Extremal Hypotheses for River Regime: An Illusion of Progress

Abstract

The extremal hypotheses of minimum stream power, minimum unit stream power, minimum energy dissipation rate, and maximum sediment transport rate, when combined with conventional sediment transport and flow resistance equations, lead to conclusions incompatible with observations. For wide, straight, unconstrained alluvial reaches in equilibrium, these conclusions include that the Einstein sediment discharge and Shields entrainment function are nearly constant, the magnitude of the particular constants depending only on the hypothesis and equations used, whereas data from flumes and natural rivers show that both expressions are highly variable in stable channels. Constancy of the Einstein and Shields expressions provides, in fact, a sufficient but unnecessary condition for channel stability. In the maximum friction factor hypothesis there is no maximum for friction factor when channel width, depth, and slope are dependent variables. Variational principles may one day supply a solution to the problem of alluvial channel stability, but current formulations of the mentioned hypotheses require redefinition.