Flow separation at the inner (convex) and outer (concave) banks of constant‐width and widening open‐channel bends

TLDR: In this paper, the authors report on successful laboratory experiments that elucidate flow structure in one constant-width bend and a second bend with an outer-bank widening, with both a flat immobile gravel bed and mobile sand bed with dominant bedload sediment transport.

Abstract: There is a paucity of data and insight in the mechanisms of, and controls on flow separation and recirculation at natural sharply-curved river bends. Herein we report on successful laboratory experiments that elucidate flow structure in one constant-width bend and a second bend with an outer-bank widening. The experiments were performed with both a flat immobile gravel bed and mobile sand bed with dominant bedload sediment transport. In the constant-width bend with immobile bed, a zone of mainly horizontal flow separation (vertical rotational axis) formed at the inner bank that did not contain detectable flow recirculation, and an outer-bank cell of secondary flow with streamwise oriented rotational axis. Surprisingly, the bend with widening at the outer bank and immobile bed did not lead to a transverse expansion of the flow. Rather, flow in the outer-bank widening weakly recirculated around a vertical axis and hardly interacted with the inner part of the bend, which behaved as a constant-width bend. In the mobile bed experiment, downstream of the bend apex a pronounced depositional bar developed at the inside of the bend and pronounced scour occurred at the outside. Moreover the deformed bed promoted flow separation over the bar, including return currents. In the constant-width bend, the topographic steering impeded the generation of an outer-bank cell of secondary flow. In the bend with outer-bank widening, the topographic steering induced an outward expansion of the flow, whereby the major part of the discharge was conveyed in the central part of the widening section. Flow in the outer-bank widening was highly three dimensional and included return currents near the bottom. In conclusion, the experiments elucidated three distinct processes of flow separation common in sharp bends: flow separation at the inner bank, an outer-bank cell of secondary flow, and flow separation and recirculation in an outer-bank widening.

Figures

Figure 7. Velocity vector at the water surface obtained by means of LS-PIV measurements in the mobile-bed experiment. The inserts show exploded view of the velocity vectors in the first and second bends. The dashed black lines indicate the entrance and exit of the first and second bend. The three-dimensional flow patterns in the section at Y=5 175m in the first (thick blue line) and in the apex of the second bend (thick green line) are shown in Figures 8 and 10, respectively.

Figure 12. Conceptualization of hydrodynamic processes in sharp open-c bed; (b) configuration with outer-bank widening and flat immobile bed; (c) co outer-bank widening and mobile bed. Comparison reveals the influences of bedload sediment transport on the hydrodynamic processes.

Figure 5. Evolution along the flume of the normalized transverse water surface slope, asuperelevation/R (Equation 3), in the immobile-bed and mobile-bed experiments. Bend-averaged values are provided in the table, and compared to experimental data of Blanckaert (2009, 2011). This figure is available in colour online at wileyonlinelibrary.com/journal/espl

Figure 6. Velocity vector at the water surface obtained by means of LS-P exploded views of the velocity vectors in the first and second bends. The da bend. The three-dimensional flow patterns in the section at Y=4 82m in th line) are shown in Figures 8 and 10, respectively.

Figure 11. Time-averaged flow in the apex of the second bend (see Figur normalized streamwise (parallel to the channel centerline) velocity, vs/U. (b) Is centerline) velocity, 100vn/U. (c) Isoline pattern of the normalized vertical velo (vn,vz)/U. The shaded areas indicate regions where the flow measurement (more details in Blanckaert, 2010). Schematic representation of the secondary fl the shallow zone induced by topographic steering; (II) secondary flow in the ou outer-bank widening. The thick red line represents the average bed elevation at The thick blue line represents the average bed elevation at dynamic equilibrium

Figure 10. Time-averaged flow in the apex of the second bend (see Figures 1 and 6) with immobile-bed configuration. (a) Isoline pattern of the normalized streamwise (parallel to the channel axis) velocity, vs/U. (b) Isoline pattern of the normalized transverse (perpendicular to the channel centerline) velocity, 100vn/U. (c) Isoline pattern of the normalized vertical velocity, 100vz/U. (d) Normalized vector presentation of the secondary flow (vn,vz)/U. Measurements were performed on two measuring grids that overlap in the region n= –0 2 to n=–0 3. The shaded areas indicate regions where the flow measurements are perturbed by the ADVP housing that touches the water surface (more details in Blanckaert, 2010). Schematic representation of the secondary flow pattern and near bank flow processes: (I) zone of inner-bank flow separation; (II) remnant centre-region cell of secondary flow from upstream bend; (III) centre-region cell of secondary flow; (IV) zone of horizontal outer-bank recirculation. Undistorted figures.

Full text

Flow separation at the inner (convex) and outer
(concave) banks of constant-width and widening
open-channel bends
Koen Blanckaert,
1,6
*
Maarten G. Kleinhans,
2
Stuart J. McLelland,
3
Wim S. J. Uijttewaal,
4
Brendan J. Murphy,
3
Anja van deKruijs,
2
Daniel R. Parsons
5
and Qiuwen Chen
1
1
State Key Laboratory of Urban and Regional Ecology, Research Centre for Eco-Environmental Sciences, Chinese Academy of
Sciences, Beijing, China
2
Faculty of Geosciences, Universiteit Utrecht, Utrecht, The Netherlands
3
Department of Geography, Environment and Earth Sciences, University of Hull, Hull, UK
4
Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, The Netherlands
5
University of Hull, Hull, UK
6
École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
Received 31 March 2012; Revised 6 August 2012; Accepted 30 August 2012
*Correspondence to: Koen Blanckaert, Chine se Academy of Sciences, China. E-mail: koen.blanckaert@epfl.ch
ABSTRACT: There is a paucity of data and insight in the mechanisms of, and controls on flow separation and recirculation at
natural sharply-curved river bends. Herein we report on successful laboratory experiments that elucidate flow structure in one
constant-width bend and a second bend with an outer-bank widening. The experiments were performed with both a flat immobile
gravel bed and mobile sand bed with dominant bedload sediment transport.
In the constant-width bend with immobile bed, a zone of mainly horizontal flow separation (vertical rotational axis) formed at the
inner bank that did not contain detectable flow recirculation, and an outer-bank cell of secondary flow with streamwise oriented
rotational axis. Surprisingly, the bend with widening at the outer bank and immobile bed did not lead to a transverse expansion of
the flow. Rather, flow in the outer-bank widening weakly recirculated around a vertical axis and hardly interacted with the inner part
of the bend, which behaved as a constant-width bend.
In the mobile bed experiment, downstream of the bend apex a pronounced depositional bar developed at the inside of the bend
and pronounced scour occurred at the outside. Moreover the deformed bed promoted flow separation over the bar, including return
currents. In the constant-width bend, the topographic steering impeded the generation of an outer-bank cell of secondary flow. In the
bend with outer-bank widening, the topographic steering induced an outward expansion of the flow, whereby the major part of the
discharge was conveyed in the central part of the widening section. Flow in the outer-bank widening was highly three dimensional
and included return currents near the bottom.
In conclusion, the experiments elucidated three distinct processes of flow separation common in sharp bends: flow separation at
the inner bank, an outer-bank cell of secondary flow, and flow separation and recirculation in an outer-bank widening. Copyright ©
2012 John Wiley & Sons, Ltd.
KEYWORDS: flow separation; open-channel bend; experiments; morphology; laboratory
Introduction
Problem definition and objective
Changes in the direction of channel boundaries that lead to an
adverse pressure gradient or induce sufficient inertia within the
flow will produce flow separation from the boundary, which
often leads to the formation of a zone of flow recirculation. This
has frequently been observed in flows around engineering
structures such as bridge piers. Such flow features also occur
naturally and are observed over a range of scales around
naturally created morphological elements such as individual
clasts (e.g. Best and Brayshaw, 1985), bedforms (e.g. Bennett
and Best, 2006), at confluence zones (e.g. Best and Reid, 1984),
downstream of bars in bedrock controlled canyons (Schmidt,
1990; Schmidt et al., 1993; W right and Kaplinski, 201 1) and in
river bends (e.g. Bagnold, 1960; Leeder and Bridges, 1975;
Hickin, 1977, 1978, 1986; Hickin and Nanson, 1984; Jackson,
1992; Andrle, 1994; Hodskinson and Ferguso n, 1998; Ferguson
et al., 2003; Kleinhans et al., 2009; Rhoads and Massey, 2012;
Parsons, 2003; Vietz et al., 2012; Schnauder and Sukhodolov,
2012).
Flow separation and the formation of recirculation zones have
broad and significant consequences for the morphodynamics of
a river. The presence of a separation zone combined with a
recirculation vortex can decrease the effective channel width
EARTH SURFACE PROCESSES AND LANDFORMS
Earth Surf. Process. Landforms (2012)
Copyright © 2012 John Wiley & Sons, Ltd.
Published online in Wiley Online Library
(wileyonlinelibrary.com) DOI: 10.1002/esp.3324

and thus reduce the channel conveyance capacity. This can alter
patterns of bed and bank erosion and can often lead to localized
and focused bank erosion (Ferguson et al., 2003; Kleinhans et al.,
2009; Parsons, 2003) and formation of a muddy counter-point
bar (e.g. Nanson and Page, 1983; Makaske and Weerts, 2005)
with potential impacts on both ecological diversity and flood-
plain sedimentology (e.g. Burge and Smith, 1999): particularly
as such zones are loci for fine-grained sedimentation, which
would otherwise only be possible on floodplains. At river bifurca-
tions, deposition and bar formation within a recirculation zone
can eventually lead to closure of one bifurcate arm and complete
channel avulsion (Bulle, 1926; Hirose et al., 2003; Kleinhans
et al., 2012). Enhancing knowledge on flow separation near
the banks is thus vital for informing environmental manage-
ment strategies, enhancing modelling capabilities, improving
design of civil engineering controls (bank protection and ship-
ping depth) and for informing longer-term investigations in sed-
imentary geology. It is particularly relevant within the context
of the recent trend to re-naturalize smaller sinuous channels,
where sharp bends are expected because of the relatively
strong banks. Such sinuous streams are often thought of as
meandering with associated biota, but their dynamics in natu-
ral states were probably very low. Hence sharp bends could
be integrated in the design to obtain favourable conditions,
including more dynamics and spatial variation of micro-
environments.
This paper will focus on flow separation and flow recirculation
in open-channel bends. The hydrodynamic and morphodynamic
processes in open-channel bends have been abundantly
investigated in the past by means of field measurements (e.g.
Rozovskii, 1957; Bathurst et al., 1979; de Vriend and Geldof,
1983; Dietrich and Smith, 1983; Dietrich, 1987; Ferguson et al.,
2003; Frothingham and Rhoads, 2003; Nanson, 2010; Rhoads
and Massey, 2012; Schnauder and Sukhodolov, 2012; Vietz
et al., 2012), laboratory experiments (e.g. Rozovskii, 1957;
Odgaard and Bergs, 1988; Blanckaert and Graf, 2001; Abad
and Garcia, 2009; Blanckaert, 2010; Jamieson et al., 2010;
Termini and Piraino, 2011) and numerical modelling (e.g.
Kikkawa et al., 1976; Leschziner and Rodi, 1979; Shimizu and
Itakura, 1989; Hodskinson and Ferguson, 1998; Wu et al.,
2000; Ferguson et al., 2003; Khosronejad et al., 2007; Zeng
et al., 2008; Stoesser et al., 2010; van Balen et al., 2010b;
Constantinescu et al., 2011; Kang and Sotiropoulos, 2011). This
previous work mainly focussed on the central region (i.e. away
from the banks) of the cross-section, particularly the nature of
the secondary flow field.
Secondary flow is defined in the present paper as the flow
component perpendicular to the channel axis. The key feature
of flow in curved open-channels is the helical motion in
the central part of the cross-section, with inward velocities near
the bed and outward velocities near the water surface. This
helical motion is essentially due to the curvature-induced
local imbalance between the outwards centrifugal force and
the inwards pressure gradient caused by the transverse tilting
of the water surface (e.g. Boussinesq, 1868; Thomson, 1876;
van Bendegom, 1947; Rozovskii, 1957). This helical motion
gives rise to a secondary flow cell in the central region of the
cross-section, which will be called ‘centre-region cell of
secondary flow’ henceforward. The centre-region cell of
secondary flow causes near-bed velocities that are inwards
directed and lead to the development of a transverse bed slope
(van Bendegom, 1947; Rozovskii, 1957; Engelund, 1974;
Odgaard, 1981). It also contributes to the redistribution of
the flow in open-channel bends (Rozovskii, 1957; Engelund,
1974; de Vriend, 1977, 1981; Yeh and Kennedy, 1993;
Blanckaert and de Vriend, 2003, 2010; Blanckaert and
Graf, 2004).
The details of the hydrodynamic and morphodynamic pro-
cesses occurring near the banks of open-channel bends have
only rarely been investigated (Table I) in spite of their
importance with respect to bank erosion, bank accretion, river
planform dynamics and hazard mitigation. In the present paper,
the term flow separation refers to distinct hydrodynamic
processes that cause the main flow body to be separated from
the channel banks. The objective of this paper is to understand
formative conditions and flow structure of three distinct
processes of flow separation at channel bends: flow separation
at the inner bank, the outer-bank cell of secondary flow and
flow separation at a widening outer bank. The three processes
will be explored experimentally with and without a mobile
bed to assess the relevance for full-scale, natural river channel
processes and dynamics.
Review
Flow separation at the inner bank (horizontal around a vertical
axis)
Flow separation and recirculation at the inner bank, has been
observed in a number of studies of natural meander bends
(e.g. Bagnold, 1960; Leeder and Bridges, 1975; Ferguson
et al., 2003; Frothingham and Rhoads, 2003; Nanson, 2010;
Rhoads and Massey, 2012; Schnauder and Sukhodolov,
2012). Ferguson et al. (2003) highlighted that flow separation
from the channel bank occurred in about 50% of bends on a
sinuous river with relatively cohesive banks, where the bar-
pool morphology acts to divide the cross-section into two
distinct regions: a shallow point bar at the inside of the bend
and a deep scour pool at the outside of the bend. Bagnold
(1960) argued that flow separation at the inner bank
concentrates the flow into the deeper outer part of the cross-
section. Leeder and Bridges (1975) also speculated that flow
separation at the inner bank reduces the effective width and
directs high-velocity flow towards the outer bank. Ferguson
et al. (2003), however, found that the reduced effective width
is more than offset by an increase in flow depth and that the
flow decelerates along the outer bank at the flow stage they
investigated. Detailed measurements in a laboratory flume by
Blanckaert (2011) clarified these seemingly contradictory
results. Blanckaert (2011) found that the reduced effective
width is indeed more than offset by an increase of flow depth,
and that the flow globally decelerates along the outer bank.
But the cross-sectional flow patterns revealed that the velocity
increases near the toe of the outer-bank, where the bank is most
vulnerable to erosion. Flow separation at the inner bank that
directs the flow towards the outer bank thus influences the
patterns of bank erosion, bar formation and sedimentary deposits
(Burge and Smith, 1999).
This ‘sharp bend style’ of river bend development is often
associated with channels that have relatively strong banks
and limited meandering dynamics (Ferguson, 1987; Kleinhans
et al., 2009; see Kleinhans, 2010, for review), but have also
been observed in channels that are more laterally active
(Hickin and Nanson, 1975; Hodskinson and Ferguson, 1998;
Ferguson et al., 2003). According to Leeder and Bridges
(1975), inner-bank flow separation is largely controlled by the
ratio of channel width to centreline radius of curvature, B/R
and the Froude number Fr, whereby an increase in bend
tightness and Froude number favours flow separation. Bagnold
(1960), on the contrary, rejected the use of the Froude number
citing that separation in pipes is similar to separation in open-
channel flows, but Fr can only be defined for open-channel
flow. The role of turbulence in the generation of inner-bank
flow separation can also be important as highlighted by recent
K. BLANCKAERT ET AL.
Copyright © 2012 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms, (2012)

numerical (van Balen et al., 2010a) and experimental (Blanckaert,
2010) investigations. Blanckaert (201 1) compared the zone of
inner-bank flow separation in experiments with flat immobile
bed and mobile bed under similar hydraulic conditions. Results
indicated that the shallowing of the inner-bend in the mobile
bed experiments favours the onset of inner -bank flow separation.
Important remaining knowledge gaps concerning inner-bank
flow separation formation and dynamics therefore include:
(i) the parameters of influence, (ii) the conditions of occurrence,
(iii) the dependence on the streamwise variation of curvature,
(iv) the dependence on the roughness and inclination of the
inner bank, (v) the mechanisms underlying flow separation,
(vi) the interaction of the hydrodynamics with a mobile bed,
and (vii) the interaction with flow processes occurring at the
outer bank.
Outer-bank cell of secondary flow (vertical around a
streamwise axis)
Outer-bank cells of secondary flow occur in the cross-section
in the corner formed by the water surface and the outer bank.
They rotate with opposite helicity to the centre-region cell of
secondary flow, i.e. velocities at the water surface are directed
away from the bank. They have been observed in mildly as well
as sharply curved bends, and near steep as well as shelving
banks. Outer-bank cells have been observed long ago in the
laboratory (e.g. Mockmore, 1943; Einstei and Harder, 1954;
Rozovskii, 1957) and in the field (e.g. Hey and Thorne, 1975;
Bathurst et al., 1977, 1979; Bridge and Jarvis, 1977; Thorne and
Hey, 1979; de Vriend and Geldof, 1983; Dietrich and Smith,
1983; Thorne et al., 1985; Markham and Thorne, 1992).
The presence of an outer-bank cell widens the outer-bank
boundary layer by repelling maximum streamwise velocities
towards the inner edge of the outer-bank cell, which decreases
the hydrodynamic forcing on the outer bank. However, its
presence also advects high-momentum fluid originating from
near the water surface towards the lower part of the outer bank,
which tends to increase the hydrodynamic forcing. Based on
observations in a natural river, Bathurst et al . (1979) postulated
that the first effect is dominant, whereas Blanckaert and Graf
(2004) found the second effect to be dominant in a laboratory
flume with mobile bed and smooth vertical banks. Blanckaert
(2011) argues that the outer-bank cell reduces outer-bank
erosion and thus reduces meander migration.
More recent investigations have considerably enhanced
knowledge on the outer-bank cell. Experimental research has
recently focussed on the dominant generating mechanisms
Table I. Available experimental data including the three components of the mean velocity and turbulence characteristics in the near-bank zones.
Reference Configuration Measured physical quantities
Inner bank flow separation and recirculation
Frothingham and Rhoads (2003) Sharply-curved bend on the Embarras
River
Measurements including the three mean velocity
components on a relatively coarse grid
Ferguson et al. (2003) Two sharply-curved bends on the River
Dean
Measurements including the three mean velocity
components at a few points
Nanson (2010) Sharply curved natural bend with outer-bank
widening
Measurements including the three mean velocity
components at a few points
Blanckaert (2010, 2011) Sharply-curved laboratory flume with mobile
bed and smooth vertical banks.
Measurements with high temporal and spatial
resolution, including the three mean velocity
components, the six turbulent stresses, higher-order
turbulent correlations and the turbulent dissipation
rate.
Blanckaert (2011) Sharply-curved laboratory flume with flat
immobile bed and smooth vertical banks.
Schnauder and Sukhodolov (2012) Sharply-curved natural bend with outer-bank
widening
Measurements including the three mean velocity
components at a few points
Flow recirculation in outer-bank
widening
Nanson (2010) Sharply curved natural bend with outer-bank
widening
Measurements including the three mean velocity
components at a few points
Vietz et al. (2012) Sharply curved natural bend with outer-bank
widening
Measurements of velocity magnitude and direction
at a few points
Schnauder and Sukhodolov (2012) Sharply-curved natural bend with outer-bank
widening
Measurements including the three mean velocity
components at a few points
Parsons (2003) Sharply-curved bend on the River Dean with
outer-bank widening
Measurements including the three mean velocity
components at a few points
Outer-bank cell of secondary flow
Blanckaert and Graf (2001) Sharply-curved laboratory flume with natural-like
bed morphology and smooth vertical banks.
Measurements with high temporal and spatial
resolution, including the three mean velocity
components, the six turbulent stresses, higher-order
turbulent correlations and the turbulent dissipation
rate.
Blanckaert (2011) Sharply-curved laboratory flume with
– Flat immobile bed and smooth vertical banks
for three flow depths
– Flat immobile bed, rough vertical bank and
rough inclined banks
Blanckaert et al. (in press) – Sharply-curved laboratory flume with flat
immobile bed.
– Vertical bank with three different roughness
configurations
Jamieson et al. (2010) Sharply-curved laboratory flume with smooth
vertical banks and mobile bed
Measurements with high temporal resolution,
including the three mean velocity components
and the six turbulent stresses
Termini and Piraino (2011) Sharply-curved laboratory flume with smooth
vertical banks and mobile bed
Measurements including the three mean velocity
components
FLOW SEPARATION IN CONSTANT-WIDTH AND WIDENING OPEN-CHANNEL BENDS
Copyright © 2012 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms, (2012)

(Blanckaert and de Vriend, 2004), such as the effect of the rel-
ative curvature H/R (Blanckaert, 2011), the bank roughness
(Blanckaert et al., in press), bank inclination (Duarte, 2008;
Blanckaert, 2011), and bed morphology (Blanckaert and Graf,
2001; Blanckaert, 2010, 2011; Jamieson et al., 2010; Termini
and Piraino, 2011). Complementary numerical investigations
performed by van Balen et al. (2009, 2010a, 2010b), Constan-
tinescu et al. (2011) and Kang and Sotiropoulos (2011) have
also improved detailed process insight. Despite these recent
advances, important knowledge gaps remain, notably the inter-
action with the presence of inner-bank flow separation and the
relation to flow separation at the outer bank.
Flow separation and recirculation at the outer bank (horizontal
around a vertical axis)
Flow separation and recirculation at the outer bank has been
observed in many natural river bends, e.g. by Hickin (1977)
on the Beatton River, by Hickin (1978) on the Squarmisch
River, by Hickin and Nanson (1984) on various rivers in western
Canada, by Jackson (1992) on the Fall River, by Hodskinson and
Ferguson (1998) on the Allt Dubhaig, by Vietz et al.(2012)on
the Ovens River, by Schnauder and Sukhodolov (2012) on the
Tollense River, by Parsons (2003) on lowland sinuous channels
in north England, and in small sinuous channels on intertidal
mud flats (Kleinhans et al., 2009).
Flow separation at the outer bank can be driven by an
adverse water surface gradient at the outer bank (Blanckaert,
2010). This implies that flow separation at the outer bank
mainly occurs in regions of increasing curvature, thus upstream
of the bend apex, where transverse tilting of the water surface
slope increases and streamwise water surface gradient at the
outer bank diminishes. Blanckaert (2010) developed a required
condition for the onset of flow separation at the outer bank,
R/B < (05 C
f
–1
H/B)
1/2
, which suggests that outer-bank flow
separation is favoured in smooth and narrow rivers. Here C
f
is the dimensionless Chézy friction coefficient and H is the
overall-averaged flow depth. The onset of outer-bank flow
separation can also depend on the inflow conditions, notably
inflow asymmetry (Hodskinson and Ferguson, 1998). Furthermore,
the occurrence of flow separation at the inner bank that
directs the flow towards the outer bank may interact with the
development of flow separation at the outer bank.
Channel widening reduces the overall flow velocities and
promotes flow separation at the outer bank, but it is not clear
if it is a required condition as suggested by Hickin (1977).
The earlier mentioned field observations, however, typically
occurred at so-called outer-bank benches on sharply-curved
bends where the channel widens upstream of the bend apex
and has a shallow planar morphology. Their morphological
structure typically consists of a basal layer of coarse sediment
overlain by organic-rich, fine sediment (Woodyer et al., 1979;
Nanson and Page, 1983; Hickin, 1986; Erskine and Livingstone,
1999; Cohen, 2003; Vietz et al., 2012). The basal layer is due to
bar formation associated with high-energy flow environments
whilst the overlying fine layer is due to sediment deposition
in the low-energy flow environment associated with flow
separation. Outer-bank benches are thought to protect the outer
bank against erosion and to cause erosion at the inner bank
upstream from the bend apex (Hickin, 1977, 1978; Page and
Nanson, 1982; Markham and Thorne, 1992; Hodskinson and
Ferguson, 1998; V ietz et al., 2012). They can, however, also
enhance erosion downstream of the bend apex where flow
reattaches to the outer bank, as observed on the Tollense River
by Schnauder and Sukhodolov (2012). However, in that river,
vegetation stabilized the point bar at the inner bank and
prevented such erosion.
Notable knowledge gaps with respect to outer-bank flow
separation remain and include the overall conditions of
occurrence, the control parameters, the influence of the widening
geometry, the interaction with the inner-bank flow separation and
the outer-bank cell of secondary flow and the influence of the
flow–sediment interaction.
Detailed objectives
The knowledge gaps identified above may largely be attributed to
the paucity of detailed experimental data, which is highlighted in
Table I. All three processes of flow separation near the channel
banks identified earlier have been observed and measured in
natural rivers, but with a spatial resolution and an accuracy that
are insufficient for a detailed analysis of their hydrodynamic
characteristics and a reliable validation of numerical models.
High-resolution and high-accuracy laboratory data are not yet
available for flow separation and recirculation at the outer bank,
and limited to one dataset over a flat immobile bed and one
dataset over a mobile bed for flow separation and recirculation
at the inner bank (Table I).
This paper reports on a set of laboratory experiments in a
schematized configuration intended to isolate and accentuate
these near-bank hydrodynamic processes, and to investigate
them with an accuracy exceeding that, which could possibly
be obtained in a field study. The main objectives of the present
paper are: (i) to provide detailed experimental data on the
hydrodynamic and morphodynamic characteristics within
sharp bends, with focus on the near-bank flow processes;
(ii) to investigate the influence of an outer-bank widening on
the hydrodynamic characteristics, and in particular on the
distinct processes of near-bank flow separation; (iii) to explore
the influence of the interaction of the flow with bedload
sediment transport on the three processes of near-bank flow
separation with a view to understanding their morphological
significance, and (iv) to contextualize and discuss the results
and to provide guidelines for future research.
The next section details the methods employed to obtain the
experimental results. The third section reports and analyses the
main experimental observations. The fourth section discusses
and contextualizes the results, and provides avenues for future
research.
Methods
Experiment design
The three processes of flow separation from the banks were
investigated in a series of dedicated laboratory flume experiments
with a variety of measurement methods. A bespoke flume chan-
nel with two bends was created within the Total Environment
Simulator (TES) facility at the University of Hull (Figure 1). The
constructed channel had fixed walls, a width of 1 m and a length
along the centreline of approximately 15m. The vertical channel
walls were constructed of Plexiglas at high precision and fixed in
position within the 12 m 6 m basin. As previous research
indicated the importance of the ratio of channel width to bend
radius, R/B with respect to flow separation, bend radius was
varied with radii of R =1m and R = 2 m in the first and second
bend, respectively. Moreover, the second bend was widened in
the outer bank region (Figure 1). Experiments were conducted
with both immobile-bed and mobile-bed conditions.
Three scaling conditions (Table II) were posed for the immobile-
bed experiments. First, the Shields number (θ) was well below
critical for motion. Second, the flow was subcritical, that is,
K. BLANCKAERT ET AL.
Copyright © 2012 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms, (2012)

the Froude number (Fr) was smaller than unity and the flow was
in the rough turbulent regime (Re > 2000 and Re
*
= uk
s
/n > 70,
where k
s
is the equivalent sand roughness of the channel bed).
Third, the backwater adaptation length was of the order of the
flume length so that the gradient was controllable by the
downstream water level, and the flow would thus be quasi-
uniform. The gravel of the immobile bed was unimodal with
D
10
=97 mm, D
50
=118 mm and D
90
=145 mm. The longitu-
dinal gradient (S) of the gravel bed was set to S =210
–3
.At
the upstream end coarser gravel was used to prevent initial in-
flow erosion and shorten the length of boundary layer adapta-
tion from the flume inlet.
The mobile-bed condition was designed to represent low-
energy lowland rivers with relatively strong banks and a bedload
dominated sediment transport regime with dune bedforms
(Table II). Bedload transport domination also enables detailed
flow measurement which would be very difficult if suspended
sediment was the dominant transport mechanism. The mobile
bed consisted of unimodal coarse sand with D
10
=0 61 mm,
D
50
=076 mm and D
90
=094 mm, which was coarse enough
to prevent the formation of ripples and promote formation of
dunes and bars with limited suspended sediment deposition on
the bars. The width/depth ratio was kept small at 83 compared
to natural channels to promote fixed alternating bars and prevent
under-damped bars and ‘overshoot’ phenomena (Struiksma
et al., 1985). The mean gradient of the bed was set to the same
as in the immobile-bed experiment at S =210
–3
. Transported
sediment was collected in a downstream trap and the entire
collected volume was recirculated in units of about 9 l per
10 minutes to ensure there was no net erosion or deposition
through the flume. The bedload dominance and the width/depth
ratio represents rivers such as the upper Columbia River
(Kleinhans et al., 2012), where strong cohesive banks cause
nearly straight channels with occasional sharp bends and a
width/depth ratio of 10 for the smaller branches, and exactly
damped bars covered by dunes.
Table II provides the basic hydraulic conditions in the experi-
ments and are based on detailed flow measurements in
the cross-section 38 m upstream of the first bend. In the
immobile-bed experiment, 13 vertical profiles were measured
in one half of the (symmetrical cross-section), whereas 15
vertical profiles were measured over the entire width of the
cross-section in the mobile-bed experiment. The discharge
(Q) was obtained by integration of the measured velocity field.
The shear velocity u
*bed
within the experiment has been
estimated from different methods described by Nezu and
Nakagawa (1993): (i) fitting a log law to the measured near-
bed velocity profile; (ii) fitting a linear profile to the measured
streamwise-vertical turbulent shear stress; (iii) fitting an
exponential profile to the measured streamwise turbulent
6 5 4 3 2 1 0
0
1
2
3
4
5
6
7
8
9
10
11
Y [m]
X [m]
upstream Q boundary
downstream H boundary
Upstream section U
first bend
Middle sec M
second bend
Downstr sec D
channel axis
channel walls
circle centres
LS−PIV
3D PIV
ADVP
levels bed & water
Figure 1. Map of the bespoke flume channel created within the Total
Environment Simulator (TES) at Hull University. Flow is from bottom to
top (scale in metres). Circular bends are constructed from Perspex. The
legend in the insert provides information on the locations of the
measurements by means of pressure transducers, Large Scale Surface
Particle Image Velocimetry (LS-PIV), three-dimensional Particle Image
Velocimetry (3D-PIV), an Acoustic Doppler Velocity Profiler (ADVP)
and a manual point gauge (bed and water surface levels).
Table II. Hydraulic and geometric conditions in the here reported experiments and in the similar experiments performed by Blanckaert (2010, 2011).
Label
Q
(l s
–1
)
Q
s
(kg s
–1
m
–1
)
H 
0005 (m)
U
(m s
–1
)
(g/C
f,bed
)
1/2
(m
1/2
s
–1
)
u
*,bed
(m s
–1
)
E
s
(10
–4
)
Re
(10
3
)
Fr
(—)
B/H
(—)
R/B
(—)
C
–1
f,bed
H/B
(—)
θ
(deg)
Hull_Immobile
(present paper)
117 — 021 055 4040042 10 117 038 4710 (first bend) 35890
20 (second bend)
Hull_Mobile
(present paper)
49 0026 012 041 2280056 17 49 037 8310 (first bend) 6490
20 (second bend)
EPFL_Immobile
(Blanckaert,
2009, 2011)
89 — 016 043 3840035 8569035 82131 264 193
EPFL_Mobile
(Blanckaert,
2010)
89 0023 014 049 2550060 26768041 92131 8
6 193
Note: Q is the flow discharge, q
s
the sediment discharge, H the flow depth, U = Q/(BH) the overall-averaged velocity, C
f,bed
the dimensionless Chézy
friction coefficient for the bed, u
*,bed
the shear velocity on the bed, E
s
is the average energy slope based on the measured water and bed elevations,
Re = UH/n is the Reynolds number,Fr ¼ U=
ffiffiffiffiffiffiffi
gH
p
the Froude number, B the flume width, R the radius of curvature of the bend, C
f
-1
H/B a parameter that
characterizes a river reach (Blanckaert, 2011) and θ the opening angle of the bend.
FLOW SEPARATION IN CONSTANT-WIDTH AND WIDENING OPEN-CHANNEL BENDS
Copyright © 2012 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms, (2012)

Frequently asked questions

Q1. What causes the scour at the projection of flow onto the outer bank?

Flow separation is promoted in sharp bends due to flow inertia, which forces the flow to abandon the inner bank and causes deep scour at the projection of flow onto the outer bank. 

Q2. What have the authors contributed in "Flow separation at the inner (convex) and outer (concave) banks of constantwidth and widening openchannel bends" ?

Herein the authors report on successful laboratory experiments that elucidate flow structure in one constant-width bend and a second bend with an outer-bank widening. 

Q3. What have the authors stated for future works in "Flow separation at the inner (convex) and outer (concave) banks of constantwidth and widening openchannel bends" ?

The paper discussed the parameters of influence of the investigated flow processes, and discussed how insight can be further enhanced by using the data in complementary combined experimentalnumerical research. Acknowledgements—Experimental data reported in this paper can be obtained from the authors: ADVP data from Blanckaert, 3D-PIV data from McLelland, LS-PIV data from Kleinhans, bed elevation data from Blanckaert and Kleinhans. 

Q4. What is the main driving force for flow separation at the inner and outer banks?

The pronounced bed morphology reduced the curvature-induced transverse tilting of the water surface, which is a major driving force for flow separation at the inner and outer banks. 

Q5. What is the common cause of a reduction in bend sharpness?

Flow separation in outer-bank widenings is often associated with the high-velocity flow impinging on the outer-bank downstream from the apex, and erosion of the inner bank and the associated depositional bar upstream of the bend apex, which can lead to a reduction in bend sharpness (Page and Nanson, 1982; Hodskinson and Ferguson, 1998; Vietz et al., 2012). 

Q6. How many imaging areas were used to provide a complete cross-section map of the three velocity?

Data were collected from about 10 imaging areas across the channel width in the first bend to ensure complete section coverage with at least 50% overlap between each vector map. 

Q7. How many vertical profiles were measured in the immobile-bed experiment?

In the immobile-bed experiment, 13 vertical profiles were measured in one half of the (symmetrical cross-section), whereas 15 vertical profiles were measured over the entire width of the cross-section in the mobile-bed experiment. 

Q8. How were the flow rates monitored and controlled?

Flow rates were monitored and controlled by continuous measurement with an electromagnetic flow meter in the pump circuit and a micro-propeller in the flume inlet, placed at 35% of the water depth above the bed. 

Q9. What was the effect of topographic steering on the flow?

Topographic steering induced an expansion of the flow, whereby the major part of the discharge was conveyed in the central part of the widening section. 

Q10. What is the effect of the immobile-bed experiment on the flow?

With sufficient accumulation of sediment, topographic steering of the flow around the shallow zones into the deep zonesIV measurements in the immobile-bed experiment. 

Q11. Where does the depositional bar at the innerbank reach its maximum height and width?

Scour at the outer-bank increases towards the bend exit, reaching amaximumat the bend exit (90 cross-section) where the depositional bar at the innerbank also reaches its maximum height and width. 

Q12. What is the dominant control parameter for bend morphodynamics?

According to Blanckaert and de Vriend (2010), however, Cf–1H/B and B/R are the dominant control parameters with respect to the flow redistribution in open-channel bends. 

Q13. What is the effect of increasing the width of a constantwidth bend on flow?

Increasing the width in a constantwidth bend reduces the interaction between flow processes at the inner and outer banks (e.g. Hodskinson and Ferguson, 1998). 

Q14. What is the onset of flow separation at the outer bank?

This implies that flow separation at the outer bank mainly occurs in regions of increasing curvature, thus upstream of the bend apex, where transverse tilting of the water surface slope increases and streamwise water surface gradient at the outer bank diminishes. 

Q15. What conditions are required for the onset of flow separation at the outer bank?

Blanckaert (2010) developed a required condition for the onset of flow separation at the outer bank, R/B< (0 5 Cf–1H/B)1/2, which suggests that outer-bank flow separation is favoured in smooth and narrow rivers. 

Q16. What was the method used to obtain detailed flow measurements within the flume?

A range of methodologies was employed to obtain detailed flow measurements within the flume, including Large Scale Surface Particle Image Velocimetry (LS-PIV), three-dimensional Particle Image Velocimetry (3D-PIV) and measurements with an Acoustic Doppler Velocity Profiler (ADVP). 

Q17. What is the definition of a required condition for flow separation at the outer bank?

Channel widening reduces the overall flow velocities and promotes flow separation at the outer bank, but it is not clear if it is a required condition as suggested by Hickin (1977). 

Q18. What is the definition of the schematized laboratory open-channel bend?

this schematized laboratory open-channel bend cannot be representative of the infinite range of configurations found in nature, which differ in geometric (planform and corresponding evolution of the radius of curvature, width, depth, bank configuration), sedimentological (sediment size and gradation, stratigraphy) and hydraulic (Froude number, Reynolds number, inflow conditions, boundary roughness) characteristics.