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.

Particle size and shape variation of Ultisol aggregates affected by abrasion under different transport distances in overland flow

“…However, little information about the particle shape variation in slope erosion processes is found. Domokos et al (2014) indicated that river-bed sediments displayed two universal downstream trends: fining, in which particle size decreased; and rounding, where pebble shapes evolved toward ellipsoids. Rounding is known to result from transport-induced abrasion.…”

A Genealogy of Convex Solids Via Local and Global Bifurcations of Gradient Vector Fields

“…In [5] it is shown that the evolution of S and U under the partial differential equations governing collisional abrasion processes can be modeled by letting S and U be random variables whose expected values decrease with time. While this trend has been verified both in laboratory experiments [6] and in the field [19], almost no pebbles in the primary classes {1, i}, {j, 1}, (i, j = 1, 2, . .…”

“…Settinġ x =ẏ = 0 in (5), and noting that y = (x 2 − µ 1 )/(2αx + µ 2 ) from the first equation, we may eliminate y from the second equation to obtain the fixed point condition (6) F µ1,µ2,α (x) = a 4 x 4 + a 3 x 3 + a 2 x 2 + a 1 x + a 0 = 0, where…”

Percutores Líticos De La Pampa Del Desierto De Atacama (Norte De Chile): Tecnología, Huellas De Uso, Decoración Y Talladores

“…Debido a que ambos ambientes presentan cinemáticas, dinámicas físicas y fuerzas disímiles, generan formas peculiares de guijarros, lo que permite distinguir su origen geológico según algunos de sus atributos morfológicos (Dobkins y Folk 1970;Kelly 1983). En los sistemas fluviales el desplazamiento del sedimento ocurre en un eje lineal y en un solo sentido, variando la intensidad y fuerza del transporte según la pendiente y alimentación del afluente, donde el ruedo por arrastre crea guijarros en general de formas esferoidales u ovoidales en el cual la abrasión se aplica similarmente en todas las superficies de la roca (Domokos et al 2014;Kelly 1983). En estos casos el grado de redondeamiento del guijarro dependerá de su ubicación en el eje de descenso del curso fluvial, presentando mayor grado de pulimento hacia su sección final debido a una historia más larga de abrasión (Attal y Lavé 2009).…”