5. Minimum Energy Dissipation Rate Theory and Its Applications for Water Resources Engineering

Minimum energy dissipation rate principle can be derived from minimum entropy production principle. Minimum entropy production principle is equivalent to the minimum energy dissipation rate principle. The concept of minimum energy dissipation rate principle is that, when an open system is at a steady nonequilibrium state, the energy dissipation rate is at its minimum value. The minimum value depends on the constraints applied to the system. If the system deviates from the steady nonequilibrium state, it will adjust itself to reach a steady nonequilibrium state. The energy dissipation rate will reach a minimum value again. In order to verify the fluid motion following minimum energy dissipation rate principle, re-normalisation group (RNG) k -ε turbulence model and general moving object (GMO) model of Flow-3D were applied to simulate fluid motion in a straight rectangular flume. The results show that fluid motion satisfies the minimum energy dissipation rate principle. Variations of energy dissipation rate of alluvial rivers have been verified with field data. When a river system is at a relative equilibrium state, the value of its energy dissipation rate is at minimum. The minimum value depends on the constraints applied to the river system. However, due to the dynamic nature of a river, the minimum value may vary around its average value. When a river system evolves from a relative state of equilibrium to another state, the process is very complicated. The energy dissipation rate does not necessarily decrease monotonically with respect to time. When a system is at a new relative state of equilibrium, the energy dissipation rate must be at a minimum value compatible with the constraints applied to the system. Hydraulic geometry relationships can be derived from the minimum energy dissipation rate principle. Combining the minimum energy dissipation rate principle with optimization technology as the objective function under the given constraints, the optimum design mathematical models can be developed for a diversion headwork bend structure and stable channel design.