex solids via local and global bifurcations of gradient vector fields
• On the Oval Shapes of Beach Stones
• The evolution of geophysical shape descriptors under distance-driven flows