AN ABSTRACT OF THE THESIS OF
William J. L’Hommedieu for the degree of Master of Science in Water Resources
Engineering presented on August 27, 2014.
Title: Effects of an Engineered Log Jam on Flow Structure and Complexity.
Abstract approved:
______________________________________________________
Desirée D. Tullos
Julia A. Jones
The installation of engineered log jams (ELJs) is a common river restoration practice,
implemented to modify flow structure and increase hydraulic complexity for the
benefit of streambank protection and fish habitat. However, few studies have directly
assessed the effects of ELJs on flow structure and complexity. This study presents a
comprehensive approach to assess the effects of a meander ELJ on flow structure and
complexity, defined herein as spatial pattern and spatial variance, respectively. A 2D
hydrodynamic model, iRIC SToRM, was used to simulate flow conditions in a 77m
reach of the Calapooia River, Oregon with and without an ELJ at 1%, 20%, and 62%
ELJ submergence. The simulated flow field was analyzed using coherent flow
structure identification, maps of turbulence measures, and wavelet analysis along
linear transects. Generally, once submerged, the ELJ appeared to primarily rearrange
the spatial pattern of flow and not affect turbulence metric magnitudes. For example,
at high flow, representing 62% ELJ submergence, a greater number of coherent flow
structures was identified in the ELJ model than in the no ELJ model run, but the
magnitudes of turbulence metrics were unaffected. At low flow, representing 1% jam
submergence, the presence of the ELJ did not affect the number of coherent flow
structures identified, but was responsible for a localized effect on turbulence metric
magnitudes. Furthermore, results indicated that the meander jam decreased the size of
the eddies in the vicinity of the jam at higher flows, with practical implications
associated with the reduction of erosive energy of flow and potentially more
favorable fish habitat at higher flows when low energy refuge habitat is often limiting
for fish. Taken together, results indicate a lack of impact of the ELJ on flow
complexity and greater impact on flow structure. In addition, the methods used in this
study for characterizing flow structure and complexity may be applied to guide future
restoration projects and to assess effectiveness of restoration designs.
©Copyright by William J. L’Hommedieu
August 27, 2014
All Rights Reserved
Effects of an Engineered Log Jam on Flow Structure and Complexity
by
William J. L’Hommedieu
A THESIS
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Master of Science
Presented August 27, 2014
Commencement June 2015
Master of Science thesis of William J. L’Hommedieu presented on August 27, 2014
APPROVED:
Major Professor, representing Water Resources Engineering
Director of the Water Resources Graduate Program
Dean of the Graduate School
I understand that my thesis will become part of the permanent collection of Oregon
State University libraries. My signature below authorizes release of my thesis to any
reader upon request.
William J. L’Hommedieu, Author
ACKNOWLEDGEMENTS
I would like to thank my advisors, Desirée Tullos and Julia Jones, for the immense
amount of guidance and encouragement they have provided. I would also like to
thank Cara Walter whose technical savvy in any number of areas saved me
throughout my research. I would like to thank Desirée Tullos, Cara Walter, Lisa
Thompson, Sam Box, and John Hammmond for assisting me in sometimes
treacherous fieldwork. A portion of this research was conducted in Scotland, and as
such I would like to thank Scott Arthur and Heriot-Watt University. This research
was made possible by the National Science Foundation. Lastly, I would like to thank
my friends in the Water Resources Graduate Program, without whose camaraderie
this endeavor would not have been possible.
TABLE OF CONTENTS
Page
1. Introduction………………………………………………………..……………..1
2. Methods……….……….……….……….……….……….……….……….……..3
2.1 Study Site.……….……….………….……….……….……….……………..3
2.2 Field Measurements.……….……….………….……….……….……….…..6
2.3 Hydrodynamic Model…….……….………….……….……….……….……7
2.4 Post-Processing Data……….……….……….……….…….……….………..9
2.5 Coherent Flow Structure Identification………………………………………9
2.6 Turbulence Metrics…………………………………………………………..10
2.7 Wavelet Analysis…………………………………………………………….10
3. Results……….……….……….……….……….……….……….……….............11
3.1 Calibration and Validation…………………………………………………...11
3.2 Flow Simulation……………………………………………………………...12
3.3 Coherent Flow Structure Identification………………………………………13
3.4 Turbulence Metrics…………………………………………………………...15
3.5 Wavelet Analysis……………………………………………………………..19
4. Discussion……….……….……….……….……….……….……….……………19
5. Conclusion……….……….……….……….……….……….……….……………23
6. References……….……….……….……….……….……….……….……………25
7. Appendix……….……….……….……….……….……….……….……………..28
LIST OF FIGURES
Figure
Page
1. Conceptual diagram of flow structure and complexity……………………………3
2. Study site……………………………………………..............................................5
3. Photo of the engineered log jam…………………………………………………...6
4. Flow simulation…………………………………………………...........................12
5. Coherent flow structure identification…………………………………………….13
6. Vortex radius distribution…………………………………………………………16
7. Maps of turbulence metrics………………………………………………………17
8. Wavelet plots of right transect at low flow……………………………………….21
LIST OF TABLES
Table
Page
1
Calibration and validation……………………………………………….. 11
2
Coherent flow structure identification summary…………………………. 15
3
Wavelet analysis by discharge………………………….………………... 20
4
Wavelet analysis by transect…………………………...………………… 20
Effects of an Engineered Log Jam on Flow Structure and
Complexity
William L’Hommedieua, Desirée Tullosb and Julia Jonesc
a
b
Water Resources Engineering, Oregon State University, Corvallis, OR, USA
Biological and Ecological Engineering, Oregon State University, Corvallis, OR, USA
c
Geography, Oregon State University, Corvallis, OR, USA
1. Introduction
Large wood plays an important role in the ecology and morphology of Pacific Northwest
(PNW) rivers, yet wood accumulations in rivers have declined over the last century
(Montgomery et al., 2003) due to logging and to efforts to increase flood conveyance. The
reduction in wood accumulations, and associated simplification of channels, has been associated
with a decrease in the fish habitat complexity and cover (Pess et al., 2012). Subsequently,
engineered log jams (ELJs) have been implemented to re-introduce habitat complexity to
simplified channels (Abbe et al., 2002), justified in part by their potential contribution to the
development of eddies and more complex flow structures, which fish use for foraging (Fausch,
1984), navigation (Liao et al., 2003), and resting (Liao, 2007). Given that complex flow
environments are generated by large roughness elements, such as boulders and large wood
(Crowder amd Diplas 2006; Gippel 1995), as well as channel planform features, such as meander
bends (Daniels and Rhoads, 2004), river restoration efforts to reintroduce complexity have
largely emphasized the reintroduction of roughness elements or channel re-meandering
(Bernhardt et al., 2005).
Although restoration projects aimed at increasing flow complexity are becoming more
common, quantitative evaluation of their success is lagging. Flow structure has multiple
definitions (e.g., Alfonsi, 2006), but can be defined as a spatially contiguous region of the flow
field in which flow variables exhibit significant correlations (Robinson, 1991). Flow structure is
2
typically assessed through coherent flow structure eduction (Adrian et al., 2000). The highresolution data required for coherent flow structure eduction is difficult to obtain from field
measurements and as such the analysis is typically performed on small-scale laboratory
experiments or numerical models. Channel complexity has been defined in various ways,
including the spatial variability of hydraulic metrics (Kozarek et al., 2010), of channel
topography (Lepori et al., 2005), and of thalweg depth and the volume of large woody debris
(Kaufmann and Faustini, 2012). In application, flow complexity has been assessed using
statistical measures describing the turbulent flow field, such as kinetic energy gradient, vorticity,
circulation, and hydraulic strain (Crowder and Diplas 2006); the hydromorphological index of
diversity (HMID) (Gostner et al., 2013); and physical biotopes, which are regions of discrete
hydraulic conditions, such as a riffle or a glide (Newson and Newson, 2000). However, HMID
lacks ability to account for localized effects in flow structure and thereby link to habitat (Gostner
et al., 2013), and biotopes are difficult to define because of the overlap between depth, velocity,
and Froude number (Harvey et al., 2008). Thus, while techniques for more comprehensive
characterization of the flow field exist in the field of fluid mechanics, they have largely lacked
application in the study of habitat restoration (but see Harrison et al., 2011; Kozarek et al., 2010)
due to challenges in acquiring adequate field data, computational resource demands, and a lack
of relevant links to ecosystems.
This study examined the response of flow structure and complexity to a meander ELJ
over a range of submergence depths in a low-gradient, fine-bedded reach of a hand-dug
secondary channel of the Calapooia River, Oregon. Flow was measured and simulated using a
2D hydrodynamic model, and flow structure and complexity were evaluated around an ELJ at
3
varying depths of submergence, at the local and reach scales (Figure 1). We evaluated the effects
of ELJs by means of spatial pattern, defined as visual assessment of mapped coherent flow
structures and turbulence metric magnitudes; heterogeneity, defined as variability of turbulence
metrics at multiple spatial scales, and patchiness, the number, size, and arrangement of areas of
definable flow conditions (Figure 1). Multi-scale heterogeneity was evaluated using wavelet
analysis of hydraulic metrics along longitudinal and transverse transects (Figure 1).
Figure 1. Conceptual diagram of components of flow structure and complexity, as well as techniques used to assess
the effects of the ELJ on flow structure and complexity, and their associated scales of analysis. Coherent flow
structure identification (CFS), maps of the magnitudes for statistical measures of the flow field, and wavelet analysis
of statistical measures along defined transects were used to characterize the flow structure and complexity.
2. Methods
2.1 Study site
Field observations for this study were collected in the Sodom Channel section of the
Calapooia River (latitude 44°24'29.42"N,longitude 123° 2'33.86"W), a tributary of the
Willamette River (Figure 2). The Calapooia River, originating in the Western Cascades, drains a
moderately steep (gradient of 0.44 to 1.94%), 947 km2 catchment of predominantly privately
owned forestlands (Kibler et al., 2010). The Sodom Channel was constructed in the 1800’s as a
4
high water diversion to minimize downstream flooding, but planform changes resulted in the
Sodom Channel receiving the majority of the flow year round (Calapooia Watershed Council,
2014). In 1890 a dam was constructed in the Sodom Channel to ensure that the historical
Calapooia River channel would receive water during low flows. The dam was later determined to
be a partial barrier to fish passage for federally listed threatened salmonid species (Calapooia
Watershed Council, 2014). The dam was removed in 2011, and the channel was reconfigured to
include grade control structures to in order to maintain a prescribed flow split between the
historical Calapooia River and the Sodom Channel, and ELJs to stabilize banks and create
habitat.
The study area consisted of a 77 m reach, representing 2.5 channel widths, located 200 m
downstream of the bifurcation of the historic Calapooia River and the Sodom Channel. The study
reach was bounded upstream and downstream by grade control riffle structures, creating a rifflepool morphology at low flows. The change in elevation from riffle-crest to riffle-crest was 1.4 m.
The ELJ in this study was a meander jam composed of several large key pieces embedded in the
bank with smaller logs interspersed within the key pieces (Figure 3).
5
Figure 2. Map and contour diagram of field site on the Sodom Channel of the Calapooia River.
The field site is indicated by the circle on the map. In the contour diagram of the study reach the
surveyed transects are shown by solid black lines (left) and wavelet transects are depicted in
dashed black lines (right). The location of the ELJ is indicated in the shaded gray region.
Contours are given in 1m intervals.
6
Figure 3. Photograph of the ELJ at 20% submergence. The ELJ is composed several large key
pieces embedded in the bank and smaller pieces wedged between the key pieces.
2.2 Field Measurements
Channel bathymetry was surveyed in February of 2013 and ground topography was
surveyed in March of 2013 (Valverde, 2013). Surveys included six cross-sections along the
reach, located 20m upstream of the ELJ, at the upstream and downstream faces of the ELJ, and at
11 m, 33 m, and 47 m downstream of the ELJ (Figure 2). In addition to the cross-sections,
elevations were surveyed along members of the ELJ, at ground points surrounding the ELJ, and
in some wadeable areas of the channel. Topography around the ELJ and within the wadeable
portions of the channel was surveyed using a Topcon GR-3 Real Time Kinematic (RTK) Global
Positioning System (GPS). In-channel bathymetry was surveyed using a raft-mounted Teledyne
WorkHorse Rio Grande Acoustic Doppler Current Profiler (ADCP) paired with RTK GPS. The
topographic dataset covered the active channel and part of the floodplain on either side of the
7
channel, with an average density of 2.1 points/m2.
Water surface elevations were collected along the reach to use as boundary conditions on
the inlet and outlet of the hydrodynamic model, as well as for model calibration and validation.
Water surface elevation data were collected from December 2013 to February 2014 at discharges
of 123.3 m3/s, 32.6 m3/s, and 5.6 m3/s corresponding to the 0.03%, 8.5%, and 48% duration
flows as calculated from hourly streamflow data. These discharges represented 77%, 56%, and
46% of bankfull flow depth conditions and ELJ submergence depths of 62%, 20% 1%,
respectively. Blockage ratios, calculated as the portion of the cross sectional flow occupied by
the ELJ, were 0.09, 0.06, and 0.03, for the 123.3 m3/s, 32.6 m3/s, and 5.6 m3/s discharges,
respectively. Water surface data were collected using ADCP, GPS, and crest gages. Crest gages
were installed, according to Sauer and Turnipseed (2010), on the right and left bank of the four
upstream cross sections and along the right bank on two farthest downstream cross sections.
Velocity observations were collected to verify the use of a local gauge, located 2.3km
downstream of the study area, to represent discharge at the study site. For validating the use of
the downstream gauge, discharge was measured using the StreamPro during a low flow period at
a discharge of 9 m3/s. Discharge measured at the study site differed from discharge at the
downstream gauge by only 2.6% (Valverde, 2013), and no tributaries contribute flow between
the study site and the downstream gage.
2.3 Hydrodynamic Model
A spatially distributed hydrodynamic model was developed using the International River
Interface Cooperative (iRIC) software with the System for Transport and River Modeling
(SToRM) model (Simões, 2013). Inputs of discharge, topography, roughness, and upstream and
8
downstream stage were used to predict the two-dimensional, depth-averaged spatial distribution
of water surface elevation, depth, and velocity. SToRM uses a finite-volume discretization
scheme and a zero-equation turbulence closure method. The governing equations of the shallowwater Navier-Stokes equations were solved in an unstructured, triangular element grid.
Model development consisted of generating a computational mesh and simulating a
steady discharge over the mesh to determine the appropriate spin-up period. The model grid was
approximately 77 meters in length, 65 meters wide, and composed of 21,835 computational
nodes, with an average area of 0.20 m2 per node. The ELJ was represented in the model as a nonporous object by raising channel bed elevation in the region of the ELJ to the surveyed ELJ
elevations. A second model grid was generated by removing the topography data associated with
the ELJ to simulate a scenario without the ELJ. The models were simulated at a steady discharge
for 200 seconds with a time step of 0.01 seconds for the three simulated discharges. Model
simulations were determined to converge when velocities reached equilibrium after 150 seconds,
based on visual inspections of velocity-time plots. Model output data for time steps before 150
seconds were discarded for all simulations. Discharges of 5.6 m3/s, 32.6 m3/s, and 123.3 m3/s
were simulated for analysis and calibration, and an additional discharge of 9 m3/s was simulated
for validating the model.
Model calibration and validation were conducted by comparing simulated and observed
water surface elevations (WSEs). The model was calibrated by adjusting the roughness
parameter to minimize the difference between simulated and observed WSEs. Roughness was
characterized in this study using Manning’s n, which was assumed to be spatially uniform across
9
the study reach. For both calibration and validation, differences between simulated and observed
WSEs were quantified using the root mean squared error (RMSE).
2.4 Post-Processing Data
Simulated output data was exported to Matlab for post-processing (MATLAB version 7.13.0.564
R2011b). Average x and y velocity components, as well as average resultant velocities were
calculated from the time-series data at each computational node. In order to facilitate the
calculation of hydraulic metrics described in section 3.3.3, a regularly spaced 0.4m grid was
generated within Matlab and turbulence metrics were mapped to the grid using linear
interpolation.
2.5 Coherent Flow Structure (CFS) Identification
Coherent flow structures, in the form of vortices within the two-dimensional flow field,
were identified using proper orthogonal decomposition (POD), coupled with a closed streamline
algorithm (see Appendix A and B). Spatial pattern was assessed based on maps of resulting
coherent flow structures (vortices), depicted as circles representing the diameter, onto vector
plots of velocity. Each coherent flow structure was considered to be a patch, and patchiness was
evaluated based on the number of coherent flow structures identified (similar to the biotope
patchiness index used by Padmore [1997]), and the fraction of wetted area occupied by coherent
flow structures (Figure 1).
10
2.6 Turbulence statistics
Three turbulence measures were calculated at all computational mesh nodes in each
model. Reynolds Stress (τ uv ), was calculated (Eq. 1) as the intensity of velocity fluctuations from
the time-ensemble average, where ρ is the density of water and u’ and v’ are instantaneous
velocity components in the x and y directions, respectively. Reynolds stress represents the
temporal variability of the flow that fish appear to avoid (Smith et al., 2005). Hydraulic strain
(S 1 ) was calculated (Eq. 2) as the spatial gradient of velocities, where u and v are the time
averaged velocity components and δx and δy are the grid spacing in the x and y directions,
respectively. Hydraulic strain represents the strength of deformation in the flow field, which fish
use to navigate and select habitat (Goodwin et al., 2006; Nestler et al., 2008). Vorticity (ζ) was
calculated (Eq. 3) as twice the angular velocity around the vertical axis of the flow, providing
information on the rotational nature of the flow (Crowder and Diplas, 2002). At high levels of
vorticity, fish have been shown to lose their ability to hold position (Tritico and Cotel, 2010).
������|
��� = |−��′�′
��(1)
��
��
��
��
�+� �+� �
�1 = � � + �
��
��
��
��
2.7 Wavelet Analysis
�� ��
�=�
−
�
�� ��
��(2)
��(3)
Wavelet analysis was conducted following methods in Torrence and Compo (1998) for
simulated data on resultant velocity magnitudes, Reynolds stress, hydraulic strain, and vorticity
(4 properties) with and without ELJ (2 scenarios) for different discharge (3 levels) along 4
longitudinal transects and 3 cross-sectional transects (Figure 2), resulting in a total of 168
wavelet analyses. Results were displayed as contoured plots of wavelet power. For each of the
11
84 pairs of plots with and without ELJ (4 properties x 3 discharge x 7 transects) the difference in
the wavelet power between the “with ELJ” and the “without ELJ” wavelet plot was visually
assessed. The assessment included the entire reach, not just the region around the ELJ, to identify
proximal and distal effects. Based on visually assessed differences in these paired plots, the
numbers of pairs of plots with increased (+) or decreased (-) wavelet power were counted by
property, by discharge, and by transect.
3. Results
3.1 Calibration and Validation
The model was calibrated by adjusting the spatially-uniform roughness parameter,
Manning’s n. Consistent with other studies (Horritt and Bates, 2002), roughness values used for
the 2D hydrodynamic models (Table 1) were considerably lower than the Manning’s n value of
0.033 expected from look-up tables based on one-dimensional models (Arcement and Schneider,
1989). A sensitivity analysis revealed that a 10% change in the Manning’s n value resulted in
less than a 1 cm change in WSE RMSE. The low sensitivity of the WSE to the roughness
parameter may have been due to the short extent of reach, and the fixed water surface elevations
of the inlet and outlet set in the model.
Table 1. Summary of Manning’s n values used for calibration and error between modeled and
observed water surface elevations (WSE), reported using RMSE, as well as error between the
validation water surface elevations (RMSE).
Calibration
Discharge (m3/s)
Manning’s n
WSE RMSE (m)
5.6
0.020
0.07
32.6
0.015
0.10
123.3
0.010
0.13
Validation
Discharge (m3/s)
Manning’s n
WSE RMSE (m)
9.0
0.020
0.02
3.2 Flow Simulation
12
Velocity, in all of the scenarios, was highest at the inlet, where flow cascaded over a
constructed riffle at lower flows and formed a high velocity jet at higher flows. At intermediate
and high discharge, a high velocity core formed and recirculation zones developed (Figure 4b
and 4c). The regions of highest velocity appeared to overlap with the greatest depths in the
narrower first half of the reach, but downstream of the large expansion of flow, the high velocity
core shifted towards river left and did not coincide with the region of greatest depth (e.g., Figure
4c vs. 4f). Flow simulations without the ELJ exhibited the same pattern with regards to velocity
and depth.
Figure 4. a), b) c) Velocity magnitude as a function of location (x and y (m)) and d), e), f) depth
for 6 m3/s, 33 m3/s, and 123 m3/s discharges modeled, respectively, with the ELJ. At higher
discharges (b,c) a higher velocity core formed as well as recirculation zones just downstream of
13
the inlet of river left (45 m E, 20 m N) and on river right near where the flow expands
considerably (50 m E, 70m N). Areas of high velocity did not correspond with areas of greatest
depth (b vs. e and c vs. f)
3.3 Coherent flow structures
The presence of the ELJ altered the spatial pattern and the patchiness of flow. The
locations, number, and size of flow structures differed with versus without the ELJ, over the
three simulated discharges, both in close proximity to the ELJ as well as upstream and
downstream of the ELJ. For all of the simulated discharges, there were more, and generally
smaller, vortices identified on the right extent of the flow, in simulations with the ELJ compared
to the no ELJ simulations (Figure 5).
14
Figure 5. Vector plots of simulated discharges of 5.6 m3/s (a,b), 32.6 m3/s (c,d), and 123.3 m3/s
(e,f) are displayed with the ELJ (a,c,e) and without the ELJ (b,d,f) . Vortices identified are shown
using red circles whose diameter corresponds to the diameter of the vortices.
There were more vortices at intermediate and low discharge in model runs with ELJ
15
compared to no ELJ, but irrespective of discharge, the presence of the ELJ had a very small
effect on the area affected by vortices (Table 2). As discharge increased, the number of vortices
and the area affected by vortices declined, both with and without the ELJ (Table 2). At higher
discharges the presence of the ELJ shifted the size distribution of vortices toward more
numerous, smaller vortices; this effect was most pronounced at high discharges (Figure 6).
Table 2. Results of POD vortex identification for each model.
Model
Number of Vortices
Fractional Area (%)
6 m3/s ELJ
6 m3/s no ELJ
33 m3/s ELJ
33 m3/s no ELJ
123 m3/s ELJ
123 m3/s no ELJ
21
21
18
15
16
12
26
27
18
18
19
18
3.4 Turbulence measures
At low flow, the spatial pattern of velocity and turbulent flow metrics (hydraulic strain,
Reynolds stress, and vorticity) was locally affected by the presence of the ELJ. Flow was
deflected around a key member of the ELJ that extended into the flow field, producing an
increase in velocity and all three turbulent flow metrics around the tip of the jam. (Figure
7a,c,e,g). Spatial patterns of turbulent flow metrics were unaffected by the ELJ at intermediate
and high discharge.
16
Figure 6. Plots of identified vortices’ radii. Identified vortices are organized and ranked in order
of ascending radius size. The rank number of each vortex, written here as vortex number, is
given on the x-axis, while the radius of the vortex is given on the y-axis. At higher discharges the
ELJ models exhibited a greater number of vortices than the no ELJ models, as seen by greater
vortex number. Additionally, at higher discharges the ELJ model exhibited a shift in distribution
towards a greater number of small-scale vortices, as seen by the longer line for the ELJ models at
low radius.
17
18
Figure 7. Velocity (a,b), Reynolds stress (c,d), hydraulic strain (e,f), and vorticity (g,h), plots
with identified vortices for the 6 m3/s models. Plots on the left are the ELJ models and plots on
the right are the no ELJ models. Circles indicate the location and diameters of coherent flow
structures and the red box indicates the region affected by the ELJ.
19
3.5 Wavelet analysis
Only 2 of 84 wavelet analyses (2.4%) showed an increase, while 27 (32%) showed a
decrease in wavelet power with ELJ compared to without ELJ, indicating little increases, but
some decreases in heterogeneity of turbulence metrics with ELJ (Table 3). Decreases in
hydraulic strain and vorticity dominated the responses (Table 3) and these changes occurred in
all transects (Table 4). Decreases in heterogeneity occurred throughout the reach, while the two
increases in heterogeneity in Reynolds stress and vorticity increased close to the ELJ, in the
right longitudinal transect, at low discharge (Table 4, Figure 8). Decreases in heterogeneity
were more frequently observed in the lower discharge scenarios than at the highest discharge
(Table 3).
4. Discussion
This study sought to address the benefits of an ELJ by assessing its impact on flow
structure and complexity at varying levels of submergence, through coherent flow structure
identification, maps of turbulence metrics, and wavelet analysis along linear transects. Coherent
flow structure identification indicated that the ELJ increased the patchiness of the fluvial
landscape at higher flows, but not at lower flows, shifting the distribution of coherent flow
structures towards more and smaller-scale structures. In contrast, visual inspection of mapped
turbulence measures revealed a detectable change only for the lowest level of submergence
where flow was accelerated around the tip of the jam. At low submergence, wavelet analysis also
exhibited a minor increase in variability near the ELJ. More generally, wavelet analysis indicated
a decrease in heterogeneity at the reach scale in hydraulic strain and vorticity for all discharges.
In the majority of cases wavelet analysis did not exhibit a change in heterogeneity between the
20
ELJ and no ELJ models. Taken together, these findings suggested that the ELJ primarily affected
flow structure and had little effect on flow complexity.
Table 3. Numbers of transects displaying increased (+) and decreased (-) wavelet power as a
function of discharge for velocity (Vxy), Reynolds stress (RS), hydraulic strain (HS), vorticity
(Vort) in wavelet analyses with ELJ compared to no ELJ. Increases and decreases were
determined by visual comparison of wavelet analyses of simulated flow with and without ELJ.
6cms
33cms
123cms
Total
(+)
(-)
(+)
(-)
(+)
(-)
(+)
(-)
Total
2
12
0
13
0
5
2
27
Velocity
0
1
0
0
0
2
0
3
Reynolds
Stress
1
0
0
1
0
0
1
1
Hydraulic
Strain
0
6
0
6
0
1
0
13
Vorticity
1
5
0
6
0
2
1
13
Table 4. Numbers of transects displaying increased (+) and decreased (-) wavelet power as a
function of transect type for velocity (Vxy), Reynolds stress (RS), hydraulic strain (HS), vorticity
(Vort) in wavelet analyses with ELJ compared to no ELJ. Increases and decreases were
determined by visual comparison of wavelet analyses of simulated flow with and without ELJ.
Reynolds
Hydraulic
Total
Velocity
Stress
Strain
Vorticity
(+)
0
0
0
0
0
L1
(-)
6
1
0
2
3
(+)
0
0
0
0
0
L2
(-)
4
0
0
2
2
(+)
0
0
0
0
0
L3
(-)
7
1
0
3
3
(+)
2
0
1
0
1
L4
(-)
4
1
0
2
1
(+)
0
0
0
0
0
T1
(-)
2
0
0
1
1
(+)
0
0
0
0
0
T2
(-)
4
0
1
1
2
(+)
0
0
0
0
0
T3
(-)
0
0
0
2
1
21
Figure 8. Comparison of heterogeneity (measured by wavelet power) of Reynolds stress (a)
with ELJ and (b) without ELJ at low discharge (6 cms) in simulated flow along a longitudinal
transect in the Sodom Ditch, Calapooia River, Oregon. The ELJ is located between the vertical
black lines. To avoid edge effects due to finite transect size, interpretations are restricted to areas
outside the hatched area.
These results differ from other studies that have investigated the flow field around ELJs.
For example, the finding that velocity in the region of the ELJ was only affected during low
flows contrasts with findings of Daniels and Rhoads (2004) that large wood in meander bends
affected the magnitude and position of the high velocity core at all flow stages. In addition, the
localized and low-flow impact of the ELJ on turbulence statistics contrasts with He et al. (2009),
who found that meander ELJs in a sand-bed southern US stream were responsible for minor
increases in velocity gradients and vorticity at all discharges. Although coherent flow structure
22
identification and wavelet analysis have both been used in analysis of turbulent flows (Alfonsi,
2006; Farge, 1992), they have not been applied to assess flow structure and complexity around
ELJs.
The results of this study provide some evidence that the ELJ is responsible for
enhancement of fish habitat at higher discharges. During low flows, fish tend to locate in the
main flow within the thalweg, while at higher flows fish are more likely to use lateral refuge
habitat, such as deflection and expansion eddies (Schwartz and Herricks, 2005). Lower energy
habitat is desirable for fish during high flow events and may influence fish survival during
critical life stages (Fausch, 1993; Schwartz and Herricks, 2005; Bell et al., 2011). At higher
flows the ELJ was associated with smaller eddies, which have lower energy due to the nature of
the turbulence energy cascade (Adrian et al., 2000). At low discharge, the ELJ was associated
with a localized increase in turbulence metric magnitudes. Individuals of some fish species select
for lower values of velocity, Reynolds stress, and vorticity (Smith et al., 2006; Tritico and Cotel,
2010). Given these considerations, the ELJ may be responsible for a localized reduction in
desirable fish habitat during low flow, not taking into consideration the habitat benefit of cover.
The study findings also provide some evidence that the ELJ is associated with greater
bank stability at higher discharges. Erosion occurs on the outside bank of meander bends as the
flow in this region has the highest velocity, and as the meander bend develops, formation of a
point bar on the inner bank steers flow towards the outer bank (Daniels and Rhoads, 2004).
Naturally occurring large wood lowers flow velocity along the outer bank and repositions the
high velocity core away from the outer bank (Daniels and Rhodes, 2004). The reduction in
energy of the smaller eddies detected in simulated flow fields at high discharge downstream of
23
the ELJ in this study is consistent with the notion that the ELJ reduces the erosive flow potential
in this reach, at high discharge.
This study revealed the importance of using complementary concepts of spatial pattern,
patchiness and heterogeneity to assess changes in flow in response to an ELJ. Findings from each
of the methods showed little overlap; because these methods analyze different aspects of the flow
field. These results demonstrate the importance of multiple analysis approaches, rather than
suggesting contradictory findings. Coherent flow structure identification is capable of detecting
changes in the location, number, and size of eddies that may not be reflected in temporal velocity
fluctuations or velocity gradients used in calculation of turbulence metrics. Mapping of
turbulence metrics is useful for detecting localized changes in flow, but do not reveal multiplescale patterns in flow that are shown by wavelet analysis.
5. Conclusion
This study examined the effects of an ELJ on flow structure and complexity across
multiple levels of ELJ submergence, assessed through coherent flow structure identification,
maps of turbulence metric magnitudes, and wavelet analysis of turbulence metrics along defined
transects. Overall it appears that the ELJ affected flow structure across all discharges, increased
patchiness of flow at higher discharges, and had little effect on heterogeneity of turbulence
metrics. Smaller, lower energy eddies associated with the presence of the ELJ at high discharge
suggest that the ELJ may enhance fish habitat and increase bank stability at higher levels of ELJ
submergence.
The techniques used here are intended to explore more effective ways to characterize the
effects of restoration projects on aquatic habitat. Most current studies on flow complexity have
24
focused on the spatial pattern of hydraulic metrics and their magnitudes. This study suggests that
these methods may not fully capture changes in habitat patches, as represented by coherent flow
structures, which may be relevant to fish habitat selection. Techniques used in this study can be
used to guide future designs to characterize the impact of projects on flow structure and
complexity.
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Appendix
A. Proper Orthogonal Decomposition
POD is an unbiased method for extracting coherent flow structures from turbulent flow
(Lumley 1967). POD produces a low-order description of the flow field by transforming a large
number of correlated data points into a sum of weighted linear functions, called modes (Chen et
al., 2012; Singha and Balachandar, 2011). Each mode represents a portion of the total flow field,
and the weighting coefficients represent the statistical weight of each mode in the total flow
field. Summing all of the modes multiplied by their corresponding coefficients produces the
original velocity vector field. Modes are produced in descending order of energy, so that largescale high-energy structures are contained within the first few modes produced by POD (Chen et
al., 2012).
The POD was conducted using the method of snapshots (Sirovich, 1987), where the
snapshots were the depth-averaged, two-dimensional velocity vector fields at each time-step,
produced as model output. Input data for the POD were K number of snapshots. The POD
produces a set of M modes, ϕ m , and the corresponding coefficients, c m (k), that can reconstruct all
K velocity distributions (Equation 1),
�
(�)
�
= � �� � ��
��(4)
�=1
where m is the mode index, with the total number of modes equal to the total number of
snapshots, M = K (Chen et al. 2012). POD was conducted using a Matlab code developed by
Chen et al., (2012). The time-averaged velocity vector field was reconstructed by averaging the
coefficients across all K snapshots, and summing the product of the average coefficients with
their respective modes (Equation 2).
�
����
�
1
= � � � �� � � ��
�
�=1
29
��(5)
�=1
In this study, reconstruction of the time-averaged velocity field was conducted using the first
mode of each flow model, which contained at least 98% of the total kinetic energy. As higher
modes contained much lower kinetic energy, less than 2% of total kinetic energy, they were
excluded to filter out small-scale flow structures that were perceived to be of limited relevance to
fish habitat and bioenergetics.
B. Closed Stream Line Algorithm
Large-scale coherent flow structures were identified using a closed-streamline approach
on the POD data, as described in Agarwal and Prasad (2002) and Singha and Balachandar
(2011). At each point in the reconstructed velocity vector field grid, a circle of increasing radius
was approximated, and an algorithm was executed to identify closed streamlines. The largest
radius at which the algorithm detected a closed streamline was determined to be the vortex
radius. The algorithm used to detect flow structures was only capable of detecting the scale of
the structure at a uniform radius. Thus, in cases where vortices were elliptical, the minor axis of
the structure was identified as the scale of the structure, and the identification underestimated the
size of the vortex. A point identified as belonging to a vortex by the closed streamline algorithm
was determined to be the vortex center if it met the following thresholds (Singha and
Balachandar, 2011):
1) 90% of velocity vectors found within the approximated circle boundary displayed
monotonic variation in angular orientation
2) 80% velocity vectors found within the approximated circle boundary were within ±
30˚ of the tangent line at that grid point.
The threshold values for the algorithm conditions were optimized by visually inspecting
identified vortices for false identification and adjusting threshold parameters.
30