Meander Flow Model. I: Development

Abstract

A model for simulating the flow and bed topography in a meandering alluvial channel is developed. The basis is a solution to the equations for conservation of mass and momentum and for lateral stability of the streambed. The bed‐stability equation is a transverse force balance for bed‐sediment particles relating the transverse bed slope to primary flow variables. The main controlling parameters are the channel's width‐depth ratio, radius‐width ratio, resistance characteristics (or gradient), and sediment Froude number. An innovative feature is the use of a simple mass‐flux balance (mass conservation) to link the equation for bed stability to the momentum equations. The mass‐flux balance relates the net lateral transport of flow volume to the streamwise variation of transverse bed slope. Thereby, the equations governing the secondary‐current velocity and the transverse bed slope become those of a damped oscillating system subjected to a driving force, the change in channel curvature. The model is tested with both laboratory and field data.