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.
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.
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.
Imagine 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.
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
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
I'm John Lienhard at the University of Houston,
where we're interested in the way inventive minds
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 Engines of Our Ingenuity is
Copyright © 1988-2009 by John H.