Potential Energy and Stream Morphology

Use of the analogy of entropy in thermodynamics reveals two basic laws which govern the formation of all stream systems. The first law is the law of average stream fall, which states that under the dynamic equilibrium condition the ratio of average fall between any two different order streams in the same river basin is unity. The second law is the law of least rate of energy expenditure, which states that during the evolution toward its equilibrium condition a natural stream chooses its course of flow in such a manner that the rate of potential energy expenditure per unit mass of water along this course is a minimum. This minimum value depends on the external constraints applied to the stream. The concavity of a river basin is shown to be the determinative factor in the formation of a stream system. On the basis of Horton's law and the law of average stream fall, longitudinal stream profiles can be calculated. The agreement between observed data and the theories found in this study is excellent.