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COMPUTING SCIENCE

Up a Lazy River

Meandering through a classic theory of why rivers meander

Brian Hayes

Shifting Sands

Let me return to the question with which I began this column: Why doesn't a river just take the shortest path to the sea? From the point of view of a drop of water moving with the current, there is no paradox in the existence of meanders. The water follows the local gravitational gradient, which always points downriver. But how does that gradient get twisted into such tortuous shapes? The issue is not how the channel guides the river but how the river carves the channel.

Watts BranchClick to Enlarge Image

Simple curves, random walks and optimization principles may not be enough to answer such questions. We may need to get into the nitty-gritty of erosion, deposition and sediment transport. Leopold dealt with these matters in his accounts of meanders, as others had before him, going back a century or more. The basic idea is that once a bend has formed, differential erosion and deposition tend to exaggerate it. Water flows more rapidly near the outer bank, which therefore tends to wash away. Meanwhile the slower current near the inner bank drops its load of sediment, forming a "point bar." The net effect is to shift the channel in a way that widens the bend.

Computer simulations of this process have produced some very realistic-looking meanders. The models are detailed and elaborate, incorporating dozens of subtle effects—cross-channel currents, graded sediment, variations in bank erodibility. The output reproduces not only the static form of natural meanders but also their evolution.

Is that the answer, then: What we need to understand meandering is not abstract mathematics but a bucket of sand and silt? I would be willing to leave it at that but for one extraordinary fact: Rivers meander even when they carry no sediment, and even when they have no banks! Meltwater streams atop glaciers, with no sand to deposit in point bars, meander much like other rivers. And the Gulf Stream, flowing unconfined in the open ocean, also meanders in a way remarkably like that of a river carving its way through continental alluvium. It appears there may be some principle at work that transcends the particular dynamics of the erosion-deposition cycle.

Reviewing the state of meander studies in 1998, David Knighton of the University of Sheffield concluded, "There is no general agreement as to how or why streams meander." That's a bit of a step backward from where I began—with admiration for Luna Leopold's simple and elegant theory. But I haven't lost my admiration, or given up on simple and elegant explanations. Although meanders have so far wriggled out of my grasp, I still think the universe will turn out to be a comprehensible place.

© Brian Hayes





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