Energy dissipation theories and optimal channel characteristics of river networks

Abstract

The effects of energy dissipation on channel properties of a river network are explored. On the basis of a local and global hypothesis of optimality in energy expenditure, we investigate the relationships between channel hydraulic geometry, flow velocity, channel bed slope, and streamflow conditions in optimal river networks. Expressions for the rate of energy dissipation per unit channel area Pa are derived as functions of cumulative drainage area and river network parameters. Optimal channel characteristics are developed that satisfy the hypothesis of local optimality, and provide constant Pa throughout the river network. We show that these optimal channel characteristics are remarkably similar to those of many natural river systems in their downstream hydraulic geometry exponents, channel bed slope scaling, spatial distribution of average flow velocity, boundary shear, resistance to flow, etc. Optimal combinations of channel downstream hydraulic geometry and basin topography were analyzed on data from Goodwin Creek. We found ranges of optimality for the combination of the downstream hydraulic geometry exponent for width of Leopold and Maddock [1953] (0.32 < b < 0.74), and the channel bed slope scaling exponent (−0.65 < z < −0.29), and argue that river networks develop average channel properties within these ranges in order to attain constant Pa throughout the network. We propose that the hypothesis of local optimality is a central principle that explains the average behavior and adjustment of channel characteristics in natural river systems.