Journal of Environmental Hydrology

ISSN 1058-3912

Electronic journal of the International Association for Environmental Hydrology 

On the World Wide Web at
JEH Volume 10 (2002), Paper 5, August 2002                   Posted August 6, 2002 

Youssef I. Hafez
Nile Research Institute, Water Research Center, Delta Barrage, El Kanater, Greater Cairo, Egypt

The hydraulic exponents which appear in the regime theory equations are predicted using different methods such as an empirical function, extremal energy slope, or extremal stream power. These hydraulic exponents represent the dynamic adjustments or response of river channels to changes in their regime. Based on experimental and theoretical data from examples of channel adjustments, an empirical function is developed which, when varied, yields the hydraulic exponents. Extremal energy slope in the form of minimum or constant energy slope, and extremal stream power in the form of minimum or constant stream power, are both derived by setting the variation of their corresponding function to zero, which results in a relation between the hydraulic exponents. Four examples for which data exist regarding the values of the hydraulic exponents are used to validate the empirical function and extremal methods. The first example is the channel response to changes in flow over a sand bed between rigid walls at constant slope. This example resembles river reaches where the banks are firm (either stiff clay or protected by riprap) or at gauging station cross-sections having relatively stable banks. In this case the flow has one degree of freedom to adjust by changing its roughness. Parallel to this case is the case in which the channel cross section, at constant slope, has a constrained width in the form of a relation between the width and depth, which accounts implicitly for the degree of bank resistance. The third example having two degrees of freedom is the response of the river cross section to change in discharge at constant slope by adjusting its width and depth. This resembles river sections where the banks are loose and free to move. The fourth example having three degrees of freedom is when the channel adjusts its slope (longitudinal profile), depth and width to accommodate for the downstream increase in discharge. This case resembles rivers in humid regions where flow increases in the downstream direction due to incoming tributary flows. The hydraulic exponents in each case are presented and compared to theoretical and field values along with discussion of the inherited mechanisms.
Reference: Hafez, Y.I.; On the Dynamic Adjustments of Stream Channels, Journal of Environmental Hydrology, Vol. 10, Paper 5, August 2002.

Youssef I. Hafez
The Nile Research Institute, National Water Research Center
El_Kanater, Delta Barrage,
Cairo 13261


Return to HydroWeb Homepage