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Energy dissipation theories and optimal channel characteristics of river networks
Author(s) -
Molnár Peter,
Ramírez Jorge A.
Publication year - 1998
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/98wr00983
Subject(s) - channel (broadcasting) , dissipation , scaling , geometry , hydrology (agriculture) , streamflow , open channel flow , exponent , energy–depth relationship in a rectangular channel , flow (mathematics) , geology , mathematics , drainage basin , geotechnical engineering , physics , geography , computer science , chézy formula , computer network , linguistics , cartography , philosophy , thermodynamics
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 P a 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 P a 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 P a 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.