River planform modelling requires physics-based bar formation
F. Schuurman1,2, M.G. Kleinhans1
1
Dept. of Geography, Fac. of Geosciences, Utrecht University, Utrecht, The Netherlands. [email protected]
2
Royal HaskoningDHV, Amersfoort, The Netherlands.
1. Introduction
River planform is the result of a complicated interaction
between flowing water, within-channel river bed,
channel banks and in many cases vegetation. The river
pattern classification is based on the river planform, as
the river pattern is defined by the number of parallel
channels. This way, a clear distinction can be made
between single-threaded rivers, often meandering, and
multi-threaded braided rivers. No general agreement
exists about the necessary conditions for either of the
two river patterns.
There are at least two different points of view to observe
a river planform and its dynamics: 1) by focussing on
the channels; and 2) by focussing on the bars. As shown
by linear analyses, bars develop first due to bed
instability, after which channelization and bar build-up
further amplify the distinction between channels and
bars. Meandering may emerge if channel splitting
processes are counteracted or inhibited. This has been
confirmed by flume experiments (Van Dijk et al., 2011)
and physics-based numerical modelling (Schuurman &
Kleinhans, 2011). In contrast, many reduced complexity
models focus on the channels or, to be more specific, on
the spatial distribution of discharge (e.g. Murray &
Paola, 1994).
As realistic bar morphodynamics is an essential requisite
for modelling realistic river planforms, we will show
that explicit physics-based modelling of flow, sediment
transport and morphodynamics is essential to elucidate
the necessary conditions for meandering and braiding.
2. Reduced complexity models
Reduced complexity river models (e.g. Murray & Paola,
1994) are based on the spatial distribution of channels
through a wide, confined ‘floodplain’. Discharge
distribution is steered by topography, whereas sediment
transport depends on discharge. Discharge is forced to
flow downstream by rule, even if that means uphill-flow
over an obstacle. Back-water effect, flow momentum
and channel curvature are neglected, so that grid sizeindependent processes such as helical flow development
in a bend or flow diverging around a downstream bar
lack from these models.
Although reduced complexity models can produce
patterns which, based on discharge, look realistic at
specific timesteps (Fig. 1a), the lack of physics can, and
often does, result in a bed topography far from natural,
with unnatural bar shapes and spatial discharge
distributions (Fig. 1c). Some reduced complexity models
are only able to produce a braided channel pattern when
a specific spatial lag between sediment transport
capacity and sediment transport rate is imposed, but this
imposes bar length as a rule rather than a model result
(Fig. 1b). Too large or too small spatial lag results in
different channel patterns.
a)
b)
c)
Figure 1: Braided rivers produced by reduced
complexity models: Timeseries of spatial Q-distribution
(a, Nicholas, 2007); Dependence on spatial lag (b, Davy
& Lague, 2009); Q-distribution and bed topography
(red: high, blue: low) (c, Murray & Paola, 1994).
3. Physics-based reductionist models
In contrast to reduced complexity models, physics-based
models, or “explicit numerical reductionism” (Murray,
2007), have a physics-based solver for the flow field,
including flow momentum, and validated predictors for
sediment transport rate and the (transverse) bed slope
effect essential for morphology. In fact, the aim is to
include all physical processes known to be relevant for
detailed channel and bar formation, whilst the number of
sub-grid processes, often implemented as empirical
relations, is minimized.
Physics-based models are nowadays capable of
reproducing river planforms, including detailed bar
morphology, on the reach scale. Furthermore, both selfformed single-threaded and multi-threaded rivers can be
produced in the same model (Fig. 2a, b). Also, the
initiation of a braided bar pattern by high-mode linguoid
bars (Fig. 3) corresponds well with flume experiments
with a wide initial channel.
Figure 2: Channel patterns produced in Delft3D (a, b)
and c) in Nays2D.
The processes of floodplain formation and bank erosion,
both essential for meandering (Van Dijk et al., 2011),
require additional physics and numerical solutions
which are still under development. Jang & Shimizu
(2010) made significant progress in combining a fully
2D morphodynamic model, a bank erosion model and a
floodplain-formation model (Fig. 2c).
Figure 5: Comparison between bar shapes from Delft3D
and empirical relations (Kelly, 2006) for different D50.
4. Conclusions
Although self-formed channel patterns can be formed in
a wide range of numerical models, only physics-based
models are yet capable of producing both meandering
and braiding rivers based on boundary conditions. The
examples given here showed that limited level of
reductionism results in more realistic channel patterns
and within-channel bar morphology, even with simple
initial and boundary conditions.
The advantage of short computational time for reduced
complexity models is becoming less important, whereas
reliable quantitative predictions of bed morphodynamics
are increasingly important. Therefore, focus of future
research should be to improve physics-based models by
embedding robust solutions for physics-based processes,
instead of using reduced complexity models that can
only provide very rough, qualitative predictions.
Figure 3: Development and evolution of a braided river,
modelled in Delft3D.
An example of bar dynamics modelled in the physicsbased model Delft3D is given in Fig. 4, which shows a
mid-channel bar in a sand-bed river. The flow at the
upstream bifurcation erodes the upstream side of the bar,
while deposition occurs at the downstream side on tailbars. This pattern corresponds qualitatively with the
conceptual models of e.g. Best (2006). Moreover, the
bar dimensions also correspond well with empirical
data, showing that the modelled bars have realistic
shapes (Fig. 5).
Figure 4: Short-term dynamics of mid-channel bar in a
sand-bed braided river: a-c) Timeseries of modelled bed
topography; d) Modelled bar edges (blue: old, red:
young); e) Conceptual model by Best (2006).
Acknowledgments
MGK and FS are supported by the Netherlands
Organization for Scientific Research (NWO) (grant
ALW-Vidi-864-08-007 to MGK).
References
Best, J. L., Woodward, J., Ashworth, J. P., Sambrook
Smith, G. H., and Simpson, C. J. (2006) Bar-top
hollows: A new element in the architecture of sandy
braided rivers, Sedim. Geology, 190(1-4), 241–255.
Davy, P., and Lague, D. (2009) Fluvial
erosion/transport equation of landscape evolution
models revisited, J. Geophys. Res., 114, F03007.
Jang, C. L., and Y. Shimizu (2005) Numerical
simulation of relatively wide, shallow channels with
erodible banks, J. Hydraul. Eng., 131(7), 565–575.
Kelly, S. (2006) Scaling and hierarchy in braided rivers
and their deposits: examples and implications for
reservoir modeling. In: Braided Rivers: Process,
Deposition, Ecology and Management, Blackwell,
Oxford, UK.
Murray, A. B., and Paola, D. (1997) Properties of a
cellular braided-stream model. Earth Surf. Processes
Landforms, 22(11), 1001–1025.
Nicholas, A. P., and Quine, T. A. (2007) Crossing the
divide: Represenation of channels and processes in
reduced-complexity river models at reach and
landscape scales. Geomorphology, 90, 318-339.
Schuurman, F., and M. Kleinhans (2011) Self-formed
braided bar pattern in a numerical model. In: Proc.
7th IAHR Meeting RCEM, Beijing, China.
Van Dijk, W. M., Lageweg, W. I., Kleinhans, M. G.
(2011) Experimental meandering river with chute
cutoffs. J. Geophys. Res., 117, F03023.