1 7 0 D O C . 1 5 4 O N F O R M A T I O N O F M E A N D E R S 154. “The Cause of the Formation of Meanders in the Courses of Rivers and of the So-Called Baer’s Law” [Einstein 1926l] Dated before 7 January 1926[1] Published 12 March 1926 In: Die Naturwissenschaften 14 (1926): 223–224. It is common knowledge that streams tend to curve in serpentine shapes instead of following the line of the maximum downhill grade of the terrain. It is also well known to geographers that the rivers of the northern hemisphere tend to erode chiefly on the right side. The rivers of the southern hemisphere behave in the op- posite manner (Baer’s law).[2] Many attempts have been made to explain this phe- nomenon, and I am not sure whether anything I say in the following pages will be new to the expert some of my considerations are certainly known. Nevertheless, having found nobody who was thoroughly familiar with the causal relationships in- volved, I think it is appropriate to give a short qualitative exposition of them.[3] First of all, it is clear that the erosion must be stronger the greater the velocity of the current where it touches the bank in question, or rather the more steeply it falls to zero at any particular point of the river wall. This is equally true under all cir- cumstances, whether the erosion is caused by mechanical or physico-chemical fac- tors (decomposition of the ground). We must therefore concentrate our attention on the circumstances which affect the steepness of the velocity gradient at the wall. In both cases the asymmetry as regards the fall in velocity is indirectly due to the formation of a circular motion to which we will next direct our attention. 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 somewhat heavier than the liquid they have dis- placed. 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, such 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. [p. 223]
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