Environmental Engineering Reference
In-Depth Information
arrows, if they are not in opposite directions, may connect to form a first order stream. Two first-order
streams meet at the confluence and form a second-order stream, and so on. There are two fifth order
rivers flowing from west to east, as shown in Fig. 1.8. There are a few close circles with arrows rotating
anticlockwise or clockwise, which are interpreted as riparian lakes.
Fig. 1.8 Homework of a student with the random walk model
Despite all these efforts at simulation, Howard (1971) commented that "the random growth models
simulate many of the characteristics of natural stream systems, but it remains uncertain to what extent
inferences may be drawn about the processes responsible for natural stream systems." He also suggested
that although natural stream systems appear to exhibit numerical relations nearly identical to those of
topologically random channel networks, the relevant geomorphic processes are deterministic and the
apparent randomness arises from independent variation of a large number of factors, such as microclimate
and lithology (Abrahams, 1984). It has also been demonstrated that networks developed by strict rules of
growth are similar to those generated by random processes, which caused Stevens (1974) to conclude that
"randomness can appear regular and regularity random."
Minimum stream power theory —Yang (1971) proposed the minimum stream power theory, which is
very useful for river researchers. From thermodynamics, the entropy ĭ is defined as
d E
T
) ³
(1.5)
where E = total thermal energy per unit mass; and T = absolute temperature used to measure thermal
energy. The entropy concept and thermal dynamic laws can be applied to a non-thermal system if the energy
in that system can be measured by a positive parameter. Yang (1971) considered potential energy the only
useful energy available to a river system, and elevation can be used to measure the potential energy in a
river system. When a unit mass or weight of water flows downstream, it releases its potential energy,
converts it into kinetic energy, and then uses it for erosion and sediment transport. Yang defined the entropy
of a river system as
d
H
Z
(1.6)
< ³
m
where H = total potential energy per unit weight of water; and Z m = elevation measured from mean sea
level for an m -th order system. Similar to the absolute temperature T in a thermal system, Z m is a positive
parameter which can be used to measure potential energy per unit weight of water in a river system.
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