WSP11681

• File Number: 8220.101.17
• Description: Glen Canyon Dam/Lake Powell
• State: AZ
• Basin: Colorado Mainstem
• Date: 4/1/1995
• Title: Measured and Predicted Velocity and Longitudinal Dispersion at Steady and Unsteady Flow / Colorado River / Glen Canyon Dam to Lake Mead
• Water Supply Pro - Doc Type: Report/Study

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Measured and Predicted Velocity and Longitudinal Dispersion at Steady and Unsteady Flow,
Colorado River, Glen Canyon Dam. to Lake Mead

better than coefficients computed by the method of
moments. The longitudinal-di8persion coefficient is
computed from model results using the relation Dr =
DI(u2dt), where Dr is the dimensionless dispersion
factor (a model-calibration parameter), D is the longi-
tudinal dispersion coefficient in length squared per
time, u is mean flow velocity, and dt is the model time
step. Jobson (1987) showed that the accuracy of the
numerical solution to the convective-dispersion equa-
tion in the Lagrangian reference frame depends on
the value of Dr and therefore on the model time step.
For Dr greater than about 0.1, the error in computed
dispersion coefficient is less than 3 percent, but the
error increases sharply for values of Dr less than
about 0.1 (Jobson, 1987, Figure 2). The error is caused
by underestimation of the concentration gradients by
the model when Dr is small and fluid parcels tracked
by the model are large (Jobson, 1987). For the 0.25-
hour time step used for model calibration, Dr of less
than 0.1 was computed for subreaches 4 and 6
(Table 4), and the model dispersion coefficients for
those subreaches may have errors of 5-10 percent
from this source.

Model Application

Time-concentration curves at dye sample sites in
the Grand Canyon reach were estimated with the
calibrated solute-transport model for three steady and
two unsteady releases. The steady releases were 226
m3/s, 425 m3/s, and 850 m3/s. The unsteady releases
were two daily release patterns selected for evalua-
tion as a part of the EIS process - the EIS low-
fluctuating and high-fluctuating flow alternatives

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(Figure 10, T. J. Randle, Bureau of Rec1amation. writ-
ten communication, 1991). Discharge was simulated
for the EIS alternatives at 0.25-hour increments for a
seven-day period in July using a daily mean discharge
of 425 m3/s with a computer program that fits a sine
function within the seasonal minimum and maximum
discharges specified by the EIS team for that alterna-
tive (J. P. Bennett, U.S. Geological Survey, written
communication, 1992). Releases selected for modeling
provide a comparison of steady releases, releases with
low fluctuations, and releases with high fluctuations
for the same daily mean discharge.
Results of computations with the solute-transport
model indicate that velocity increases linearly with
discharge for steady releases. Although measured
velocity increased with discharge in the Glen Canyon
reach, dispersion was much greater at the lowest
measured flow than at the highest two flows mea-
sured (Figure 3). The difference between the observa-
tions in the Glen Canyon reach and the model
predictions for the Grand Canyon reach may be
caused by the inability of the model, calibrated at
425 m3/s, to account for changes in the effective geom-
etry at lower flows.
The model predicts that velocity in individual sub-
reaches will be higher or lower for unsteady flows
than for steady flows, depending on the timing ofthe
passage of the trough and peak of the discharge wave
(Figures 2 and 11). Averaged over the entire Grand
Canyon reach, the model predicts that velocity is
about the same for steady and unsteady releases as
was found from the measurements for unsteady and
steady releases. The degree of unsteadiness has a sys-
tematic effect on unit-peak concentration - the high-
fluctuating flow alternative produces the lowest
unit-peak concentration at each sampling site and

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TABLE 4, Average Velocity and Longitudinal-Dispersion Coefficients at Steady Releases
of 425 Cubic Meters Per Second, Grand Canyon Reach,

[Subreach 2 _ Lees Ferry to Nautiloid Canyon; 3 - Nautiloid to gage above the Little Colorado River; 4 - Little Colorado gage to
Nevill's Rapid; 5-Nevill's Rapid to Mile 118 Camp; 6 -Mile 118 Camp to National Canyon; 7 -National Canyon to
Pumpkin Springs; 8 - Pumpkin Springs to Gneiss Canyon. Average velocity was computed as velocity
of the peak concentration orthe model predicted time-concentration curve.]

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Subreaeh

Len&th
(kilometers)

Averare Velocity
(meters per lleeond)

2
3
4
5
6
7
8

57.7
40.6
24.9
66.1
78.6
75.7
36.9

0.91
.79
1.0
.98
1.1
1.1
1.0

Dispersion
Factor
(Dr>

Longitudinal DiaperBion
Coefficient
(square meterB per Becond)
Method of
Model Moment.

0.20
.30
.06
.18
.09
.20
.15

164
213
55.1
159
87.5
194
139

109
181
lOB
68.1
102
202
243

WATER RESOURCES BULLETIN

277