COMPUTING SCIENCE
Up a Lazy River
Meandering through a classic theory of why rivers meander
Brian Hayes
Water runs downhill—we all know that. As a rule, it follows the
path of steepest descent, seeking out the shortest and fastest route
from top to bottom. So how can we make sense of meandering rivers,
which wiggle-waggle down the valley, prolonging their journey to the
sea and greatly lengthening their course? Why doesn't the flowing
water—acting under the tug of gravity—just carve out a
shortcut across all those loops?
I first encountered the mysteries of meanders in an article by Luna
B. Leopold and Walter Langbein, published 40 years ago in
Scientific American. They gave a lucid account of how
meanders form and why they assume their characteristic sinuous
shapes. I was a student at the time, and the article made a lasting
impression. Not that I was inspired to go off and pursue a career in
potamology, but the Leopold-Langbein theory of meanders was an
eye-opener all the same. It brought home to me the curious fact that
the world is a comprehensible place: You can look at a landform,
say, and expect to understand what you see. The patterns of nature
make sense, if you know how to read them.
Luna Leopold died last February at age 90. Reading accounts of his
life and work led me back to that fondly remembered Scientific
American article from 1966, as well as another article
published a few years earlier in American Scientist. I
found them still lucid and engaging—and yet, on reflection,
not quite fully satisfying. It's not so much that the answers now
seemed less compelling, but they led to many further questions,
which I had lacked the wit to ask the first time around. Maybe
nature is indeed comprehensible, but I couldn't say that I truly
understood river meanders. So I delved deeper into the work of
Leopold and his colleagues, and I looked at how others have
approached the same problems. I even tried a few simplistic computer
experiments of my own. After all that, there's still no shortage of questions.
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