#
Journal of Environmental Hydrology

**ISSN 1058-3912**
*Electronic journal of the International Association
for Environmental Hydrology
*

**On the World Wide Web at http://www.hydroweb.com
**

JEH Volume 10 (2002), Paper 5, August 2002
Posted August 6, 2002

ON THE DYNAMIC ADJUSTMENTS OF STREAM CHANNELS
*Youssef I. Hafez*

*Nile Research Institute, Water Research Center, Delta Barrage, El
Kanater, Greater Cairo, Egypt
*

**ABSTRACT**

*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.

**CONTACT:**

*Youssef I. Hafez*

*The Nile Research Institute, National Water Research Center*

*El_Kanater, Delta Barrage,*

*Cairo 13261*

*Egypt*
**E-mail: youssef_hafez@usa.net**

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