The instability of hydraulic geometry

Abstract

At‐a‐station hydraulic geometry of stream channels has been explained with varying degrees of success by several different theoretical approaches. Regardless, observed variability in hydraulic geometry relations and theoretical shortcomings in existing approaches both indicate that a satisfactory generally applicable model is lacking. The problem is approached by a qualitative asymptotic stability analysis of an equation system based on the Darcy‐Weisbach flow resistance equation. No unique quantitative solution exists for the general case, but results show that the system is unstable. A change or perturbation in one or more system components (hydraulic radius, velocity, slope, resistance) will result in a new equilibrium condition, rather than restoration of the pre‐disturbance condition. Even small changes in the channel are likely to result in new combinations of the flow variables. It is thus not surprising that at‐a‐station hydraulic geometry is quite variable, and that a satisfactory generally‐applicable model has not been found.