Figure 5.30. Domains of meander behavior (from Hooke 1991).
Most of the mathematical models have been tested or verified in flumes, some of which had
fixed beds or constant radius of curvature segments connected to straight segments
(Odgaard and Bergs 1987). Even when model testing is done on rivers with constantly-
varying radii of curvature and mobile bed materials, problems with measurement accuracy of
the various model components often dominate the final result (Dietrich and Smith 1983).
One difficulty is the assumption that all meanders are simple, whereas as Hooke (1991)
demonstrates they are not. In addition to other controls on meander migration, the mode of
bank retreat varies from grain by grain removal to mass failure (Hasegawa 1989; Knighton
There are many authors who believe that it is combinations of processes that are important
(e.g., Hooke 1979; Thorne 1982; Lawler 1986). In view of the wide range of alluvial
materials, riverine forms and hydroclimatic environments, the limitations of mathematical
models are many and the range of validity of the models is limited. Therefore a reasonable
forecast of the future planform of the river has not yet been realized successfully and
remains a challenging topic (Thein 1994).
Mosselman (1995) states that the non-periodicity of meanders, which develop from a straight
alignment in the numerical models of Howard and Knutson (1984) and others "suggest
chaotic behavior, that is, a sensitive dependence on initial and boundary conditions." He
concludes that this "chaotic behavior bears on the predictability of river meandering."
It is only by considering the great variety of meander configurations and how they influence
future patterns that reasonable predictions of meander shift can be accomplished. Indeed,
Howard (1996) concludes that the chaotic behavior suggests that "even the most detailed
model has limited predictive power." This is perhaps because "small differences in initial
geometry or boundary conditions between two identical streams will cause different meander
patterns" (Howard 1996). In addition, he concludes that "predictability of future meander
patterns decrease with time."