Geometry of river meanders

THERE are many factors affecting the geometry of rivers. Width, depth, slope, flow velocity and plan shape are all influenced by discharge, sediment load, sediment types, and valley slope through the operation of the continuity, flow resistance, bed load, bank competence and meander equations. If each of these equations could be determined accurately then their simultaneous solution would define the three-dimensional geometry of alluvial channels1,2. Although the equations cannot be specified accurately the basic mechanical principles underlying most of the relevant processes are understood. The one exception is the process responsible for plan geometry. Indeed, many theories have been presented to explain the development and maintenance of these patterns, with varying degrees of success. I show here that meander arc length may be a unique function of channel width.