Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 12.7.3 - Particle Dispersion under Tidal Bores: Application to Sediments and Fish Eggs
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 Material Information
Title: 12.7.3 - Particle Dispersion under Tidal Bores: Application to Sediments and Fish Eggs Environmental and Geophysical Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Chanson, H.
Tan, K.-K.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: tidal bores
turbulent mixing
particle dispersion
 Notes
Abstract: A tidal bore is a surge of water propagating upstream as the tidal flow turns to rising into an estuary with a tidal range larger than 5 to 6 m and a bathymetry that amplifies the tidal wave. The bore front is a shock characterised by a singularity of the free-surface and pressure and velocity fields. This study aims to characterise the tidal bore propagation and the induced turbulent mixing under controlled flow conditions. Some physical modelling was performed based upon a Froude similitude and the tracking of light particles was conducted with both undular and breaking bores. Some large fluctuations of horizontal and vertical particle velocity components were observed during the undular bore propagation beneath the undulations. A major result was the identification of large-scale vortical structures generated below the front of the tidal bore. These large coherent turbulent structures must be responsible for some bed erosion and vertical mixing of the water column when a tidal bore propagates upstream in the estuarine zone of a natural system. The large-scale eddies are also responsible to the rapid longitudinal dispersion of fish eggs reducing the impact of predators, with some form of preferential motion depending upon the eggs' vertical elevation.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Particle Dispersion under Tidal Bores: Application to Sediments and Fish Eggs


Hubert Chanson and Kok-Keng Tan

The University of Queensland, School of Civil Engineering
Brisbane QLD 4072, Australia
E-mail: h.chanson@uq.edu.au


Keywords: tidal bores, turbulent mixing, particle dispersion




Abstract

A tidal bore is a surge of water propagating upstream as the tidal flow turns to rising into an estuary with a tidal range larger
than 5 to 6 m and a bathymetry that amplifies the tidal wave. The bore front is a shock characterized by a singularity of the
free-surface and pressure and velocity fields. This study aims to characterise the tidal bore propagation and the induced
turbulent mixing under controlled flow conditions. Some physical modelling was performed based upon a Froude similitude
and the tracking of light particles was conducted with both undular and breaking bores. Some large fluctuations of horizontal
and vertical particle velocity components were observed during the undular bore propagation beneath the undulations. A major
result was the identification of large-scale vortical structures generated below the front of the tidal bore. These large coherent
turbulent structures must be responsible for some bed erosion and vertical mixing of the water column when a tidal bore
propagates upstream in the estuarine zone of a natural system. The large-scale eddies are also responsible to the rapid
longitudinal dispersion of fish eggs reducing the impact of predators, with some form of preferential motion depending upon
the eggs' vertical elevation.


Introduction

A tidal bore forms during spring tide conditions when the
tidal range exceeds 5 to 6 m and the flood tide is confined to
a narrow funnelled estuary (Chanson 2010a). A bore is a
surge of water propagating upstream as the tidal flow turns
to rising. When the ocean level at the river mouth rises with
time during the early flood tide, the leading edge of the tidal
wave becomes steeper and steeper, until it forms an abrupt
front that is the tidal bore (Fig. 1). The bore is a fascinating,
intense and powerful natural phenomenon, attracting
tourists, kayakers and surfers (Fig. la). However, the tidal
bore processes remain poorly understood today because of a
lack of field observations and comprehensive studies
(Simpson et al. 2004, Wolanski et al. 2004).
A tidal bore is a positive surge associated with a
discontinuity in water depth and a sudden rise of the water
elevation. The bore front is a shock characterized by a
singularity of the water depth and pressure and velocity
fields. In Nature, a tidal bore may have a variety of different
shapes (Fig. 1). The photographs illustrate in particular that
the bore front is not a sharp, vertical discontinuity of the
water surface because of the necessary curvature of the
streamline and the associated pressure and velocity
redistributions.
In absence of detailed field measurements, it is the aim of
this study to characterise the tidal bore propagation and the
induced turbulent mixing under controlled flow conditions.
This was achieved through some physical modelling based
upon a Froude dynamic similarity. The tracking of light
particles was conducted with both undular and breaking


bores to provide some new Lagrangian description of the
particle mixing processes beneath the tidal bore front. The
results complement earlier Eulerian velocity measurements
performed in the same facility, and provide a new
understanding of the turbulent mixing and dispersion of
particulates such as light sediment materials and fish eggs.


(a) Undular tidal bore of the Dordogne River on 30 Sept
2008 afternoon The kayakers rode the 2nd wave crest
while the surfer was ahead of the 3rd wave crest






Paper No


tu) O cIitc 1V'i uual ui UUMCil IY 3DVL. LUVVO 111iu1muu1g DUIC
propagating from left to right Note the breaking front in
the foreground and the undulations in the deeper section
Figure 1: Photographs of tidal bores.


Nomenclature

aw wave amplitude (m)
B channel width (m)
Dx turbulent mixing coefficient (m2s-) in the
x-direction
Dz turbulent mixing coefficient (m2s ) in the
z-direction
do initially steady flow depth (m)
Fr tidal bore Froude number
f Darcy-Weisbach friction factor
g gravitational acceleration (ms-2)
Lw wave length (m)
Q initially steady flow rate (m3s)
q discharge per unit width (m2s'): q = Q/B
s particle specific density
U tidal bore celerity (ms ') for an observer standing
on the bank, positive upstream
t time (s)
t' time (s) with t'=0 when the particle passed
beneath the bore front
Vo initially steady flow velocity (ms'1)
ws particle fall velocity (ms'1) in still water
X longitudinal co-ordinate (m)
x longitudinal co-ordinate (m) measured from the
test section upstream end, positive downstream
x' longitudinal co-ordinate (m) positive
downstream with x'=0 when the particle passed
beneath the bore front
z vertical elevation (m) positive upwards
Greek symbols
sz vertical mixing coefficient (m2s ) in
fully-developed open channel flows
CT mean square displacement (m) of particles in the
x-direction
oC mean square displacement (m) of particles in the
z-direction
0 diameter (m)
Subscripts
avg ensemble-average
o initially steady flow conditions


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

x longitudinal component
z vertical component


Experimental Facility

The experiments were performed in a 12 m long 0.5 m wide
rectangular open channel test section (Fig. 2). The flume
was horizontal and made of smooth PVC bed and glass
walls. The waters were supplied by a constant head tank
feeding a large intake basin (2.1 m long, 1.1 m wide, 1.1 m
deep) leading to the test section through a bed and sidewall
convergent. A radial gate was located at the channel
downstream end (x = 11.9 m) where x is the longitudinal
distance from the channel test section upstream end and was
used to control the initial water depth; its position did not
change during an experiment. A fast-closing tainter gate was
also located at x = 11.15 m and the gate was closed rapidly
(completely or partially) to generate the tidal bore
propagating upstream in the channel.
The initially steady discharge was measured with two
orifice meters that were designed based upon the British
Standards (1943). In steady flows, the water depths were
measured using rail mounted pointer gauges. The bore
propagation was studied with a series of acoustic
displacement meters MicrosonicTM Mic+25/IU/TC located
along the channel between x = 10.8 and 4 m, and above the
water surface (Fig. 3). Further observations were recorded
between x = 5.65 and 4.85 m using a digital video camera
Panasonic NV-GS300 (30 fps) and digital still cameras.


Tainter gate


Acoustic
displacement
meter
Bore front meter
U
--r-- I


Y---------x
Ovcrfall
Figure 2: Sketch of the channel test section.

Generation of the tidal bore
The experimental geometry and configuration were chosen
to have an initially steady open channel flow with a
discharge Q between 0.013 and 0.058 m3s- (Table 1). The
opening of the downstream radial gate controlled the initial
steady flow depth do and velocity Vo.
The tidal bore was generated by the rapid closure of the
downstream tainter gate. The gate was identical to that used
by Koch and Chanson (2008,2009) and Chanson (2010b);
its closure time was less than 0.2 s. After the rapid closure,
the bore propagated upstream (Fig. 3) and each run was
stopped when the tidal bore front reached the upstream
intake structure (x < 0), to avoid any wave reflection in the
test section.






Paper No


Figure 3: Breaking tidal bore (Fr = 1.5, Q = 0.0578 m3s-,
do = 0.139 m) Looking at the incoming bore Note the
displacement meter sensor above the bore front and the
pointer gauge in background.

Ref Q do U Fr Comment
nm3s-1 m ms-1
Homung et 0 1.5 to Smooth bed.
al. (1995) 6
Koch & 0.040 0.079 0.14 to 1.3 to B = 0.5 m.
Chanson 0.68 2.0 Smooth bed.
(2009)
Chanson 0.058 0.14 0.5 to 1.1 to B = 0.5 m.
(2010b) 0.9 1.5 Smooth &
rough beds.
Present 0.013 to 0.0505 0.33 to 1.01 B =0.5 m.
study 0.058 to 1.19 to 1.7 Smooth bed.
0.196

Table 1: Experimental investigations of tidal bores.

Q Vo do U Fr Type of
m3s- ms-1 m ms-1 tidal bore
0.013 0.335 0.0775 0.67 1.15 Undularbore.
0.515 0.0505 0.55 1.51 Breaking bore.

Table 2: Particle tracking experiments in undular and
breaking tidal bores (Present study).

Particles and particle tracking experiments
For one initial discharge, the turbulent mixing of
light-weight particles was systematically recorded between
x = 5.65 and 4.85 m with an undular bore and a breaking
bore (Table 2). The particles were spherical-shaped beads
with an average diameter of 3.72 mm 0.2 mm. Their
relative density was deduced from some particle fall
velocity experiments conducted in a 2 m high, 0.10 m 0
water column. The experimental data yielded a particle fall
velocity ws = 0.047 0.012 m/s corresponding to a relative
density s = 1.037 0.012.
The particle density corresponded to some light-weight
particles slightly heavier than water. Their diameter and
density were close to those of striped bass (Morone
saxatilis) fish eggs. In the Bay of Fundy, Rulifson and Tull
(1999) observed typical fish egg diameters of about 4 mm
with a specific density s between 1.0016 and 1.0066
depending upon their stages of development. The lightest
eggs were unfertilised water hardened eggs. Fertilised eggs
less than 10 hours old had a relative density of 1.0029 and


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

the heaviest eggs were in the final stages of development
(Rulifson and Tull 1999).
In the present study, the particles were injected on the
channel centreline and advected downstream by the initially
steady flow. Their turbulent mixing in the bore front was
recorded through the glass sidewalls using the video camera
Panasonic NV-GS300.


Basic Flow Patterns

Some visual observations and free-surface measurements
were conducted for a range of flow conditions with
initially-steady subcritical open channel flow (Table 1).
Several flow patterns were observed depending upon the
tidal bore Froude number Fr = (Vo + U)/ g d where do is
the initial flow depth, Vo is the initial flow velocity positive
downstream, g is the gravity acceleration and U is the surge
front celerity for an observer standing on the bank and
positive upstream. Fr is the Froude number defined in the
system of co-ordinates in translation with the tidal bore. For
a Froude number between unity and 1.5 to 1.6, the tidal bore
was undular: that is, the wave front was followed by a train
of secondary, quasi-periodic waves called undulations (Fig.
la). For larger Froude numbers, a breaking bore was
observed (Fig. lb & 3). The basic flow pattern observations
were consistent with the earlier findings of Favre (1935),
Benet and Cunge (1971) and Treske (1994). Two examples
of undular and breaking bore profiles are shown in Figure 4,
presenting in dimensionless form the water depth as a
function of time.
The undular tidal bore had a smooth, quasi-two-dimensional
free-surface profile for Fr < 1.2 to 1.25. For 1.2 to 1.25 < Fr,
some slight cross-waves (shock waves) were observed,
starting next to the sidewalls upstream of the first wave crest
and intersecting next to the first crest on the channel
centreline. For 1.35 < Fr < 1.5 to 1.6, some slight wave
breaking was observed at the bore front, and the secondary
waves were flatter. The findings were comparable to those
of earlier studies (Koch and Chanson 2009, Chanson
2010b).
At the largest bore Froude numbers (i.e. Fr > 1.5 to 1.6), the
bore had a marked roller, and appeared to be
quasi-two-dimensional (Fig. 3). Behind the roller, the
free-surface was about horizontal although large
free-surface fluctuations were observed. Some air
entrainment and intense turbulent mixing was observed in
the bore roller.
Note that the flow patterns were basically independent of
the initially steady flow Froude number Vo / Jg d while
an earlier study showed that these were also independent of
the bed roughness (Chanson 2010b).






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


0.9
S0.75
S0.6
0.45
0.3
0.15


100 110 120 130

(a) Undular tidal bore (
0.107 m, U = 0.73 ms 1)


0.8

0.4


140 150 160
t sqrt(g/do)
Fr = 1.20,


I I I I I I I I I I
-


170 180 190 200 210

Q = 0.025 m3s1, do


60 65 70 75 80 85 90 95 100 105 110 115
t sqrt(g/do)
(b) Breaking tidal bore (Fr = 1.56, Q = 0.058 m3s-', do =
0.1315 m,U = 0.99ms1)
Figure 4: Instantaneous dimensionless free-surface
profiles (measurements at x = 5 m).

Free-surface undulation properties
A key feature of the undular tidal bores is the
pseudo-periodic appearance of the secondary waves. The
characteristics of the undulations were systematically
recorded for three discharges (Q = 0.025, 0040 & 0.058
m3s-1) and for a range of initial flow depths for each flow
rate (Table 1). Some typical results are shown in Figures 5
and 6 in terms of the dimensionless wave length L,/do and
steepness a,/Lw, where a, and L, are respectively the wave
amplitude and steepness of the first length. The present
experimental data are compared with the linear wave theory
and Boussinesq equation solution in Figures 5 and 6. While
the wave length decayed exponentially with increasing
Froude number, the wave steepness data exhibited a local
maximum about Fr = 1.3 to 1.4. It is believed that the
apparition of some wave breaking for Fr > 1.35 was
responsible for the lesser energy dissipated in the secondary
wave motion at larger Froude numbers and hence the
smaller wave steepness for Fr > 1.3 to 1.4.


1 1.08 1.16 1.24 1.32 1.4 1.48 1.56 1.64 1.72 1.8
Fr
Figure 5: Dimensionless wave length of the first wave
length of undular tidal bores Comparison between present
data and the Boussinesq equation (Andersen 1978).


1 1.08 1.16 1.24 1.32 1.4 1.48 1.56 1.64 1.72 1.8
Fr
Figure 6: Dimensionless wave steepness of the first wave
length of undular tidal bores Comparison between present
data, the Boussinesq equation (Andersen 1978) and the
linear wave theory (Lemoine 1948).


Particle Tracking Results

For a constant initial discharge, the particle dispersion in
undular and breaking tidal bores were tested (Table 2).
Figure 7 presents some instantaneous free-surface profiles
for both experiments. The observations were recorded at
about x = 5 m where the bore propagated upstream with a
constant celerity U. The distinctive shape of the first wave
length is illustrated; for the undular bore experiment, the
wave period was about 0.8 s. In Figure 7, the data are
presented as the dimensionless water depth d/do as a
function of the longitudinal distance X/do, where d is the


Paper No


S11
^-]


I I I I I I I I I






Paper No


water depth measured above the bed and X is a longitudinal
co-ordinate positive in the downstream direction. (The
origin of X was x = 4.85 m in Figure 7.)
Some typical particle trajectories are presented in Figures 8
and 9 for the undular and breaking tidal bores respectively.
Figures 8 and 9 show some sideview of the particle
trajectories. In each graph, the horizontal axis is the
longitudinal coordinate x' positive downstream with x' =0
when the particle passed beneath the leading edge of the
bore front and the vertical axis is the particle vertical
elevation z. Each trajectory starts at x' = 0 and the time
interval between each data point is 1/30 s. On the graphs,
the tidal bore propagates from left to right with x' positive to
the left as in Figure 2.


11 10 9 8 7 6 5 4 3 2 1 0
X/do
Figure 7: Dimensionless instantaneous free-surface
profiles of tidal bores for the particle tracking experiments
(Q = 0.013 m3s-1, Fr = 1.15 and 1.5) Bore propagation
from left to right.

In the undular bore, a range of particle trajectory patterns
were observed with two distinctive trends (Fig. 8). Among
the particles released in the upper flow region (z/do > 0.5), a
significant proportion followed a helicoidal pattern
illustrated in Figure 8 (Particles 6a, 6c, 6d, 8b). The particles
followed an orbital path beneath the wave crest where they
reached a maximum elevation, and were then advected
downstream beneath the next wave trough. These orbital
trajectories were somehow comparable to the particle
motion beneath regular wave crests (Sawaragi 1995), but the
entire trajectories were a combination of orbital paths
superposed to a downstream advection. When the particles
were injected closer to the bed (z/do < 0.5), they were often
subjected to some recirculation motion, with an initially
rapid deceleration followed by an upstream advection
behind the bore front. For example in Figure 8 (Bottom), the
particles 2, 4c and 5b were recirculated upstream with a
advection velocity Vx/Vo = -0.5 in average. The two
distinctive trends are illustrated in Figure 8.
In a breaking tidal bore, the particle trajectories were more
complicated. Most particles that were injected very close to
the bed (z/do < 0.2) were subjected to a sudden deceleration
and then an upstream motion: e.g., the particle trajectory b8
with red circular symbols in Figure 9. The other particles


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

were subjected to a pseudo-chaotic motion induced by the
large scale turbulent eddies generated in the mixing layer of
the bore roller. Some examples of such particle trajectories
are presented in Figure 9 (particles b2a, b6a, b9b, blOc).


2 1.75 1.5 1.25


2 1.75 1.5 1.25


1 0.75 0.5 0.25
x'/do


0 -0.25 -0.5


1 0.75 0.5 0.25 0 -0.25 -0.5
x'/do


Figure 8: Dimensionless particle trajectories in the
undular tidal bore (Fr = 1.15, Q = 0.013 m3s-1, do = 0.0775
m).


.%,--
- E -

_q I


P -a -r- 6-





Particle 6a
0 Particle 6d
S- Particle 8b
l I I l l I


- V V V v -

V y 'V -






V Undular bore (Fr=1.15)
Beaking bore (Fr=1.5)


0.8

0.6


































4.5 3.5 2.5 1.5 0.5 -0.5 -1.5


5.5 4.5 3.5


2.5 1.5
x'/do


0.5 -0.5 -1.5


Figure 9: Dimensionless particle trajectories in the
breaking tidal bore (Fr = 1.51, Q = 0.013 m3s-1, do = 0.0505
m).

Particle velocities
Beneath the undular tidal bore, the particle motion data
yielded large fluctuations of horizontal and vertical particle
velocity components during the undular bore propagation
beneath the undulations. The long-lasting impact of the
free-surface undulations is a key feature of undular tidal
bores in natural systems (Koch and Chanson 2008). The
comparative observations with a same initial flow rate
suggested that the undular bore induced a greater particle
mixing compared to the breaking bore, especially in the
upper flow region (z/do > 0.5).
The ensemble-averaged particle velocity data are presented
in Figures 10 and 11 in terms of the dimensionless
horizontal and vertical particle velocity components
(Vx)avgVo and (Vz)avg/Vo respectively. Both figures have
identical horizontal and vertical scales. The entire data sets
corresponded to a study period of 1.3 s in each case and the
time interval between each data point was 1/30 s. The


Paper No


3 2.7 2.4 2.1 1.8


1.5 1.2
X'avg/do


0.9 0.6 0.3 0


I I I I I I I I I I I I





E









*.
0 D !
S Particle b8
A Particle b9b
- Particle blOc -
S- Particle bl lb
I I I I I I I


3 2.7 2.4 2.1 1.8 1.5
X'avg/do


1.2 0.9 0.6 0.3 0


Figure 11: Ensemble-averaged horizontal and vertical


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

results presented some common trends as well as
highlighted some differences between undular and breaking
tidal bores.
In both cases, the light-weight particles were subjected to a
rapid deceleration shortly after the bore front passage (Fig.
10 & 11). Next to the bed, some turbulent recirculation
motion was observed. The findings were consistent with the
turbulence measurements of Koch and Chanson (2009) and
Chanson (2010b), and the numerical results of Lubin et al.
(2010). The particle recirculatory motion is believed to be
caused by the large vortical structures produced next to the
bed during the tidal bore propagation.
In the undular bore, however, the particle motion was
strongly influenced by the free-surface undulation pattern,
including the orbital trajectory motion seen in Figure 8 and
large vertical velocity fluctuations (Fig. 10).


0.8
(Vx)avg
0.7 (V)avg

0.6 -
0.5- -

S0.4 -

0.3- -

S0.2 -

0.1 -

0

-0.1

-0.2
S I I I I I I I I I I I I I I I I I I


0.6 7

0.4 -

0.2

0 L
5.5


Figure 10: Ensemble-averaged horizontal and vertical
particle velocity components beneath an undular tidal bore
(Fr= 1.15, Q = 0.013 m3s-, do = 0.0775 m).


0.8 11111 111111
(Vx)avg
0.7 (V)avg

0.6-

0.5-

S0.4 -

S0.3

a 0.2

0.1
o~

-0.1

-0.2 -
_nf I I1 1 1 1 I I I I I I II 1 I






Paper No


particle velocity components beneath a breaking undular
tidal bore (Fr = 1.51, Q = 0.013 m3s-1, do = 0.0505 m).


Discussion

Assuming a homogenous, stationary turbulence behind the
tidal bore front, the turbulent diffusion coefficient may be
estimated from the mean square displacement of the
particles:

(1) Dx -x
2 t'

(2) Dz = C
2 t'
where Dx and Dz are the turbulent mixing coefficients in the
x- and z-directions respectively, o, and oz are respectively
the mean square displacement of the particles in the x- and
z-directions, and t' is the time scale with t' = 0 when the
particle passed beneath the leading edge of the bore front.
Equations (1) and (2) may be derived using Langevin's
model of turbulent dispersion or the random walk model
assuming that t' is much larger than the Lagrangian time
scale (Pope 2000, Chanson 2004). The experimental results
are presented in Figure 11 where q is the discharge per unit
width. Herein Dx and Dz characterized the turbulent
diffusion of the light-weight particles immediately behind
the tidal bore front, and the results are summarised in Table
3. Despite the simplistic assumptions underlying Equations
(1) and (2), the data suggested that the longitudinal mixing
coefficient was nearly one order of magnitude greater than
the vertical diffusion coefficient (Table 3). For comparison,
in a fully-developed open channel, the average vertical
mixing coefficient is sz/q = 0.067 -/8 where f is the
Darcy-Weisbach friction factor (Rutherford 1994, Chanson
2004). The present observations of vertical diffusion
coefficients behind tidal bores were one order of magnitude
larger than the vertical diffusion coefficient in a
fully-developed open channel flow, with relatively little
difference between undular and breaking tidal bores (Fig.
11). Overall the experimental data highlighted the strong
longitudinal and vertical mixing behind both undular and
breaking tidal bores.


0.5
0.3
0.2
0.1
0.05
S0.03
0.02
0.01 /
0.005
0.003
0.002
0.001
0 2 4 6 8 10

Figure 11: Dimensionless turbulent diffi


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

particles in the x- and z-directions immediately behind
undular and breaking tidal bore fronts.


Table 3: Turbulent diffusion coefficients immediately
behind undular and breaking tidal bores (Present study).

A key feature of the present findings is the wide range of
particle trajectories and trajectory patterns beneath a tidal
bore front, as well as the vortical motion induced by
turbulence (Fig. 8 & 9). Both qualitative and quantitative
observations implied the existence of large scale vortices in
which the light-weight particles were trapped and advected
within. Earlier physical and numerical studies documented
the production of large coherent structures (Koch and
Chanson 2009, Lubin et al. 2010). The energetic turbulent
events beneath and shortly after the tidal bore front implied
the generation of vorticity in and behind the bore front. The
presence of these persisting coherent structures indicated
that a great amount of sediment could be placed into
suspension and transported by the main flow. The present
observations with light-weight particles suggested that the
tidal bore process contributes efficiently to the longitudinal
dispersion of the eggs, reducing the efficiency of the
predators in tidal-bore affected estuaries as proposed by
Rulifson and Tull (1999) and Morris et al. (2003).
In a natural system, the fish eggs are typically advected
downstream by the ebb tide. The arrival of the tidal bore
does induce a marked longitudinal spread of the eggs. Those
located in the upper flow region do continue to flow
downstream, while the others reverse their course, flowing
upstream behind the bore. Simply the tidal bore induces a
very rapid longitudinal spread of the eggs with some form
of preferential motion depending upon their vertical position
in the water column. The lowest, typically heaviest fish eggs
are advected upstream immediately after the tidal bore
passage. The higher, typically neutrally buoyant eggs
located next to the surface continue their journey
downstream for sometimes, although the strong flood flow
may bring them back into the upper estuary at a later stage
of the tide.


Practical considerations
The present findings have a number of limitations. The
experimental setup characterized the two-dimensional flow
motion. Some qualitative tests were conducted by placing a
camera above the channel. The observations indicated that
the particles remained qualitatively along the channel
centreline, but the visual observations were adversely
affected by the free-surface turbulence during and
immediately after the bore front propagation. Newer
experiments could be conducted using a transparent channel
Dx Undular bore bed, but the technique could only apply to a smooth channel
- D Undular bore bed.
Dx Breaking bore
Dz Breaking bore Furthermore the initial particle relative elevation had some
impact on the particle trajectories. For example, the particles
12 14 16 18 released close to the bed tended to remain close to the
bottom. It was however extremely difficult to control the
usion coefficients of initial particle elevation with some accuracy in the turbulent






Paper No


flow, without impacting adversely the initial flow motion
and boundary conditions.


Conclusions

This physical study focused on the turbulent dispersion of
light-weight particles beneath a tidal bore. Small particles
with properties close to striped bass (Morone saxatilis) fish
eggs were used and their turbulent dispersion associated
with the passage of undular and breaking bores was
documented.
The findings were consistent with some earlier experimental
and numerical results, including the observations of rapid
flow deceleration and flow reversal beneath the breaking
bore roller. Some large velocity fluctuations of horizontal
and vertical particle velocity components were observed
during the undular bore propagation beneath the undulations.
Some interesting features were highlighted, including some
large-scale motion implying the existence of large coherent
vortical structures. These large turbulent eddies must be
responsible for some bed erosion and vertical mixing of the
water column when a tidal bore propagates upstream in the
estuarine zone of a natural system (Fig. 1). The large-scale
vortices are also responsible to the longitudinal dispersion
of fish eggs reducing the impact of predators. The present
results showed that the tidal bore induces a very rapid
longitudinal spread of the eggs with some form of
preferential motion depending upon their vertical elevation
within the water column. The estimates of the longitudinal
and vertical diffusion coefficients showed quantitative
results that were one to two orders of magnitude larger than
those in fully-developed open channel flows, with relatively
little difference between undular and breaking tidal bore
flow motion.
Finally it must be noted that the present experiments were
performed with an unique particle size and density. Future
tests should encompass a range of particle sizes and density.


Acknowledgements

The authors acknowledge the technical assistance of
Graham Illidge and Clive Booth (The University of
Queensland).


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