Theory Of Non-Equilibrium Thermodynamics And Its Application For Field Of River Dynamics

The two basic theories of non-equilibrium thermodynamics, the minimum entropy production and the dissipative structure, are introduced. It will be shown that, by using the relationship between the entropy production and the rate of energy dissipation, the minimum entropy production is equivalent to the minimum rate of energy dissipation. The theory of minimum rate of energy dissipation and the dissipative structure can be extended to the field of river dynamics. The main aspects of work by using the two basic theories in this paper have been studied as follows:(1) Some errors of the minimum rate of energy dissipation proposed by Yang C.T. and others are found, and the expression of minimum rate of energy dissipation of flow is re-derived based on the theory of minimum entropy production.(2) It will be pointed out that the entropy is different from the entropy production in a river system. The dynamic adjustment of an alluvial river has a tendency that the entropy production or the rate of energy dissipation of flow is minimum rather than the entropy is maximum when a river is in a relative equilibrium condition. The theory of minimum entropy production or minimum rate of energy dissipation shows that a river is stable when it is in a relative equilibrium condition.(3) The river facies formulas of alluvial river have been developed using the theory of minimum rate of energy dissipation together with flow continuity and motion equations, suspended load transport or bed load transport equation.(4) The causes of the river patterns are explained using the theory of minimum rate of energy dissipation. The different patterns of nature rivers are result of internal cause and external causes. Internal cause is all rivers have a tendency to adjust pattern so that the rate of energy dissipation of flow is minimum. External causes are all outside conditions to restrict flow.(5) The theory of dissipative structure is used to explain the change of the river patterns. This change is a break when the outside conditions exceed a threshold value with gradually variety. The break is equal to the non-equilibrium phase transition in thermodynamics.(6) There are two kinds of stable channels. The one is regime channel; the other is equilibrium of eroding and silting channel. Different designs are available for them. The optimum design mathematical models of both kind channels are developed in accordance with the theory of minimum rate of energy dissipation. The rate of energy dissipation of flow is used as the objective function, and the condition of both non-eroding and non-silting, or the condition of equilibrium of eroding and silting is the constraint. The bottom width, flow depth, slop, and flow velocity of the stable channels are given by this calculation.(7) An optimum design method for the artificial bend channel in diversion headwork of bend type by the theory of minimum rate of energy dissipation. The rate of energy dissipation of flow is used as the objective function, to make a set of decision variables, which minimize the objective function under the restrictions related to bend channel. The calculation results are given for the bottom width, curvature radius, channel length, slope, flow depth, and flow velocity of the bendchannel.(8) A lot of practical experiences have proved that upstream channel of sedimentation can be restored to natural river channel only when the bed-forming discharge is released by the outlet sluice, the backwater caused by the project does not occur, so natural flow is kept. Therefore, the flow depth and flow velocity before the sluice are calculated by the river facies formula, then using the weir formula to gain the outlet sluice width.