Brian Hayes in American Scientist:
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.