that the discharge calculated for those measurements was less than could be tolerated by the
depth at that location. Points just beneath the dashed line might be locations where the
present bottom was eroded by discharges slightly greater than those measured during the field
exercises. Many of the data points well below the line came from inlet cross-sections either
slightly seaward of the jetties where depths are controlled by waves and longshore currents; or
landward of the entrance channel where the tidal current is insufficient to scour the channel,
and depths have been increased by dredging.
Another explanation for data scatter below the dashed line is that depths at some of
the locations are scoured by a different cross-channel flow distribution that occurs during the
reverse maximum tidal flow. Finally, there is the possibility that some of the depths are the
result of scouring that occurred during episodic events such as storm surges or river discharge
combined with ebb flow. Regardless of the reason, depths associated with data points below
the dashed line are not in equilibrium with the measured discharge. In other words these
depths would be able to accommodate increased flow discharge without additional scouring of
the bottom.
The dashed line in Figure 7 corresponds to Ce = 5.12 in Eqn. 8, which can now be
expressed as an empirical equation for equilibrium maximum discharge per unit width, i.e.,
1/2
de3/8 h9/8
qe = 5.12 [g (Ss - 1)]
(10)
For a given noncohesive sediment there is an equilibrium scour depth, he, associated with
8/9
0.234 qe
he =
(11)
1/3
4/9
[g(Ss - 1)]
de
Although it might be possible to have depths greater than the equilibrium scour depth, these
depths would have to be caused by some process other than the maximum discharge at that
location. Estimates of equilibrium scour depth from Eqn. 11 should be considered conservative
because the estimates represent the outer envelope of the field data. In reality the maximum
discharge per unit width may not persist long enough to allow scoured depths to reach the
predicted equilibrium depth.
Finally, substitution of the value of Ce into Eqn. 7 and rearranging provides a relationship
for mean velocity at a location in terms of the equilibrium depth and sand parameters, i.e.,
1/2
de3/8 h1/8
V = 5.12 [g (Ss - 1)]
(12)
e
18
Hughes/Schwichtenberg
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