Theory of Minimum Rate of Energy Dissipation

by Chih Ted Yang, (M.ASCE), Civ. Engr.; U.S. Bureau of Reclamation, Engrg. Research Center, Denver Federal Center, Denver, Colo.,
Charles C.S. Song, (M.ASCE), Assoc. Prof. of Civ. Engrg.; Univ. of Minnesota, Minneapolis, Minn.,

Serial Information: Journal of the Hydraulics Division, 1979, Vol. 105, Issue 7, Pg. 769-784

Document Type: Journal Paper


A general theory of minimum rate of energy dissipation for a class of open channel flows with or without the movement of sediment is proposed in this paper. This theory states that the rate of energy dissipation is a minimum under steady equilibrium or gradually varied flow conditions. The theory is derived from the Navier-Stoke's equations of motion for gradually varied open channel flow without sediment transport. It applies to turbulent and laminar flows as long as the inertia forces due to the time-averaged velocity distribution is small compared with the forces due to gravity and shear. The theory in different degrees of generality can be used to explain the fluvial processes from the movement of sediment to the change of velocity, slope, roughness, channel geometry, pattern, and profile of a river under an eqiulibrium condition or during the process of self-adjustment to reach an equilibrium condition.

Subject Headings: Sediment transport | Open channel flow | Energy dissipation | Equilibrium | Gradually varied flow | Navier-Stokes equations | Equations of motion | Turbulent flow

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