Dynamic and variational approaches to the river regime relation

Abstract

A lemma, useful to prove the equivalence of different variational formulations of related problems, is proposed. Extremal hypotheses about regime alluvial channels are then examined and an equivalence class between them is pointed out, including the minimum stream power and the maximum transport principles. Evidence is produced of contradictions between statements derived from this class of hypotheses and well-established opinions about regime channel. The internal consistency of the theory of minimum dissipation rate is examined, and it is shown that it can't be derived from the principles of mechanics. The physical basis of extremum hypotheses about alluvial channels is analyzed, and a functional is proposed whose minimum should be equivalent to transversal equilibrium of the channel section. -Author