What might rice piles tell us about non-local sediment transport?

Abstract:

Our research objective is to identify sediment transport systems that exhibit non local signals, such as those seen in the long-profile of fluvial surfaces. In previous work we have shown that appropriate nonlocal models of sediment transport under various tectonic forcing, can lead to fluvial surface shapes that are distinct from those obtained with local models. For example, in the study of a sediment bypass system, a nonlocal model for the sediment flux predicts a concave down fluvial surface in contrast to the linear surface predicted with a local flux model.

It is well known that hold ups and fast paths in transport systems lead to non-local behaviors. And we think that the mechanism that creates the unexpected curvatures in fluvial profiles is one of "storage and release". Perhaps the classic storage and release system is that seen in rice pile experiments. One set up for this experiment involves the formation of a rice pile in the gap (~25mm) between two vertical glass plates resting on a solid surface. In this system rice is added at a constant rate at the left and allowed to freely exit a distance (~0.5m) downstream; the system is run until a steady state is approached. Of course, an exact steady state is not reached because the rice does not move steadily down the pile surface but rather advances in a series of avalanches, with multiple length scales, separated by waiting times; in other words is transported via storage and release. The naive expectancy is that at the steady state the surface of the rice pile will exhibit a constant angle of repose. Our experiments with the system, however, indicate that while the storage and release mechanism invokes large temporal fluctuations in the pile its surface exhibits a persistent concave down shape. In this paper, we present the main findings of our rice pile experiment, explore models that might explain the persistence of the curved surface, and uncover the behavioral links between the rice pile model and non-local signals in fluvial sediment transport.

The authors acknowledge support from the National Science Foundation through Grant EAR-1318593, Generalized Transport Models in Earth Surface Dynamics.