ALBERT EINSTEIN AND MEANDERING RIVERS

Kent A. Bowker, Chevron U.S.A. Inc., P.O. Box 1635, Houston, TX 77251

Search and Discovery Article #70001 (1999)

(Published in Earth Science History, v. 1, no. 1, 1988, and presented here with permission of Earth Science History, Mott Greene, editor, and the author.)

I have always believed that Albert Einstein possessed a ken surpassed by few, and one must admire his ability to simplify seemingly complex ideas. He usually did this via illustrative "thought experiments" and facile analogies. Many subjects are covered in his writings; fortunately for geologists, meandering rivers is one of them (Einstein 1954).

At least one author, James Thomson (1876), preceded Einstein (who originally published his work in the German periodical Die Naturwissenschaften in 1926) in the description of helical flow in some rivers and the resultant meandering pattern. However, Einstein was the first to understand how helical flow helps to determine meander length and to promote down-current migration of the meanders.

Einstein's explanation for the formation of helical flow is the most lucid I've read (p. 250):

I begin with a little experiment which anybody can easily repeat. Imagine a flat-bottomed cup full of tea. At the bottom there are some tea leaves, which stay there because they are rather heavier than the liquid they have replaced. If the liquid is made to rotate by a spoon, the leaves will soon collect in the center of the bottom of the cup. The explanation of this phenomenon is as follows: the rotation of the liquid causes a centrifugal force to act on it. This in itself would give rise to no change in the flow of the liquid if the latter rotated like a solid body. But in the neighborhood of the walls of the cup the liquid is restrained by friction, so that the angular velocity with which it rotates is less there than in other places nearer the center. In particular, the angular velocity of rotation, and therefore the centrifugal force, will be smaller near the bottom than higher up. The result of this will be a circular movement [helical flow] of the liquid of the type illustrated in [the figure] which goes on increasing until, under the influence of ground friction, it becomes stationary. The tea leaves are swept into the center by the circular movement and act as proof of its existence. [The tea leaves are homologous to the sediment that comprises point bar deposits.]

Einstein goes on to explain how helical flow develops in a meandering river, and that because the higher-velocity portions of the stream will be driven to the outside (concave) portion of the river bend, erosion will be greater there.

He also noted that because the helical flow possesses inertia, the circulation (and the erosion) will be at their maximum beyond the inflection of the curve. Hence, the wave-form of the river will migrate in a down-current direction. Finally, Einstein explained that the larger the cross-sectional area of a river, the slower the helical flow will be absorbed by friction; which explains why larger rivers have meander patterns with longer wavelengths.

Several authors subsequently described and quantified the points made by Einstein (see, for example, Friedkin 1945, Leopold and Wolman 1960, Allen 1970, and Jackson 1975). However, I have only read one reference to Einstein's paper - a short comment by Schumm (1972, p. 234) that the formation of river meanders has attracted some of the world's greatest thinkers. Several textbooks state that rivers meander as a result of helical flow, but none that I have read give the original reference or acknowledge Einstein's contribution.

I hope that someday soon, Albert Einstein's thoughts on meandering rivers will become recognized within our science.

References

Allen, J.R.L., 1970, A quantitative model of grain size and sedimentary structures in lateral deposits: Geol. Jour., v. 7, pp. 129-146.

Einstein, A., 1954, The cause of the formation of meanders in the courses of rivers and of the so-called Baer's Law, pp. 249-253 in Ideas and Opinions: New York, Bonanza Books, 337 p.

Friedkin, J.F., 1945, A laboratory study of the meandering of alluvial rivers: Vicksburg, Miss., U.S. Army, Corps of Engineers, Mississippi River Comm., Waterways Ext. Sta., 40p. (Reprinted 1972, pp. 237-281 in Schumm, S.A., ed., River Morphology [Benchmark papers in geology]: Stroudsburg, Pa., Dowden, Hutchinson, and Ross, Inc., 429 p.)

Jackson, R.G., 1975, Velocity, bed-form, texture patterns of meander bends in the lower Wabash River of Illinois and Indiana: Geol. Soc. America, Bull., v. 86, pp. 1511-1522.

Leopold, L.B., and M.G. Wolman, 1960, River Meanders: Geol. Soc. America, Bull., v. 71, pp. 769-794.

Schumm, S.A., ed., 1972, River Morphology: Benchmark papers in geology: Stroudsburg, Pa., Dowden, Hutchinson, and Ross, Inc., 429 p.

Thomson, J., 1876, On the windings of rivers in alluvial plains: Royal Soc. London Proc., v. 25, pp. 5-8.