Sediment Shape Evolution Due to Pebble Abrasion in the Rio Mameyes, Puerto Rico

<p>Data collected from the Rio Mameyes to characterize change in size and shape of river sediment due to abrasion.  Complete details on measurement and calculation techniques can be found in the following paper: <em>Qunatifying the significance of abrasion and selective transport on downstream pebble evolution, </em>Journal of Geophysical Review: Earth Surface, (in review).</p

Two-phase abrasion illustration.

<p>The 2D schematic shows two well-separated phases emerging spontaneously from Gaussian-curvature-driven abrasion: In Phase I edges abrade but axis ratios remain constant; in Phase II, axis ratios evolve towards the sphere. Accompanying perspective images are topographic laser scans that illustrate the two phases in 3D; they were performed for a separate experiment with a smaller cuboid having similar axis ratios.</p

Comparison of experimental and numerical results

<p>. (a–e) Evolution of shape parameters versus volume, <i>V</i>. Shown are: axis ratios (a) <i>y₁</i> and (b) <i>y₂</i>, (c) convexity index β, (d) Wadell sphericity, <i>r</i>, and (e) superellipsoid exponent, <i>n</i>. (f) Evolution of <i>V</i> versus the rotation number (<i>rot</i>), a proxy for time. Gray line: experimental data. Black solid line: level-set method approximation of the PDE (<b>Eq. 2</b>). Dashed line: chopping model approximation (<b>Eq. 3</b>). Best fit coefficients correspond to pure Gaussian flow. Note abrupt change for all shape parameters (a–e) at transition from Phase I to Phase II, shown with vertical dashed line. Pebble volume exhibits no abrupt change through time (f); the fitted exponential trend is identical in Phase I and Phase II. Data used to generate this figure are contained in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0088657#pone.0088657.s001" target="_blank">File S1</a>.</p

Experimental images of abrasion.

<p>Three rows correspond to three orthogonal views of the specimen, and columns show time evolution in terms of number of drum rotations. Separation of Phases I and II can be observed by visual inspection.</p

Shape evolution of a tetrahedron under the purely Gaussian chopping model in Eq. 3 with <i>p</i> = 1.

<p>(a) Initial facets are shown in red; the transition to Phase II abrasion occurs when these facets have been entirely removed. (b) As with the cuboid, surface convexity <i>β</i> increases during Phase I and stabilizes at <i>β</i>≈1 in Phase II.</p

Definition sketch.

<p>(a) 2D schematic of the physical situation studied, showing an abrading cuboid colliding with a flat plane. Zone of positive curvature on the colliding corner is highlighted with arrows indicating surface-normal abrasion. (b) Three scenarios of the chopping model: Vertex chopping (Event A) corresponding to Gaussian-curvature-driven abrasion, edge chopping (Event B) corresponding to Mean-Curvature-driven abrasion, and face chopping (Event C) corresponding to uniform (Eikonal) abrasion.</p