Why Are Rivers So Mathematical?

Wadis, or river valleys that are dry in winter months, in Yemen are pictured from the International Space Station as it orbited 256 miles above. via NASA

 

Sometimes meandering, sometimes turbulent, every river seems to have its own character. But the behavior and nature of river networks follow mathematical rules. In 1957, USGS scientist John Hack discovered what became known as Hack’s law: The length of any stream is proportional to its drainage area raised to the power of 0.6. ( L ~ A^0.6). Earlier this year, scientists discovered that Hack’s law also holds for river deltas. Read on to learn about rivers and their mathematical bedrock from Natalie Wolchover on Quanta Magezine:

Systems that branch in this way are “transport networks”: They transport some fluid substance (water, blood, traffic) from every place to a single place (the sea, a heart, a city center). Of the various examples, rivers are especially revealing, I think, since they arise from neither biological evolution nor urban planning, but rather chaotic Earth processes. Yet they obey simple, universal laws.

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