Dimensioning the Sine‐Generated Curve Meander Geometry1

Abstract

Mecklenburg, Daniel E. and Anand D. Jayakaran, 2012. Dimensioning the Sine‐Generated Curve Meander Geometry. Journal of the American Water Resources Association (JAWRA) 48(3): 635‐642. DOI: 10.1111/j.1752‐1688.2012.00638.xAbstract: The sine‐generated curve (SGC) presented by Langbein and Leopold (1966) is widely acknowledged as an idealized description of river meander form. However, as originally presented, the SGC application to the field, laboratory, or models is not a trivial task. The SGC function simply provides the direction of the flow path as its rate of change continually varies from most gradual at the crossover to most rapid at the apex of bends. Although the commonly used dimensions of meander length, stream length per meander, sinuosity, and amplitude have been approximated previously, this technical note precisely defines these dimensions by solving the integrals of the sine and cosine of the SGC function. This is performed using integral representations of the Bessel and Struve functions for the zero order and their power‐series expansions. Higher precision offered by this technique will be of particular value to modeling and flume‐based studies where better conformity to the SGC is necessary. The note goes on to present two simple line and arc patterns optimally fit to the SGC as simplified yet more precise methods for practical design in river restoration schemes. Equations are presented defining the geometry of the arc and line pattern and relating meander length, amplitude, radius of curvature, and sinuosity.