River Meanders and the Theory of Minimum Variance

Abstract

So ubiquitous are curves in rivers and so common are smooth and regular meander forms that they have attracted the interest of investigators from many disciplines. Also, investigations of the physical characteristics of glaciers and oceans have led to the recognition that analogous forms occur in melt-water channels developed on glaciers and even in the currents of the Gulf Stream. The striking similarity in physical form of curves in these various settings is the result of certain geometric proportions apparently common to all, that is, a nearly constant ratio of radius of curvature to meander length and of radius of curvature to channel width (Leopold and Wolman, 1960, p. 774). This leads to visual similarity regardless of scale.