Regular meander path models

Existing mathematical models for regular meander paths are shown to be members of a general family of differential equations in which the rate of change of curvature along the channel is an odd function of path direction and bends are symmetric. The physical assumptions of the general model and possible justifications of the particular cases are outlined. Each model is specified by one scale parameter (path or axial wavelength) and one shape parameter (maximum deviation, sinuosity, or maximum curvature). Exact analytic expressions for geometric properties of circular arcs, Fargue's spiral, Von Schelling's curve, and the sine‐generated curve are presented and illustrated by dimensionless plots; the last three models are generally similar. Properties of natural meander bends show fair agreement with these three regular models, although bend size and shape vary along individual channels, possibly because of nonuniform floodplain topography and sediments.