Diffusive evolution of experimental braided rivers

Meredith D. Reitz, Douglas J. Jerolmack, Eric Lajeunesse, Angela Limare, Olivier Devauchelle, and François Métivier

Phys. Rev. E 89, 052809 – Published 15 May 2014

Abstract

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 $\sim 1$ 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.

Received 4 October 2013
Revised 6 March 2014

DOI:https://doi.org/10.1103/PhysRevE.89.052809

Authors & Affiliations

Meredith D. Reitz^1,*, Douglas J. Jerolmack², Eric Lajeunesse³, Angela Limare³, Olivier Devauchelle³, and François Métivier³

¹Lamont-Doherty Earth Observatory, Columbia University, Palisades, New York, USA
²Department of Earth and Environmental Science, University of Pennsylvania, Philadelphia, Pennsylvania, USA
³Equipe de Dynamique des Fluides Geologiques, Institut de Physique du Globe de Paris, Paris, France

^*mreitz@ldeo.columbia.edu

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Issue

Vol. 89, Iss. 5 — May 2014

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Images

Figure 1
(a) Side view (above) and plane view (below) sketches of experimental apparatus. Water and sediment are fed into the top of a tilted rectangular bed. Overlain is an image of the sine wave fringe projected onto the braided river bed. (b) Water flow location data from a scan of the experimental braided river bed. Flow is from right to left of image. (c) Field example of a braided river in New Zealand. Photo taken by Greg O'Beirne, adapted with GFDL/Creative Commons permissions.
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Figure 2
(a) A scan of the topography of the braided river, with flow in the $x$ direction from top to bottom of the image. (b) The differenced topography between the scan in (a) and the scan taken 5 min later, giving a map of the erosion and deposition that has occurred in the interval.
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Figure 3
Trend of median channel width-to-depth ratio with time for R1 (solid line). The dotted line guides the eye to show the constant nature of the ratio, and the black circle on this line marks the approximate time at which the channels have attained equilibrium. Inset: Trend of width-to-depth ratio with channel width, for all channels averaged (solid line) and for an early snapshot of ratio establishment at 10 min into the run (dashed line).
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Figure 4
An example profile of the channel geometry, with $y$ as the cross-stream and $z$ as the vertical coordinates, together with the Shields stress profile. The profiles are the average of all $\sim 100$ of the cross-stream profiles of Shields stress and channel geometry for this given width within a scan. The widths averaged fell within the range of an individual pixel's width of 0.93 mm.
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Figure 5
Dynamical estimates of diffusivity. (a) Decorrelation of wet fraction with time (asterisks), plotted in ln-linear space with the best-fit exponential decline (solid line); straight line correspondence supports the behavior as exponential. Diffusivity estimated using Eq. (2). (b) Growth of the downstream correlation length of topography for R2 (asterisks), plotted against the square root of time (solid line); best-fit line yields an estimate of diffusivity [Eq. (3)], while the fit of a straight line confirms the diffusive square root of time scaling. (c) Overlain plots of downstream slope as its equilibrium value is established during the experiment (“slope establishment,” light green dotted line) and the increase in the cumulative fraction of the surface visited by water (space filling) for R1 (black dashed line), each normalized to their initial and final equilibrium values. Also plotted is the exponential fit to slope establishment data (solid red line), which allows an estimate of diffusivity in a similar manner to (a).
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