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.
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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