Engines of Our Ingenuity

No. 2453

by John H. Lienhard

Jet plane shadow with rainbow halo Today, we look down on a river. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

I know -- it's uncool to stare out airplane windows, but I do anyway. And such sights to see! The shadow, cast by our plane upon a cloud, is surrounded by a circular rainbow. The perfect pentagonal shape of historic Fort Warren is cold, isolated, and mantled in snow on its Boston Harbor island.

Fort Warren

Then there's the wild twisting Bartholomew Bayou in northeastern Louisiana -- and the Mississippi River just beyond it, surging east, west and even north, as it feels its way south. Big Sunflower Bayou in northern Mississippi wanders like a drunkard trying to find his way home. Their meandering seems to defy all sense.

Bartholomew Bayou

The word meander comes from the Meander River, lurching its way across ancient Phrygia. Some meandering rivers have the regularity of humps on an imagined sea serpent. But irregularities in most flat regions throw those loops out of kilter.

Oxbow in Bartholomew Bayou, LAImagine a river moving in a nearly straight line. The flow on the outer side of any small bend moves a bit faster, causing slightly greater scouring on that side. So the bend gradually keeps bowing further and further outward. It keeps growing until it forms a full circle. Then the river rejoins itself, isolating the loop into what's called an oxbow.

A pattern of waves and loops thus forms and sprawls across the land. Familiar as this action is, we need to see the pattern from above to understand the utter madness in the forms it takes.

In Texas Piney Woods And the plot thickens. Nineteenth-century naturalist Karl Ernst von Baer observed that rivers in the northern hemisphere do most of their erosion on the side to the right of the direction of flow, and on the left in the southern hemisphere -- a result of the same Coriolis Effect that determines the rotation of hurricanes.

Albert Einstein looked at Baer's Law in 1926. In a note for the journal Naturwissenschaften, he said: Yes, we understand that scouring is greater on the outside of the bend. But how does Coriolis action add to the obvious centripetal forces?

A New England river Einstein used no mathematics in his paper. He simply observed that, as river flows bend to Earth's surface, the Coriolis Effect adds rotation to the water's flow. Water actually corkscrews its way downstream. The crosswise part of the flow drags on the river bed and moves rather slowly up the left-hand side. Then it gains speed as it comes across the surface. It does its scouring as it comes down the right-hand bank.

Other mathematicians added the equations, but Einstein already had the answer. Thirty years later, I worked one summer for Einstein's civil engineer son Hans. He was studying, not relativity theory, but the transport of particles in channel flows. Now I finally know just how that twig had been bent. And that is why I'll keep looking out airplane windows. So much is so subtly revealed, when we finally get to view it from above.

I'm John Lienhard at the University of Houston, where we're interested in the way inventive minds work.

(Theme music)

A. Einstein, The Cause of the Formation of Meanders in the Courses of Rivers and of the So-Called Baer's Law. Die Naturwissenschaften, Vol. 14, 1926. This may be read in translation in A. Einstein, Ideas and Opinions. (Three Rivers Press, 1995) pp. 249-253, or online here.

See also Kent Bowker's online discussion of Einstein's classic paper; and the Wikipedia article on Meandering.

My thanks to John H. Lienhard V at MIT for his counsel. Photos by J. Lienhard (IV)

The Neches River in Big Thicket National Preserve
The Neches River in Big Thicket National Preserve

The Engines of Our Ingenuity is Copyright © 1988-2009 by John H. Lienhard.