A cellular computational model of braided streams

A. B. Murray and C. Paola

The standard definition of a braided stream is that it is one characterized by a network of interconnected channels, each of relatively low sinuosity. The planform description misses the time dynamics of a braided system, however, which involves the continuous rerouting of water and sediment through various paths in the network. One truly never does see the same river twice: the essence of an active braided network is near-continuous shifting of flow from one part of the network to another as bars grow, old channels are choked with sediment and new channels cut, and channels shift laterally by bank erosion. The dynamics result from an interplay between two processes: the tendency of free-surface flow over an erodible bed to channelize itself, and the localization of deposition within the channels, leading to local channel superelevation, choking, and damming. Occupation of a path by water brings with it a flow of sediment that eventually makes the path useless. The network is thus in a constant state of destroying and reforming itself.

The detailed mechanics of flow in a braided system are formidably complex. Even if the flow is steady overall, the continuous instability of the channel network results in a local time variation; in addition, strong local spatial accelerations are set up by channel curvature, variation in channel width, and bar and confluence topography. This complexity begs the strategic question: to what extend do the large-scale dynamics really depend on the details of this complex, small-scale flow: One way of approaching this problem is to examine the behavior of models that intentionally leave out most of the small-scale dynamics, retaining only the most basic features-like the tendency of the water to prefer the steepest slope, and simple laws of sediment transport and deposition.

We have developed a simple cellular model of the flow of water and noncohesive sediment under conditions of weak lateral constraint. Water leaving each cell is distributed among the three adjoining downstream cells according to bed slope (possibly raised to some exponent). Sediment is transported as a power-law function of water discharge of the product of slope and discharge, and the topographic dynamics is determined by sediment mass balance. We have experimented with a range of combinations of rules, including: slope exponents in the flow-routing law from 0 to 1; exponents in the sediment-flux law from 1 to 2.5; using discharge or slope-discharge product to calculate sediment flux,; allowing for sediment transport on horizontal surfaces; and allowing for lateral sediment transport in the presence of lateral slopes. We begin a run by introducing water onto a surface with small-amplitude random topography. The model produces some form of braiding for nearly all sets of rules; the only absolute requirement for braiding seems to be nonlineariity in the sediment-flux law. The braiding we observe is a form of deterministic chaos. There is considerable variation in the realism of the braiding dynamics produced; the best model includes both lateral sediment transport and transport on horizontal slopes. This model reproduces the global qualitative behavior described above, including such important subprocesses as flow switching, bar formation and dissection, and lateral channel migration. Our work is by now means a comp0lete model of braided systems, but it is a striking example of the richness of dynamics that can be produced by relatively simple physics.