Physical Modelling in Fluvial Geomorphology

236 SCIENTIFIC NATURE OF GEOMORPHOLOGY
Vegetation
Although vegetation plays an important role in strengthening the banks and floodplain
(e.g. Zimmerman et al. 1967; Smith 1976), particularly in coarse-grained rivers where
inter-particle cohesion is largely unimportant, there are very few examples of physical
models that incorporate the effects of vegetation. Recent experimental work has
documented the interaction between within-channel vegetation and flow structure (e.g.
Ikeda and Kanazawa 1995; Tsujimoto 1996) but the significance and magnitude of these
effects have yet to be considered within physical scale models. Marsden (1981)
experimented with different densities of toothpicks and planted wheat, rape, cress, lawn
and budgie seed, before successfully growing mustard on the floodplain of an analogue
braided model. The results demonstrate an optimal planting density for maximum
floodplain accretion, and Marsden (1981) recommended that the approach be extended to
larger models that could incorporate scale effects.
Scaling of Time
One of the primary objectives of physical modelling is to change the rate of the formative
processes, thus permitting study of landform evolution over long prototype time periods.
Two different approaches to the modelling of time are possible, one based on dimensional
analysis and the other on magnitude-frequency analysis.
Dimensional analysis of time scales
The time scale for mean flow velocity (λt)u is given by dimensional analysis as (λt)u. =
(λ L) 0.5 . This scale differs from the previously derived time scale for sediment transport,
(λt)s, which has a scale ratio of (λ L) 1.5 (equation (17)). Similarly, the fall velocity of a
particle as characterised by Stokes' law, has a time scale of (λt)ug = (λL) -1 . Yalin (1971)
also notes a series of other time scales relevant to scale modelling of river channels
(λt)y = (λL) 2 (21)
(λt)x = (λL) 0.5
(22)
(λt)m = (λL) -1 (23)
where (λt)y is vertical erosion/accretion; (λt)x is the downstream displacement of individual
sediment grains; and (λt)m is the grain motion during saltation in either the horizontal or
vertical dimensions. Vertical bed surface change is therefore the fastest time scale
operating in the model relative to the prototype (see Figure 9.7), followed by sediment
transport rate, the displacement of sediment or fluid in the downstream direction, particle
fall velocity and the individual motion of grains during saltation:
(λt)y < (λt)s < (λt)x (λt)u < (λt)m(λt)ug
These different time scales may cause confusion when trying to interpret experimental
results. For example, there has been debate as to whether short-term fluctuations in
bedload rates should be scaled in terms of either total sediment transport rate, (λL) 1.5 , or
downstream displacement of grains, (λL) 0.5 (Ashmore 1988; Young and Davies 1991).
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