River‐Meander Model. I: Development

Abstract

Meander flow and meander‐planform development are described. The basis is a steady, two‐dimensional model of flow and bed topography in an alluvial channel with variable curvature. The model is developed from the equations for conservation of mass (water and sediment) and momentum, and from a stability criterion for sediment particles on the stream bed. By order of magnitude considerations and linearization, these equations are reduced to those of a damped, oscillating system. The meander development is described by forcing a traveling, small‐amplitude channel alignment wave on the system, and determining the growth characteristics of the wave. The growth rate of the amplitude is determined by relating the alignment wave and the change in channel alignment through a bankerosion model. Formulas are thereby developed for calculation of: (1) Velocity and depth distribution in meandering channels; and (2) rate and direction of channel migration. Laboratory and field data are used to verify the formulas.