Theoretical derivation of hydraulic geometry equations for a gravel bed river channel*

The geomorphic relations of hydraulic geometry at-a-station and downstream, expressed as power laws, are derived for a straight, single thread, gravel river channel. The cross-section has a plane central bed, narrow or wide, flanked by curved sides or banks. The analysis employs mechanistic formulae for fixed and mobile bed flow resistance, downchannel bedslope, bedload transport and the novel introduction of bedload ratings all expressed as power laws. Steady uniform flow and equilibrium bedload transport conditions are assumed to occur above the central section. Water discharge and sediment size are assumed to be the only known variables. Exponents of the relations of hydraulic geometry are fixed and are consistent with reported theoretical estimates and field measurements. Coefficients are also explicitly derived and are consistent with field measurements and vary owing to the presence of independent variables in their definition. Here aspect ratio has the major influence. The derived equations can provide coarse estimates for the design of canal and river control works. Conditional separate relations between both width and depth, and bed material size or bed slope are also determined for the occurrence of at-many-stations hydraulic geometry. To improve generality, future work should consider the hydraulic geometry of straight gravel channels with bedload transport, but having an irregular cross-section.

Automated summary

This study analyzes the hydraulic geometry of a straight gravel river channel and derives power law equations to express the relationships. The study finds that the exponents of the hydraulic geometry relations are fixed, while the coefficients vary due to the presence of independent variables. These equations can be used for the design of canal and river control works and the study also identifies the influence of other factors on hydraulic geometry.