Modeling Vegetated Channel Flows: Challenges & Opportunities
T. STOESSER, V. NEARY, C.A.M.E. WILSON



Institute for Hydromechanics
Karlsruhe University
76128 Karlsruhe
GERMANY
Dept. of Civil & Envir. Engrg., Tennessee Tech, PO Box 5015, Cookeville, TN 38505
Hydroenvironmental Research Centre, Cardiff University, PO Box 925, Newport Road, Cardiff, UK CF24 0YF
Abstract: - Research on vegetative resistance in open channel flows has been motivated by the need to develop better
methods for evaluating flow and transport processes through vegetated channels, floodplains, and wetlands.
Fundamental to this problem is the need to quantify the additional flow resistance caused by the presence of vegetation.
Once this is achieved the hydrodynamic processes that are responsible for sedimentation and transport processes also
need to be assessed. Past research includes a number of field and laboratory investigations that have related vegetative
resistance parameters, such as drag coefficients and Manning’s n values, to plant properties, including height, density,
and flexibility. This information has led to the development of semi-empirical formulas for calculating bulk flow
parameters and velocity profiles. Computational fluid dynamics (CFD) models have been developed that solve the
Reynolds averaged Navier-Stokes (RANS) equations using two-equation isotropic turbulence models. This paper
summarizes the more recent attempts at modeling vegetated channel flows, the main challenges in modeling vegetation
effects, and the opportunities for future model development.
Key Words: - CFD, Flow Resistance, Vegetation, RANS, LES, Turbulence
1 Introduction
Both aquatic and riparian vegetation have become
central to river and coastal restoration schemes, the
creation of flood retention space and coastal protection
projects. Aquatic and riparian plants obstruct the flow
and reduce the mean flow velocities relative to nonvegetated regions and the additional drag exerted by
plants strongly influence the transport processes and
system morphology. Until recently, 1D models have
been applied and are typically calibrated by adjusting a
bulk energy loss coefficient (e.g. Mannings n or Chezy’s
C) to achieve an acceptable match between sparse
observed data and model predictions. Yet, as the
possible range of friction parameters for any given
environment is wide, and the appropriate distributions
are model- and grid-dependent, the hydrodynamic and
geomorphologic impact of vegetation is largely
uncharacterised in these approaches.
As a consequence we should explore both conceptuallyand physically-based representations of vegetation-flow
interactions and aim to reduce calibration uncertainty
rather than add further intangible parameters to our
modelling framework. The development of such CFD
codes will potentially have enormous consequences for
environmental modellers, not least as it will remove or
reduce the ability to subsume under-represented
processes and data uncertainties within the calibration
process. A 3D CFD code with a physically based
vegetation roughness closure implementation may be
most appropriate in applications where there are
considerable velocity gradients (both laterally and
vertically) and strong secondary currents, flow
characteristics that are especially present in flows
through partially-vegetated channels or submerged
vegetation. However, an emergent homogenous plant
canopy may require a simpler vegetation model than a
submerged heterogeneous plant canopy where there may
be considerable variation in velocity over the flow depth
resulting in shear layer formation between the canopy
and surface-flow regions. As scientists and engineers we
ultimately need to examine and explore many ways to
explain and describe flow through natural vegetation and
evaluate a suitable level of representation necessary in
order to deliver accurate predictions.
In this paper we present recent multi-dimensional
approaches for the numerical representation of flow over
and through vegetation and we summarize the main
problems and challenges in modeling vegetation effects,
as well as the opportunities for future model
development. We furthermore introduce a physicallybased numerical concept for the representation of
vegetation within a 3D finite-volume model framework
and present examples from validation studies and the
upscaling of such a model to the field environment.
2 3-D Modeling Strategies
Numerical modeling of vegetation effects in an on open
channel flow can follow several approaches, where each
approach allows a specific range of flow features to be
simulated. These Computational Fluid Dynamics (CFD)
models have been developed to solve the 3D steady or
unsteady
Reynolds-averaged-Navier-Stokes
(RANS/URANS) equations, which resolve local flow
and turbulence features of the temporally averaged
turbulent flow field. Recently, Large Eddy Simulation
(LES) CFD models have been developed to solve the
unsteady, filtered 3D Navier-Stokes equations. These
models can provide a complete description of the
instantaneous unsteady 3D turbulent flow field,
capturing organized large-scale unsteadiness and
asymmetries (coherent structures) resulting from flow
instabilities. The characterization of the flow resistance
of vegetation is a topic that will continue to command
the attention of both researchers and practitioners alike.
In the following we will give a brief overview of this
subject.
2.1 Characterization of flow resistance of vegetation
For flow through vegetation, where the ratio of plant
height K to flow depth d is greater than 0.5, resistance is
generally due more to form drag of the vegetation than
from bed shear. Emergent vegetation can also induce
wave resistance from free surface distortion. Plant
properties that affect form drag include the degree of
relative submergence (K/d), plant density, spatial
distribution, and flexibility.
Further complicating
matters involve unsteady non-uniform flow conditions
which often prevail, wake interference effects that can
reduce drag and the various different riparian plant
species are typically found in combination, which causes
the spatial distribution of plant properties to vary greatly.
While it is important to consider the various
complexities of flow resistance encountered in fluvial
channels, most of our current knowledge on vegetative
flow resistance is derived from laboratory flume
experiments of steady fully developed flow through
simulated vegetation of uniform density within rigid
boundary rectangular flumes. These investigations have
related vegetative resistance parameters, such as drag
coefficients, Manning’s n values, and friction factors f,
to plant properties, including height, density, and
flexibility (e.g. Kouwen and Unny, 1973; Nepf, 1999;
Kouwen and Fathi-Moghadam, 2000; Wu et al., 2000;
Stone and Shen, 2002; Wilson et al., 2003). However,
the inclusion of Mannings n friction factors in a 3D
model may be enough to ensure accurate predictions of
water levels, the hydrodynamics of the flow and the
pollutant and sediment transport processes can not be
represented purely by a coefficient which affects only
the bed shear. What follows is the need for a more
physically based approach to account for vegetational
roughness. In the following we present such an approach
and the implementation into a finite volume CFD code.
2.2 Implementation of a physically based resistance
scheme into a multi-dimensional CFD code
Modification of Navier-Stokes equations
As suggested by Wilson and Shaw (1977), a drag-related
force term can be included into the Navier-Stokes
equation to account for the flow resistance of vegetation.
This drag force FD usually takes the form:
U2
FD  ρ
CD A
2
Where CD = drag coefficient and A representing the
projected area of a single plant in streamwise direction.
The drag coefficient can be determined from
experiments or evaluated for simple geometries from the
plants’ base shape and the Reynolds number.
This force can be included as subgrid force per fluid
mass unit in a finite volume cell and is commonly
calculated with the definition of plant density as in Fig.
1.
FD  
u2
CD 
2
with:
CD = drag coefficient
u = bulk streamwise velocity
 = vegetative coefficient as:

projected area of plant
total volume
D

ax a y
Figure 1: Definition of drag force in a FV cell
The implementation of the drag force into the finitevolume discretized form of the Navier-Stokes equations
is accomplished using the iterative nature of the code as:
( AP  
uP
CD z )  uP 
2

6
m 1
Am  um  QPu ,
m  E ,W , N , S , T , B
Here the drag force is added to the matrix coefficient AP
of the numerical point P, which has to equal the
surrounding matrix coefficients Am at locations East (E),
West (W), North (N), South (S), Top (T), Bottom (B),
plus an external Source QPm.
Modification of k- turbulence model
Based on the assumption that the drag force produces
additional turbulent energy in the flow and increases the
dissipation rate, the turbulent production term Pk is
modified as (Wilson and Shaw, 1977):
Pk  Pk  C fk FDi  ui 
for the k-equation, and as:
Pk  Pk  C f FDi  ui 
for the  equation, where subscript k refers to the
turbulence energy. The weighting coefficients C fk and
C f have to be calibrated (Shimizu et al., 1994; Lopez
and Garcia, 1997) in order to optimize numerical
predictions.
2.3 Steady RANS CFD Models for Flow through and
above vegetation
Presently, steady RANS models are the most practical
approaches for high Reynolds number fluvial hydraulics
applications despite the rapid advancements in
computational power and numerical algorithm
development. These steady RANS models allow
resolution of the time-averaged turbulent flow field by
adding the above introduced source term to the RANS
and turbulence transport equations to account for
vegetative drag effects. Such methods for multidimensional flow problems have been developed by
Shimizu and Tsujimoto (1994) and Lopez and Garcia
(1997) using a two-equation turbulence closure
approach. A modified k- turbulence closure model is
used, introducing drag-related sink terms into the
turbulent transport equations. Laboratory experiments by
have been used to validate the model. Shimizu and
Tsujimoto (1994) calibrated their model by adjusting two
additional weightings that appear by introducing the
vegetative sink into the turbulence equations, to
reproduce observed mean velocities and Reynolds
stresses. Lopez and Garcia (1997) numerically modelled
similar test cases (those experimentally investigated by
Dunn et al., 1996) and modified the same weighting
factors of the k- model but reported calibrated values
which differed by about 500% from those of Shimizu et
al. More recently Lopez and Garcia (2001) tested the k model and another two-equation closure known as the
k-ω formulation. A constant CD value of 1.13 was used
in the drag force sink term in the momentum equations
and no modifications were made to the five standard
constants of the k- model. However, values for the
weighting coefficients for the drag-related source terms
for the k and  equations (Cfk = 1.0 and Cf = 1.33) were
again found to be inconsistent with those previously
reported.
These researchers claim that the
inconsistencies in weighting coefficient values are due to
the spatial and temporal averaging technique used within
this study to account for the heterogeneous nature of the
velocity and turbulence intensity field. No significant
difference was found between the numerical
performances of either turbulence model. To eliminate
the calibration from the validation procedure, FischerAntze et al. (2001) developed a similar drag-force
approach but only introduced sink terms into the NavierStokes equations and hence made no modification to the
k-ε model. The turbulence closure thus used the standard
values for the turbulence coefficients and a CD equal to
unity. The model was used to simulate rigid and
emergent vegetation in simple-section and compoundsection channel arrangements (experimentally conducted
by Tsujimoto et al., 1992 and Pasche and Rouve, 1985
respectively) and good agreement was found between
the computed and observed streamwise velocity
distributions. Neary (2000) employed the near wall k-
model for turbulence closure but reported no
improvement compared to the k- model while using the
weighting coefficients adopted by Shimizu and
Tsujimoto (1994). Naot et al. (1996) were the first who
have used a higher order anisotropic closure, the
Reynold's Stress model (RSM), to simulate the flow
through rigid submerged vegetation elements. They have
also used the drag force approach as described above but
have additionally accounted for the effect of shading, i.e.
the effect of upstream rods resulting in weaker ambient
flow and reducing the drag force on the vegetational
elements. Furthermore they have related the two
vegetative weighting coefficients to a characteristic
length scale that can be estimated from the configuration
and geometry of the plants. However, according to Naot
et al. the sensitivity of this characteristic length and the
shading factors indicated the importance of these terms.
Choi and Kang (2001) also used a higher-order
anisotropic closure (Reynold Stress Model, RSM) and
compared these results against the k- model for the data
set collected by Dunn et al. (1996). Both models
employed a CD value of 1.13. Within the vegetated layer
there was no significant difference between the
performances in the prediction of the mean velocity
profile for the one condition examined. However, within
the surface layer region there was a significant
improvement in the computed mean velocity, turbulent
intensity and Reynolds stress profiles for the RSM
relative to the k- model.
Tsujimoto and Kitamura (1998) have incorporated a
stem deformation model to extend RANS simulations to
flexible vegetation. While Wilson et al. (2004) have
incorporated the additional projected area of the plants
when in bending through the vegetative coefficient used
in the classical cylinder drag force approach (this is
described in section 3.3). Naot et al. (1996) and FischerAntze et al. (2001) have developed 3D RANS models for
vegetated flows in compound channels with vegetation
zones in riparian areas and flood plains. These models
have enabled prediction of the effects of vegetation on
sediment transport in fluvial channels (e.g., Okabe et al.,
1998; López and García, 1998).
Mean flow features resolved by the steady RANS
models include: (1) the suppression of the streamwise
velocity profile in the vegetated zone, (2) the inflection
of the velocity profile at the top of the vegetation zone,
and (3) the vertical distribution of the streamwise
Reynolds stress (turbulent shear), with its maximum
value at the top of the vegetation zone. However, for
some of the experimental test cases, these models have
been less successful at predicting the streamwise
turbulence intensity. Also, the bulge in the velocity
profile that is sometimes present near the bed cannot be
resolved. This feature has been observed for some test
cases reported by Shimizu and Tsujimoto (1994) and
Fairbanks and Diplas (1998) despite a uniform vertical
plant density distribution.
The present limitations of the RANS models are due
mainly to spatial and temporal averaging, and possibly
failure to model the effects of turbulence anisotropy.
Some of these deficiencies may be offset somewhat
through the treatment of the drag and weighting
coefficients in the governing equations that account for
vegetative drag effects. However, adopting nonuniversal drag coefficients or non-theoretical based
weighting coefficients to make up for model deficiencies
is not particularly desirable (see López and García,
1997; Neary, 2003).
The 3D models distribute the drag uniformly throughout
the vegetation layer by introducing body force terms in
the RANS equations. Hence, to date 3D models have
not simulated flow around individual stems. Due to this
simplification, streamwise vortices (secondary motion),
a suspected mechanism for momentum transfer that
produces the near bed velocity bulge (Neary, 2000,
2003), cannot be simulated with any of the present
RANS models.
As a result of time averaging, RANS models also cannot
capture the organized large-scale unsteadiness and
asymmetries (coherent structures) resulting from
turbulent flow instabilities due to unsteady shear and
pressure gradients induced by vegetation. These
coherent structures include: (1) the transverse and other
secondary vortices described by Finnegan (2000), which
occur at the top of the vegetation layer as a result of a
Kelvin-Helmholtz instability due to the inflection of the
streamwise velocity profile (Figure 2), and (2) 3D
vortices produced by the complex interaction of the
approach flow with the stem (e.g horseshoe and necklace
vortices) and the oblique vortex shedding in the wake of
the stem due to spanwise pressure gradients (Figure 3).
These unsteady vortices would also contribute, or
possibly play a dominant role, in redistributing
momentum and producing the near bed velocity bulge.
The use of Reynolds stress transport (RST) turbulence
closures to be used in a steady RANS model in order to
account for turbulence anisotropy and its effects has
received only limited numerical investigation [Choi and
Kang, 2001] and its benefits are not yet apparent. The
laboratory experiments by Nezu and Onitzuka [2001]
demonstrate that riparian vegetation has significant
effects on secondary currents due to turbulence
anisotropy, which increases with Froude number.
However, coherent structures may account for a
significantly larger percentage of the total Reynolds
stresses and anisotropy [Ge et al. 2003]. Under such
circumstances, RST modeling would only have limited
value.
Figure 2: Organized flow structures above vegetation layers
(Finnigan, 2000)
Figure 3: 3D vortices separating at vegetation stems
(Finnigan, 2000)
2.4 URANS / LES
Future numerical modeling efforts will focus on
advanced CFD modeling techniques—namely statistical
turbulence models that directly resolve large scale,
organized, unsteady structures in the flow and advanced
numerical techniques for simulating flows around
multiple flexible bodies. These would include unsteady
3D Reynolds-averaged Navier-Stokes models (URANS;
Paik et al., 2003; Ge et al., 2003) and large eddy
simulation models (Cui and Neary, 2002). Such
techniques will elucidate the large-scale coherent
structures described above, their important role in
vegetative resistance, and their interaction and feedback
with Reynolds stresses and lift forces that initiate
sediment transport and bed form development. To our
knowledge the first LES calculations for flow over
vegetation were presented by Deardoff (1972) where the
atmospheric boundary layer over a wheat field was
simulated. Further LES calculations have come from the
boundary layer meteorology where the flow and the
turbulent structures above forests have been studied (e.g.
Moeng, 1984, Shaw and Shumann, 1992, Kanda and
Hino, 1993, Dwyer et al., 1997). The advantage of LES
lies in the fact that a highly resolved temporal and spatial
picture of the flow field can be obtained. Shaw and
Shumann (1992) note, that the turbulent coherent
structures which play a dominate role in terms of the
mass and momentum exchange cannot be captured by a
steady RANS model. Kanda and Hino, (1993) showed
that utilising a LES resulted in the simulation of the
above mentioned coherent structures in the form of
“rolls” (vortices with horizontal axis in the crossstreamwise direction) and “ribs” (vortices with horizontal
axis in the streamwise direction), as observed and
schematised by Finnigan (2000) (see Fig 2). Furthermore
the vertical distribution of Reynolds stresses and
turbulent fluctuations as calculated with LES are in very
good agreement to laboratory and field observations.
These simulations show the enormous potential of LES in
accurately predicting the flow and its associated timedependent structures.
In both the meteorological and open channel Large-Eddy
Simulations the drag-force approach is used to represent
the flow resistance of the canopy layer. The drag
coefficient which is generally set to unity, varies
throughout these simulations depending on boundary
conditions, vegetation type, Reynolds number etc. A
future possibility is to represent the vegetational flow
resistance by explicit representation of the plants
analogous to the flow around a circular cylinder (e.g.
Breuer, 1998) or over a matrix of cubes (Stoesser et al.,
2003a). This can be achieved by relating the plan-view
mesh to plant geometry and out-blocking particular cells
to represent the presence of vegetal obstructions (Fig 4).
This approach however is computationally extremely
demanding since the boundary layer developing at each
individual element has to be represented (not necessarily
resolved), such that flow separation is adequately
modelled. The accompanying vortex shedding as well as
the development of associated flow structures, forces and
stresses and the correct representation of transport
processes may be worth the increased computational
effort.
Above mentioned direct modelling of the vegetation is
restricted to well-defined singular elements and not
applicable to a tree which is submerged past the level of
its branches. Nevertheless, the rigid part of a submerged
plant (i.e. the trunk or stipe) may be distinct in terms of
its location and geometry, and hence this part may be
represented as a discrete element whilst the branches and
leaves may still be treated by the subgrid drag force
approach as known from steady RANS models. In what
follows is a roughness treatment which may be
applicable to real field situations in the near future.
Figure 4: Resolved vegetation elements in a channel
with emergent vegetation
3 Some Examples
Further research into basic mechanisms of the flow
interaction between vegetation and the accompanying
correlations between plant biomechanical properties,
plant bending and plant movement due to the
hydrodynamic forces will allow more sophisticated
mathematical formulations for closing roughness to be
developed. Prior to this, the drag-force approach
provides a useful and practical tool with which to begin
exploring the simulation of flow over and through
vegetation canopies.
3.1 Rigid Submerged Vegetation in a Straight Flume
Numerical simulations of the flume experiments of
Tsujimoto et al. (1992) and Lopez and Garcia (1997)
were carried out to simulate submerged vegetation
[Stoesser, 2002]. The drag force coefficient CD was
evaluated for all experiments to be equal to 1.0 for the
given Reynolds numbers. Computed velocity
distributions were compared to observed data. Good
agreement between measured and computed velocities
for HYDRO3D and the model used by Fisher-Antze et al
(2001) could be achieved for both Tsujimoto et al.’s
experiment A31 and for Lopez et al.’s experiment No 9
(see Figure 5). Here there is little difference between the
CFD models and the main difference is in the choice of
the bed roughness value and the grid resolution. No
information was available for the bed roughness of the
flume and both studies have employed different values
for the bed roughness: Mannings n values of 0.0143 and
0.02 were used for the HYDRO3D and Fischer-Antze’s
studies respectively. The HYDRO3D study used a
higher grid resolution (see Fig 5 for computational
points). As is evident, a better match to the observed
data in the vegetation layer could be achieved using
HYDRO3D although there is slight overprediction of the
velocity near the surface compared to Fischer Antze et
al. (2001). For the Tsujimoto et al. (1992) test case,
HYDRO3D computed the velocity at the first grid point
at the boundary with better accuracy than that of
Fischer-Antze et al. For both simulations the weighing
factors C fk and C f were chosen to be zero, however it
was found that the difference in predictions with and
without these additional terms was negligible.
erroneous and hence the evaluation of the drag force is
erroneous as well, leading to an incorrect flow field.
This was apparent in all simulations of flow through
vegetation performed in the course of a validation series
(Stoesser, 2002). Furthermore, it is important to note that
the inclusion of drag-related sink terms in the
momentum equations is physically incorrect, since it
only accounts for the advective fluxes, ignoring diffusive
fluxes and local pressure gradients. Hence a scheme that
includes the effects of mean velocity gradients and
pressure differences generated by the vegetational
obstacles in the flow would be ideal. A possible solution
of how to remedy this shortfall is above-mentioned
“direct” or explicit modelling of the vegetal elements.
Shimizu A31
0.10
Shimizu et al.
HYDRO3D
z [m]
Fischer-Antze at al.
0.05
Top of Vegetation Layer
0.00
0.0
0.1
0.2
0.3
u [m/s]
Lopez Exp. 9
0.3
Lopez at al.
HYDRO3D
Fischer-Antze et al.
z [m]
0.2
Top of Vegetation Layer
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
u [m/s]
Figure 5: Calculated and observed vertical velocity
distribution of Shimizu et al.’s A31 experiment and Lopez et
al.’s Exp. 9
In all the test cases of flow through vegetation that were
performed within the validation study of HYDRO3D a
drag force approach was used and it was apparent that
the channel bed roughness seemed to be an important
issue from a mathematical point of view (not from a
physical sense as stated by Nepf, 1999). The reason for
this lies in the mathematical formulation and the iterative
solution scheme employed. Since the calculation of the
velocity field is dependent on the calculation of the drag
force, which in turn depends on the calculated oncoming
velocity, the drag force is only correctly evaluated at the
end of the iterative procedure. Hence, if for instance
external forces like the bed shear stress are falsely
predicted (due to an over or underestimation of bed
roughness), the velocity at the first grid point is
3,2 Up-scaling to the Field – The Rhine Example
As pointed out earlier, central to any river design project
is the accurate prediction of the flow field in and around
riparian vegetation. However, the approaches introduced
above to model the flow resistance due to vegetation
need to be simplified to be used at field scale in order to
provide a practical but physically-based roughness
closure approach for vegetative resistance which
involves a minimum of parameter calibration. The
German Association for Hydraulic Engineering
(DVWK, 1991) recommends a method for defining the
roughness parameter  at large scale. This relates the
vegetation geometric properties, including plant
diameter and spacing, to the drag force. To implement
the method, geometric vegetation parameters of an
existing established riparian forest were quantified and
used as input to the drag force roughness closure. For the
field HYDRO3D was used with the classical drag force
approach. The model was then validated in two stages.
Firstly, computed water levels were compared against
measured water levels. Secondly, the floodplain flow
velocity for a 1 in 100 year event was measured by
dilution gauging to allow the computed floodplain
velocities to be verified.
Determination and classification of flow resistance
parameters
An established groyne field was used as a reference site
in order to quantify the vegetation parameters of the
existing plant communities. It was composed of a welldeveloped riparian forest with a rich mixture of rigid
trees and flexible bushes. An area of 77 m x 45 m was
surveyed in terms of vegetation type and its relative
location. The vegetation varied over the entire
monitoring patch and was classified into five
characteristic strips, for which average values of
vegetation parameters and an average vegetative flow
resistance coefficient were determined.
Floodplain velocity measurements
Velocity measurements are complicated in the case of
vegetated floodplains as the plants act as vertical
obstructions to the flow. This results in the production of
vortices immediately downstream of the vegetational
elements and generates a strongly heterogeneous flow
field. Hence, dilution gauging was performed to
determine the mean velocity um as a bulk parameter in
submerged or emergent vegetation, as this appears to be
a good alternative to conventional point velocity
measurement methods (e.g. Nepf, 1999). The gulp
injection or integration method was employed and the
tracer was released from a boat. Three locations in the
groin field were selected for the release station, and
sampling stations 1 and 2. The injection station and
sampling station 1 (SaSt1) were 54 m apart, whilst the
injection station and the sampling station 2 (SaSt1) were
99.5 m apart. The concentration was sampled at intervals
of 10 seconds for a 10-minute period. In order to acquire
an accurate measurement of the mean flow velocities,
the tracer injection and concentration measurement was
repeated four times. The centroid of the time–
concentration curve was evaluated in order to estimate
the travel times from the injection point to the sampling
stations. The average value of mean flow velocity was
evaluated as um  0.07 m/s with a standard deviation of
0.07 m/s.
errors in determining vegetation geometric properties
this indicates that within a framework where the drag
coefficient is believed to be unity, this is the level of
precision necessary to achieve these measurements.
These calibrated values for bed roughness and form
roughness were then used to simulate the 1999 flood. As
Figure 6 shows the agreement between observed and
calculated waterlevels for the 1999 event is fairly
satisfying and provides a simple split-sample test of
model prediction skill.
Numerical Simulations
The test reach of the Rhine between km 190.0 and km
193.46 was discretised according to 26 cross-sections,
which were surveyed in 1986. The grain roughness ks
was calculated from the average gradation curve of the
bed material determined through particle sieve analysis.
To provide increased confidence in the hydraulic
resistance values, the bed roughness of the main channel
and the form roughness of the vegetated floodplains
were independently verified using two different flow
conditions. These correspond to flow situations where
both the water level observations and discharge
measurements are available: (Food event on 2.11.1998,
where Q = 700 m³/s and flood event on 29.05.1994,
where Q = 3040 m³/s). During the 1998 event most of
the vegetated floodplains were not inundated, hence this
flow condition was used to verify the value of main
channel bed roughness. For this flow the bed friction
parameter was adjusted, and an optimum value of n =
0.032 was found. The difference between calibrated (n =
0.032) and uncalibrated (n = 0.033) values was
negligible and good correspondence could be obtained
between the measured and computed water surface
profiles for this event for both parameterizations. The
vegetative roughness coefficient  was verified using the
larger flow event (3040 m3/s) where all floodplains were
inundated. The parameter  was adjusted from 0.11 m-1
to 0.082 m-1 in order to achieve a good match between
the observed and computed water levels. If we assume
that this need for recalibration is predominately due to
Figure 7 shows the distribution of flow velocities in the
cross section of the Rhine corresponding to the test site
where the dilution gauging was undertaken. There is a
marked reduction in velocity at the main
channel/riparian floodplain interface, where floodplain
flow velocities are approximately between 1.0 - 1.3 m/s.
In contrast to the main channel velocity distribution with
depth, the floodplain velocity follows a relatively
uniform vertical velocity profile. This is in keeping with
findings from experimental investigations whereby the
velocity profile within both rigid and flexible vegetation
layers no longer follows the logarithmic law (Tsujimoto
et al, 1992; Nepf and Vivoni, 1999). The uniformlydistributed velocity (over floodplain width and depth) as
computed, corresponds well with the observed mean
velocity from the tracer field tests.
1999 Flood
222.0
3D Calculation
221.0
WL. Observed 22.02.99
Wl. [m a.s.l]
220.0
219.0
218.0
217.0
216.0
189.0
190.0
191.0
192.0
193.0
194.0
195.0
Rhine km
Figure 6: Comparison of observed and computed water
surface elevation after the main channel bed roughness and
the floodplain vegetative parameters were calibrated
Figure 7: Verification of the computed resultant velocity in a
Rhine cross section. Velocity magnitude parameter UV is given
in m/s.
Whilst the roughness closure approach presented herein
does not eliminate entirely the process of calibration, we
have presented and applied a method which is based on
3.3 Up-scaling to the Field – The Wienfluss Example
The Wienfluss test channel in Vienna comprises of a 114
m reach, which is composed of an asymmetric compound
channel approximately 7 m in width and is relatively
straight in alignment (Fig 8). In the 2001 flood event
presented in this paper a relatively large proportion of the
willows were submerged. The degree of bending was
difficult to quantify from a video as the willow stands are
submerged below the water surface and were not visible.
It can be postulated that the willow stands were bent from
anything between zero and 75 degrees to the vertical.
The bending of the willow stands were modeled using the
rigid cylinder drag force approach (Fig 1) implemented
into a 3D finite volume code with standard k-
turbulence closure. No modification was made to the
weighting coefficients in the k- model. Bending was
accounted for by the following two effects. Firstly when
the plant bends, its height decreases in the vertical plane
and hence the height of the water column on which the
drag force is acting is reduced. Secondly, due to bending
a larger portion of form drag and stands’ momentum
absorbing area is transferred to lower parts of the flow
depth than if the plant were rigid and vertical. This
results in a change in the distribution of the frontal
projected area with height, with a greater projected area
closer to the bed. This was accounted for in the
redistribution of the vegetation coefficient in the drag
force model.
The average plant height and corresponding proportion of
the water column that was occupied by the willow
canopy was based on the arithmetic mean and this was
accounted for in the drag force model. The vegetative
coefficient  (as defined in Fig 1) as a function of height
(known hereafter as the non-uniform density approach)
was coded into the vegetation flow resistance model. It is
a well established fact that for many trees the trunk
diameter decreases with increasing height above the base
and this can be observed for the willows in this study. A
linear relationship was assumed to exist between the
diameter at the base and at one metre height. The nonuniform density approach was tested as well as modeling
the vegetation as a uniform diameter with plant height.
In the latter case the basal diameter was used.
uniform approach less drag is exerted relative to the
uniform approach resulting in an increase in velocities in
the floodplain zone (see Fig 9a and b). In some locations
the computed velocity profile reproduces the measured
profile with good accuracy in terms of both magnitude
and profile shape (see Fig 9a). Within the vegetated layer
region, velocities are reproduced with reasonable
accuracy depending on the lateral floodplain location (see
Fig 9a, and b). It may be postulated that some of the trees
are in pronation, due to the shape of the measured profile
depending on the degree of deflection. This deflection
transfers a larger portion of the form drag and momentum
absorbing area to the lower parts of the flow depth than if
the plant were rigid and vertical. This therefore leads to
an under-prediction in the upper half of the floodplain
flow depth and may account for why the velocities are
over-predicted in the near bed region (Fig 9b).
In summary this study showed that the degree of bending
is an important parameter that should be determined in
future field studies. Using this information together with
the plant stand diameter and density a simplified model
can be formed that is based on the drag force approach.
The effect of increasing the drag coefficient from unity to
1.5 decreased the computed velocity by a minimal
amount and the degree by which the willow stands were
in bending had a greater impact on the computed velocity
profile. The impact of using a non-uniform density
distribution was greater when the plants are modeled
vertically than when the plants are modeled at high
degrees of bending. More details and results of this study
can be found in Wilson et al. (2004).
One of the main aims of this study has been to minimize
the need for roughness calibration. This method can
significantly reduce the uncertainties of traditional
methods of friction calibration. This study showed that
modeling the bending of riparian vegetation can have a
significant impact on the computed velocities and hence
this critical parameter should be determined in
subsequent field studies.
2.5
2
Depth [m]
the physics of flow resistance and which significantly
reduces the modelling uncertainties associated with
traditional methods of calibration. More details of this
study can be found in Stoesser et al. (2003b).
1.5
1
measured
uniform
0.5
non-uniform
mean plant height
6 ,8 m
0
113 ,5 m
Figure 8: Schematic view of reach indicating velocity
measurement section and willow monitoring patches
When the vegetation canopy is modeled using the non-
0
1
2
3
Velocity [ms-1]
[a]
4
5
2.5
2
1.5
1
measured
uniform
0.5
non-uniform
mean plant height
0
0
1
2
3
4
5
Velocity [ms-1]
[b]
Figure 9: Measured and computed velocity profiles for two
different lateral locations on the floodplain. Elevation refers to
a datum level.
4 Summary and Conclusion
This paper has demonstrated how recent research studies
are at last beginning to generate an understanding of the
interaction of flow with natural vegetation and how this
is beginning to inform new conceptual and mathematical
representations of these effects that can be incorporated
in numerical models. These initial studies confirm the
complexity of vegetation-flow interaction and highlight
why this particular area of hydraulics has for so long
defied effective treatment. Vegetation-flow interactions
are, clearly, an area where our hydraulic understanding is
weak, yet they are central to many problems of practical
interest to hydraulic engineers including flood risk
studies, sediment transport studies and the analysis of the
hydraulic performance of river restoration schemes.
However, the increasing availability of sophisticated
velocity measurement equipment (such as Acoustic
Doppler Velocimeters) as standard tools in hydraulic
laboratories and in field, and the hosting of
Computational Fluid Dynamics codes on desktop
computers rather than mainframes, has in recent years
allowed considerable progress to be made.
Through analysis of vegetation-flow interaction, and in
particular the energy losses generated, we are now
beginning to unpack the various components of hydraulic
resistance in natural channels. In doing so the primary
aim has been to move away from lumped, and often
unknowable, friction parameterizations to physicallybased laws describing each component contributing to
the energy loss source term in the Navier-Stokes
equations. This process marks the beginning of the
development of what could be best described as
‘roughness closure’ schemes and these are deserving of
the same attention in hydraulics as turbulence closure
schemes have had over the last 20 years. Given the
availability of a number of adequate, if not perfect,
methods of turbulence closure such as the k- scheme
and LES methods, roughness closure is arguably a
similar important and less well understood problem. The
comparison with turbulence modelling is instructive, as
both are in effect subgrid-scale closures with strong scale
and model dimension dependency.
Whilst the role of vegetation in generating energy losses
is key, this paper attempts to highlight the challenges of
modeling vegetation-flow interactions. It is clear that we
need to consider the generation of resistance and
turbulence as linked processes in numerical models.
Indeed, this is just one of many potential research areas
that require investigation, and, although progress is
being made, in general our understanding of vegetationflow interaction is still limited. We need to elucidate
many basic hydraulic mechanisms and show how these
depend on specific plant biophysical properties. In terms
of numerical modelling and the incorporation of these
processes into CFD codes, we require better model
validation data sets for both flume and field situations.
Moreover, in beginning to develop roughness closure
methods driven by physically measurable plant
parameters we need to develop methods to generate the
necessary input data, perhaps through remote sensing.
Finally, although progress has been made in
understanding the hydraulics of flow-vegetation
interaction, almost no research has yet been conducted
into the influence of vegetation on sediment transport
and this is likely to be a key area for studies of the
hydraulic behavior and morphologic development of
river restoration schemes.
In summary, the hydraulic impact of vegetation is a new
and exciting area of hydraulics research where there is
considerable scope for the development of better
physical understanding and theory. These tasks need to
be pursued in conjunction with a programme of
numerical model development as both a further facet of
scientific enquiry and in order to translate the knowledge
gained into practical tools for hydraulic engineers.
Acknowledgements
We gratefully acknowledge the donation of the field data
from the Wienfluss study from H. P. Rauch from the
Institute of Soil Bioengineering and Landscape
Construction University of Natural Resources and
Applied Life Science, Vienna.
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