5.8.5 Advances in Predicting Meander Migration
Meander Behavior. According to Hooke (1991), it has long been assumed that, after initial
development, meanders tend towards an equilibrium of form, given stability of external
conditions. These ideas were based on early experiments in flumes (Friedkin 1945) and on
the analysis of process-form relations in the 1960s in which statistical relationships were
established, e.g., between meander wavelengths and discharge (Carlston 1965). Much
evidence has now been accumulated that many meanders exhibit no such equilibrium
(Carson and Lapointe 1983, Hooke 1984).
If the behavior of individual bends on active rivers is examined (using for example, historical
evidence or meander scrolls) then a continuous evolution with an increasing complexity of
pattern is frequently found. Meanders may migrate at first, but then they begin to grow in
amplitude, then to become compound in form. Based on analysis of historical sequences of
meander change on rivers using maps and aerial photographs, models of meander
development have been produced (Hooke 1991; Harvey 1989; Keller 1972).
These show a sequence from low sinuosity bends to bends of symmetrical form which tend
to migrate; then bends enter a phase of rapid growth with maximum erosion at the apex
leading to extension in the cross-valley direction. Beyond a certain increase in path length
(Hooke and Harvey 1983) the bends start to become compound in form by development of
lobes on one or both parts of the apex. These lobes may go on to develop into separate
bends if there is space. This increasing asymmetry and complexity is similar to other models
such as those of Brice (1974) and Hickin and Nanson (1975).
This process of growth cannot, of course, go on indefinitely. Eventually the bends are likely
to intersect or spatial limits of the floodplain are reached so that cut-offs take place.
Therefore, following a phase of growth, cutoffs are likely. Rivers show an early phase of
increasing sinuosity then oscillating sinuosity thereafter.
Of course, not all bends exhibit complexity or rapid growth. Some simply progressively
migrate or tend to stabilize at various stages. This could be for a number of reasons, e.g.,
slope and overall energy in the system, floodplain form, or it could simply be that changes
are progressing at a very slow rate. Different domains of meander behavior can therefore
be visualized (Figure 5.30). Theoretically, it should be possible to identify domains of
behavior with thresholds between them. The thresholds will vary with the actual river and
may be rather 'fuzzy.' Further work is needed to substantiate whether they do indeed exist,
but the indication is that any single mathematical model of meander behavior will be
inadequate. This is supported by problems with existing models.
The mathematical modeling of helical and cross channel flows and their related channel
characteristics has proved to be difficult. Most such models are based on simplifications of
the equations of continuity for water and sediment and on the Reynold's (or St. Venant's)
equations of motion (Engelund 1974; Smith and McLean 1984; Odgaard 1986). As noted by
several researchers (Odgaard and Bergs 1987; Yen and Ho 1990), most of these models
simulate bend flow and channel topography only in the "fully developed" portions of the
bend, i.e., where velocity and thalweg depth do not vary longitudinally. Other models predict
these characteristics throughout the bend, even when velocity and depth change
downstream (Dietrich and Smith 1983; Engelund 1974; Odgaard 1986; Yen and Ho 1990).
In addition, considerable disagreement exists over the simplifications and eliminations that
have been used to solve these equations (Dietrich and Smith 1983).
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