How river rocks round: resolving the shape-size paradox

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.Comment: 11 pages, 5 figure

Multiscale Bed Form Interactions and Their Implications for the Abruptness and Stability of the Downwind Dune Field Margin at White Sands, New Mexico, USA

The downwind margin of White Sands dune field is an abrupt transition from mobile aeolian dunes to a dune-free vegetated surface. This margin is also relatively stable; over the past 60 years it has migrated several times more slowly than the slowest dunes within the dune field, resulting in a zone of dune coalescence, aggradation, and, along most of the margin, development of a dune complex (i.e., dunes superimposed on draas). Repeat terrestrial laser scanning surveys conducted over a 3 month period demonstrate that sediment fluxes within the dune complex decrease on approach to the margin. Computational fluid dynamics modeling indicates that this decrease is due, in part, to a decrease in mean turbulent bed shear stress on the lee side of the dune complex as a result of flow line divergence or sheltering of the lee-side dunes by the stoss side of the dune complex. Conservation of mass demands that this decrease in bed shear stress causes aggradation. We speculate that aggradation on the lee side of the dune complex further enhances the sheltering effect in a positive feedback, contributing to the growth and/or maintenance of the dune complex and a relatively abrupt and stable dune field margin. Our model and data add to a growing body of evidence that aeolian dune field patterns are influenced by feedbacks that occur at scales larger than individual dunes

Experimental Alluvial Fan Evolution: Channel Dynamics, Slope Controls, and Shoreline Growth

River deltas and alluvial fans have channelization and deposition dynamics that are not entirely understood, but which dictate the evolution of landscapes of great social, economic, and ecologic value. Our lack of a process-based understanding of fan dynamics hampers our ability to construct accurate prediction and hazard models, leaving these regions vulnerable. Here we describe the growth of a series of experimental alluvial fans composed of a noncohesive grain mixture bimodal in size and density. We impose conditions that simulate a gravel/sand fan prograding into a static basin with constant water and sediment influx, and the resulting fans display realistic channelization and avulsion dynamics. We find that we can describe the dynamics of our fans in terms of a few processes: (1) an avulsion sequence with a timescale dictated by mass conservation between incoming flux and deposit volume; (2) a tendency for flow to reoccupy former channel paths; and (3) bistable slopes corresponding to separate entrainment and deposition conditions for grains. Several important observations related to these processes are: an avulsion timescale that increases with time and decreases with sediment feed rate; fan lobes that grow in a self-similar, quasi-radial pattern; and channel geometry that is adjusted to the threshold entrainment stress. We propose that the formation of well-defined channels in noncohesive fans is a transient phenomenon resulting from incision following avulsion, and can be directly described with dual transport thresholds. We present a fairly complete, process-based description of the mechanics of avulsion and its resulting timescale on our fans. Because the relevant dynamics depend only on threshold transport conditions and conservation of mass, we show how results may be directly applied to field-scale systems

Flooding and Flow Path Selection on Alluvial Fans and Deltas

The surfaces of alluvial fans and river deltas (collectively fans) are often dissected by a small number of channels radiating from the fan apex. On long timescales, channels migrate via avulsion, the process of channel bed deposition and abandonment that often results in catastrophic flooding and loss of life on densely populated fans. We present results of an experimental fan that creates realistic channel patterns by avulsion. The avulsion cycle occurs with a period that is predictable from conservation of mass. Selection of a new flow path is inherently stochastic; however, once a network of 4–5 channels is established, flow oscillates among these channels indefinitely. We demonstrate that a directed random walk model with memory quantitatively reproduces these dynamics and limiting behavior, and is consistent with natural fans

Sorting Out Abrasion in a Gypsum Dune Field

Grain size distributions in eolian settings are the result of both sorting and abrasion of grains by saltation. The two are tightly coupled because mobility of particles determines abrasion rate, while abrasion affects the mobility of particles by changing their mass and shape; few field studies have examined this quantitatively. We measured grain size and shape over a 9 km transect downwind of a line sediment source at White Sands National Monument, a gypsum dune field. The sediment source is composed of rodlike (elongate), coarse particles whose shapes appear to reflect the crystalline structure of gypsum. Dispersion in grain size decreases rapidly from the source. Coarse particles gradually become less elongate, while an enrichment of smaller, more elongate grains is observed along the transect. Transport calculations confirm that White Sands is a threshold sand sea in which (1) the predominant particle diameter reflects grains transported in saltation under the dune-forming wind velocity and (2) smaller, elongate grains move in suspension under this dominant wind. Size-selective transport explains first-order trends in grain size; however, abrasion changes the shape of saltating grains and produces elongate, smaller grains that are spallation and breaking products of larger particles. Both shape and size changes saturate 5–6 km downwind of the source. As large particles become more equant, abrasion rates slow down because protruding regions have been removed. Such asymptotic behavior of shape and abrasion rate has been observed in theory and experiment and is likely a generic result of the abrasion process in any environment

Generalized Sorting Profile of Alluvial Fans

Alluvial rivers often exhibit self-similar gravel size distributions and abrupt gravel-sand transitions. Experiments suggest that these sorting patterns are established rapidly, but how—and how fast—this convergence occurs in the field is unknown. We examine the establishment of downstream sorting patterns in a kilometer-scale alluvial fan. The sharp transition from canyon to unconfined, channelized fan provides a well-defined boundary condition. The channel changes from deep and entrenched at the fan apex to shallow and depositional over a short distance, exhibiting nonequilibrium behavior. The resulting gravel-fining profile is not self-similar; the particle size distribution narrows until approximate equal mobility is achieved. Downfan, the gravel-sand transition appears to exhibit a self-similar form; field and laboratory data collapse when downstream distance is normalized by the location of the transition. Results suggest a generalized sorting profile for alluvial fans as a consequence of the threshold of motion and nonequilibrium channels

Barchan-Parabolic Dune Pattern Transition From Vegetation Stability Threshold

Many dune fields exhibit a downwind transition from forward-pointing barchan dunes to stabilized, backward-pointing parabolic dunes, accompanied by an increase in vegetation. A recent model predicts this pattern transition occurs when dune surface erosion/deposition rates decrease below a threshold of half the vegetation growth rate. We provide a direct test using a unique data set of repeat topographic surveys across White Sands Dune Field and find strong quantitative support for the model threshold. We also show the threshold hypothesis applied to a barchan dune results naturally in its curvature inversion, as the point of threshold crossing progresses from the horns to the crest. This simple, general threshold framework can be an extremely useful tool for predicting the response of dune landscapes to changes in wind speed, sediment supply, or vegetation growth rate. Near the threshold, a small environmental change could result in a drastic change in dune pattern and activity

Diffusive Evolution of Experimental Braided Rivers

Water flowing over a loose granular bed organizes into a braided river, a network of ephemeral and interacting channels. The temporal and spatial evolution of this network of braided channels is not yet quantitatively understood. In ∼1 m-scale experiments, we found that individual channels exhibit a self-similar geometry and near-threshold transport conditions. Measurements of the rate of growth of topographic correlation length scales, the time scale of system-slope establishment, and the random spatial decorrelation of channel locations indicate together that the evolution of the braided river system may be diffusive in nature. This diffusion is due to the separation of scales between channel formation and network evolution, and the random motion of interacting channels when viewed at a coarse-grained scale