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River meanders - Theory of minimum variance

Professional Paper 422-H

By:
and

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Abstract

Meanders are the result of erosion-deposition processes tending toward the most stable form in which the variability of certain essential properties is minimized. This minimization involves the adjustment of the planimetric geometry and the hydraulic factors of depth, velocity, and local slope.

The planimetric geometry of a meander is that of a random walk whose most frequent form minimizes the sum of the squares of the changes in direction in each successive unit length. The direction angles are then sine functions of channel distance. This yields a meander shape typically present in meandering rivers and has the characteristic that the ratio of meander length to average radius of curvature in the bend is 4.7.

Depth, velocity, and slope are shown by field observations to be adjusted so as to decrease the variance of shear and the friction factor in a meander curve over that in an otherwise comparable straight reach of the same river

Since theory and observation indicate meanders achieve the minimum variance postulated, it follows that for channels in which alternating pools and riffles occur, meandering is the most probable form of channel geometry and thus is more stable geometry than a straight or nonmeandering alinement.

Additional publication details

Publication type:
Report
Publication Subtype:
USGS Numbered Series
Title:
River meanders - Theory of minimum variance
Series title:
Professional Paper
Series number:
422
Chapter:
H
Year Published:
1966
Language:
English
Publisher:
U.S. Government Printing Office
Publisher location:
Washington, D.C.
Description:
iv, 16 p.
First page:
H1
Last page:
H15