Excess energy theory for river curvature and meandering

Abstract

It is shown that the imbalance between the valley slope and the regime channel slope is the primary cause of river meandering when the sediment load is less than the load transporting capacity and if bank erodibility permits. When a river reach is confronted by a steep valley-slope it tries to maintain uniformity in energy-expenditure by expending the excess energy through channel curvature. Novel equations are analytically developed for the channel radius of curvature, sinuosity, wave length, arc length, initial arc angle, the meander path and a modified sine-generated curve based on width, depth, flow, sediment load, and roughness. These equations are more general than geometrical correlations between meander variables and width that were previously proposed in the literature. The developed channel sinuosity and wave length equations compare well with the available field data. Meandering in both alluvial and tidal channels, as well as in sediment-less environments (supraglacial channels) could be explained by the theory.