Figure 1
.
Channel Meandering:
River meanders form one of the most beautiful patterns in nature. Who has not flown over a meandering river and not wondered why rivers do that? The geometry of meanders is illustrated in Figure 1.
Figure 1
Meandering is an instability in which bends of a certain size grow because flow is directed toward the bend by the point bar and subsequently erodes faster on the outer bank than on the inner bank. It is actually not certain whether this topographic steering mechanism is the underlying cause for meandering since there are other characteristics of the flow that concentrate shear stress at the outer bank. However, the instability is related to greater outer bank erosion as the bend develops (for bends of a certain size) (Figure 2).
Figure 2
Point bars and scroll bars are easily seen on the images
of Figures 3-5. Figure 5, a map of scroll bars of the Mississippi River,
clearly illustrates how meanders may translate downstream much faster than
they outward.
Figure 3
Figure 4
Figure 5
If valley downcutting is much faster than bank migration, entrenched meanders develop such as those in the Goosenecks of the Colorado Plateau (Figure 6).
Figure 6
The evolution of channel cross-sections is illustrated in Figure 7. The stable cross-section has most of its steepness on the outer bank with a very gentle decline on the inner bank. As the outer bank recedes material is deposited on the point bar of the inner bank resulting in an outward translation of the cross-sectional form.
Figure 7
Meanders develop both by bank migration normal to the
tangent of the bank and by downstream translation of the loop resulting
from an increase in flow velocity in straight segments flowing in the
direction
of the regional slope aspect. Maps of channel changes such as those of
the Powder River in Wyoming (Figure 8) can help in understanding the
meandering
process.
Figure 8
One of the most remarkable aspects of meandering is that
there is a simple proportionality between meander wavelength and channel
width: l=aw where l is the wavelength, w is the width, and a, the constant
of proportionality, is between 7 and 10. The wavelength is defined as the
straight-line distance between two inflection points. Figure 9 plots
meander
wavelength versus discharge over a very wide range of scales. What is even
more remarkable is that the relationship between wavelength and width for
lava channels on Venus (Figure 10) and the moon (Figure 11) lie on the
same line as terrestrial rivers. Even meanders in Gulf Stream currents
(Figure 12) follow the same relationship! This suggests that there may
be a fairly simple geometric argument that explains the relationship
between
meander wavelength and width.
Figure 9
Figure 10
Figure 11
Figure 12
.
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