Extremal hypotheses for river behavior

Abstract

The hypotheses of minimum energy dissipation, minimum stream power, and minimum unit stream power are summarized and compared. Their derivation from analogies with laminar flow and linear thermodynamics is criticized on the grounds that these situations differ fundamentally from river flows, which are usually highly turbulent and strongly nonlinear. The authors' empirical hypothesis of maximum friction factor seems preferable to the minimization hypotheses because it is compatible with the known behavior of turbulent flows and nonlinear processes, it is applicable with a wider range of independent variables, and it is more in keeping with trends shown by experimental data under all constraints. The minimization hypotheses seem likely to give incorrect predictions when flow rate and depth are independent variables. The empirical success of the minimization hypotheses is confined to situations in which they predict similar behavior to the maximum friction factor hypothesis; they may be considered as special cases of this more general hypothesis.