Annual
Journal of
of Hydraulic
Hydraulic Engineering,
Engineering, JSCE,
JSCE, Vol.53,
Vol.53, 2009,
2009, February
February
Annual Journal
TURBULENT FLOW IN BOTTOM LAYER
OF THE OHTA RIVER
Mahdi RAZAZ1, Kiyosi KAWANISI2, Tomoya YOKOYAMA3
1 Member of JSCE, Dr. Student., Coastal Engineering, Dept. of Civil and Environmental Engineering, Hiroshima
University (Kagamiyama 1-4-1, Higashi Hiroshima, 739-8527, Japan)
2 Member of JSCE, Dr. of Eng., Associate Prof., Coastal Engineering, Dept. of Civil and Environmental Engineering,
Hiroshima University (Kagamiyama 1-4-1, Higashi Hiroshima, 739-8527, Japan)
3 Member of JSCE, Graduate Student, Coastal Engineering, Dept. of Civil and Environmental Engineering,
Hiroshima University (Kagamiyama 1-4-1, Higashi Hiroshima, 739-8527, Japan)
A point in the center of the Ohta Floodway in 2.8 km far from mouth was selected to deploy
instruments during 25 hours of Aug. 2008. Ohta Floodway is a part of tidally-dominated Ohta River. A
high-resolution current profiler (HRCP) was used to measure vertical profiles of turbulence parameters
like Reynolds stress, eddy viscosity, and production/dissipation rates. An ADV was used to measure velocity
components near the bed. Density data was collected every hour throughout the water column by a CTD.
In the first ebb, the regime of flow was deeply disturbed by an unknown phenomenon that influenced all
turbulence parameters. The stability function SM and proportionality constant B1 in Mellor-Yamada (MY) model was investigated and found to be different with suggested value in M-Y model.
Key Words: Estuaries, tidal currents, turbulence, stratified flow, M-Y model
1. INTRODUCTION
2. STUDY AREA AND OBSERVATION
METHOD
Aspect of cohesive sediment transport in
estuaries is important to engineering projects
including riverbank stability, residual onshore
sediment transport, scouring around bridge piers,
navigation, water quality and ecological problems.
Various factors are involved in estuaries like: tidal
oscillation, river discharge, and wind driven waves,
therefore studying estuarine areas using laboratory
methods hardly will have realistic conclusions.
However, because of highly unsteady conditions it
is hard to conduct in situ measurements. To
overcome
measuring
difficulties,
precise
instruments are required. Kawanisi1) studied
structure of turbulent flow in Ohta River, Japan. He
examined velocity turbulent variables and density
profiles. Also, stability function SM in M-Y model
(Mellor and Yamada2)) was redefined by him.
At present work, we conducted observation for
25 hours in the center of the Ohta Floodway to study
turbulent structure and suspended sediment
transport in a tidally-dominated estuary during a
complete tidal phase. For improving knowledge
about Y-M model (Mellor-Yamada 2)) we will
examine stability function and proportionality
constant in a complete cycle of a semi-diurnal tide.
Ohta Floodway is the most-west branch of the
Ohta River with a length of nearly 9 km. It is a
tidally-dominated river and the maximum tidal
range in an extreme spring tide can reach 4 m
(Fig.1). Recently, devices based on the Doppler
Effect referred to as pulse-to-pulse coherent Doppler
sonar have been developed to gather data on
velocity and density profiles in situ with high
quality and coherently throughout the water column.
Here, we used a commercially-available highresolution current profiler (HRCP): HR-AquaDopp
and an acoustic Doppler velocimeter (ADV):
Vectrino + , both developed by NORTEK AS.
Velocity data collected by ADV and Acoustic
Doppler Current Profiler (ADCP) are assumed to be
closely identical (Stone and Hotchkiss 3) ). To
measure velocity profile precisely, the HRCP was
mounted downwardly on a special frame to prevent
device from being shaken. Data collected at 1.0 Hz
sampling rate and 2.0 cm cell depth. HRCP location
was changed from 0.65 to 1.1 m above the bed
(mab) in order to match horizontal velocity range of
the HRCP and highest horizontal current speed. To
- 193 -
Gion Sluice
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*
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Aug. 21
Aug. 22
æ
-3
1.2 (b)æ
æ
æ
æ
u (cm/s)
Ohsiba
Sluice
N
Ohta
Flood-way
Observation
Sta.A
τc ,τ0 (Pa)
Point
0.8
Hiroshima Bay
measure the turbulence just near to the bed we
deployed the Vectrino with a synchronized compass
in about 8 cm far from the bed. ADV beams
intersect at approximately 50 mm far from the
center of sampling volume. A Compact CTD
developed by Alec Electronics was used to check
salinity and density profiles every hour in 10-cm
depth-triggered mode. Observation fulfilled through
21-22 Aug. 2008 using three described instruments
in a point that is located 2.8 km far from the river
mouth at the center of the river (Fig. 1).
3. VELOCITYAND DENSITY PROFILES
z (m)
h (m)
The water depth variation ranged from 0.8 to
3.6 m during observation as shown in Fig. 2(a). The
depth-time variation of density is plotted in Fig.
2(b). According to this plot, stratification noticeably
changes with tidal phase. Tidal straining and winddriven currents are responsible for this stratification
changes as cited in Kawanisi1). Fig. 2(c) shows
temporal variations of streamwise velocity at 0.02
and 0.30 mab acquired from HRCP data. Receding
from the bed, current speed slightly increased in
comparison with the near-bottom layer. Usually, fast
movements of particles in a high turbulent field lead
to low data correlation of acoustic Doppler
instruments. This can be recognized as spiky data.
1A
2A
3A
4A
1B
2B
3B
u (m/s)
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18
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20 22 0
2
4
Local Time (hours)
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10
where, d= sediment particle diameter, g=
gravitational acceleration, s= ρs/ρw-1= submerged
specific weight of sediment, and ρs and ρw= densities
of fluid and sediment, respectively. In order to
calculate θc instead of using Shields diagram we can
solve an equation that provides a satisfactory
approximation (Cao et al.5)):
2.5795
⎤
ln θc = − ln R* + 0.5003ln ⎡1 + ( 0.1359R* )
⎣
⎦
(3)
− 1.7148
σt 1015 kg/m3
where, shear Reynolds number R*=u*d/ν and ν=
kinematic viscosity of fluid. By solving Eq. (3) and
replacing θc in Eq. (2) assuming s= 2.65, d= 0.4 mm,
it is concluded that during observation critical shear
stress τc was always more than currents induced
shear stress τ0. The ratio of τ0/τc ranges from 0.02 in
HWS to 0.65 in the flood.
1023
0.4
0.2
z= 0.3m
4. TURBULENCE PARAMETERS
z= 0.02m
Aug. 21
14
16
18
Aug. 22
20 22 0
2
4
Local Time (hours)
6
8
10
Fig. 2 Temporal variations of (a) water depth, (b) density (σt)
profile, and (c) streamwise velocity.
æ æ
æ
æ
æ
Velocity profiles during ebb follow logarithmic
distribution for a stratified flow and are expressed
by the log-linear law:
z − z0 ⎞
u ⎛ z
uˆ = * ⎜ ln + β
(1)
⎟
L ⎠
κ ⎝ z0
where, û= is the time averaged velocity, u*= friction
velocity, κ= von Karman’s constant, z0= roughness
length, β= empirical constant, and L= MoninObukov length. Critical condition for incipient
motion of sediment is examined. According to
Kawanisi1) and Kawanisi et al.4) we assumed during
flood (ebb) phase β/L=0.025 (0.2) cm-1, z0= 5 mm,
κ= 0.4. The results are denoted in Fig. 3(a). Yet, it is
unknown to authors why the direction of shear
velocity is toward the downstream most of the times.
Critical Shields parameter θc is a well-known
parameter for testing incipient motion of sediments
and is defined as:
τc
u2
θc =
= *
(2)
( ρs − ρw ) gd sgd
4B
0.6
0.0
0.2 (c)
0.0
-0.2
-0.4
0.2
0.0
-0.2
-0.4
10 12
æ
æ
Fig. 3 Temporal variations of (a) shear velocity measured by
ADV, (b) critical (●) and near-bed (○) shear stresses.
2 km
Fig. 1 Schematic map of the observation point.
4
3
2
1 (a)
0
0.8 (b)
æ
0.4
0.
0
æ
æ
ææ
As mentioned in Mellor and Yamada2) and
Kawanisi1) the rate of shear production Ps is a
function of Reynolds shear stress and mean shear:
- 194 -
(a)
∂u
∂v 

Ps = −  u ′w′
+ v′w′ 
(4)
∂z
∂z 

where, u= streamwise velocity, v= transverse
velocity, and w= vertical velocity. Prime sign
denotes the fluctuations. Mixing parameters: vertical
eddy viscosity KM and mixing length lm are
estimated from Eqs. (5) and (6):
K M = Ps S 2
(5)
1/ 2
(6)
GM = ( lS q )
2
(10)
l
g ∂ρ
(11)
2
q ρ0 ∂z
From Eq. (4) and Eqs. (8)-(11) it can be written that:
Ps ε = B1 S M GM , Pb ε = B1 S H GH
(12)
Also, from Eqs. (5), (6), and (7) it is concluded:
qlSM = lM2 S
(13)
GH =
2
5. DEPTH-TIME VARIATION OF TURBULENCE
Fig. 4 shows the depth-time variation of the
turbulence parameters averaged over 5-minute
intervals obtained from AquaDopp data. Areas with
absolute white color denote the omitted erroneous
data. Fig. 4(a) shows the Reynolds stress −u ′w′ .
Interestingly, in 14-18 of Aug. 21 (ebb) | u′w′ | was
remarkably higher than that of in 20-24 (flood).
Although such a phenomenon was not repeated in
the next half of the tide, during the ebb and flood
amounts of | u′w′ | were roughly the same. In HWS,
when the river is relatively calm the lowest
Reynolds stresses can be detected. Usually, it is
expected to find the highest magnitudes of the TKE
shear production Ps in flood time. Nevertheless, as it
is depicted in Fig. 4(b) here Ps reached its peak in
ebb time on Aug. 21; meanwhile, largest values of
0
0.5
0.4
0.3
0.2
0.1
logK M 0 cm2/s
(c)
z (m)
2 1/ 2
(7)
S = (∂u ∂z ) + (∂v ∂z ) 


Energy dissipation rate ε is calculated by:
ε = q3 ( B1l )
(8)
where, q is the rms value of velocity components
fluctuation, l is the turbulent length scale, and B1 is
an empirical constant. Buoyant production Pb is
estimated by:
g
∂ρ
Pb =
KH
(9)
ρ0
∂z
where, KH= diffusivity coefficient for density. In MY model KM and KH are functions of q, l, and
stability functions SM and SH. Besides, SM, SH=
f(GM,GH) where:
logPs -2 cm2/s3
z (m)
(b)
Mean shear stress S can be deduced from:
2
5
0.5
0.4
0.3
0.2
0.1
z (m)
lm = ( Ps S 3 )
2 2
u ' w ' 0 cm /s
_
2
0.5
0.4
0.3
0.2
0.1
10
12
14
16
18
Aug. 21
20 22 0
2 4
6
Aug. 22
Local Time (hours)
8
10
Fig. 4 Depth-time distributions of (a) Reynolds stress, (b) shear
production, and (c) vertical eddy viscosity.
| u′w′ | are recognizable. Magnitude of Ps rarely
exceeded unity. In the next day this phenomenon
repeated again but with relatively lower intensity,
e.g. around 6 a.m. of Aug. 22 Ps was slightly larger
than 8 a.m. of the same date. Lower amounts of
| u′w′ | resulted in undermost magnitudes of Ps during
HWS and Low water slack (LWS). Negative values
of Ps that are omitted from Fig. 4(b) may be a
correspondence to the sign reversal of −u ′w′ around
the end of ebb, e.g. 16-18 of Aug. 21. Other
incorrect data may be the consequence of unreliable
stress estimations or HRCP limitations in highly
stratified flow. Fig. 4(c) illustrates variations of
eddy viscosity coefficient KM calculated from Eq.
(5). This coefficient is a function of Ps and mean
velocity gradients; hence its highest magnitudes
came up at the same time as Ps and or −u ′w′ peaks.
In contrast with previous two parameters, magnitude
of KM in flood portion of the tide is larger than that
of during the ebb in the second tidal phase. KM
varies in a range from 102 cm2/s in the first ebb to
10-3 cm2/s in the following LWS. KM increased with
receding from bed especially during flood phases.
During ebb time and particularly LWS, KM had very
small values near the bottom, corresponding to weak
near-bed-generated turbulence.
In Fig. 5(a) Richardson number Ri at 0.02 and
0.26 mab is plotted. Dash line denotes the critical
value of ¼. Ri in the near-bottom layer rarely
exceeds ¼, though largest values of Ri that may
reach 102 can be seen in the upper layers during
HWS and LWS. In Fig. 5(b) temporal variations of
eddy viscosity coefficient KM without negative
- 195 -
( )
0.02
)
KM (cm2/s)
Ri
where, | u′w′ |0.02 is the absolute value of the Reynolds
stress at 0.02 mab and u ( z ) is the averaged velocity
over each 5 minutes. Values of plotted variables
according to Mellor and Yamada 2) in a neutral
equilibrium boundary layer is defined as: | u′w′ | /q2≈
0.15, σu/u*≈2, and σw/σu≈0.5. On the other hand,
Nezu and Nakagawa6) showed that | u′w′ | /q2 varies
between 0.1 near the bed, reaches 0.04 near the
water surface, and in the middle of water column is
0.15. Neglecting dispersions at the first and the end
of observation period, σ u /u * ≈3, however no
fluctuations comparable with tidal fluctuations
(Kawanisi1)) can be recognized. Fig. 5(b) reveals
that value of σw/σu changed noticeably in HWS/
LWS. High turbulence occurred on the first day
made a relative peak. Least values of | u′w′ | /q2 were
observed during calm periods: HWS/LWS that
means inactive and effectively irrotational part of
turbulence was larger during these times as cited in
Bradshaw 7) . Inactive part of turbulence doesn’t
produce any shear stress and is determined by the
turbulence in the outer layer. This inactive motion is
produced as a result of density interface in water
column that acts like a free surface and suppresses
the vertical movement of eddies. Considering Eqs.
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10 12 14 16 18 20 22 0 2 4 6 8 10
Aug. 21
Aug. 22
Local Time (hours)
Fig. 5 Temporal variations of (a) Local gradient Richardson
number at 0.02 (○) and 0.26 mab (●), and (b) vertical
eddy viscosity at 0.02 (○) and 0.26 mab (●).
σu / u 'w'
σ w / σu
u ' w ' / q2
( )
(
(a)
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10 12 14 16 18 20 22 0 2 4 6 8 10
Aug. 21
Aug. 22
Local Time (hours)
Cf
values is plotted. It seems that vertical eddy
viscosity coefficient is a function of Richardson
number Ri. Near-bottom KM reached its least values
in HWS/LWS as a result of weak near-bed
generated turbulence that stems from baroclinic
pressure gradient. Also, there is a high-amplitude
fluctuation in KM that was produced by a strong
turbulent current around 4 p.m. of Aug. 21. Source
of this strong turbulence is unknown to authors.
Fig. 6 demonstrates temporal variations of
turbulent velocity variables and resistance
coefficient Cf at 0.02 and 0.26 mab. In this figure:
1/ 2
1/ 2
σ u = u ′2
, σ w = w′2
. Here, resistance coefficient
can be evaluated from:
u ′w′
0.02
C f = 0.58
(14)
∫ u ( z )dz 0.56
1/ 2
Fig. 6 Temporal variations of (a) ratio of longitudinal turbulent
intensity to local shear velocity, (b) ratio of longitudinal
to vertical turbulent intensity, (c) ratio of Reynolds
shear stress to turbulent energy at 0.02 (○) and 0.26 mab
(●), and (d) resistance coefficient.
(7) and (8), and assuming l=lm it is deducted that:
| u′w′ | /q2= S M2 . According to Stacey et al.11)
equivalency of l and lm in stratified turbulent
boundary layer is acceptable. Comparing Figs. 6(c)
and 2(a) reveals that SM in boundary layer can be a
function of tidal phase. As well, in 0.26 mab SM
fluctuations are comparable with that of Richardson
number in Fig. 5(a). Highest (lowest) estimates of
resistance coefficient Cf were recorded in HWS
(LWS).
6. VARIATIONS OF THE TURBULENCE
PROFILES WITH TIDAL PHASE
Vertical profiles of the mean velocity, and
different turbulence parameters are shown in Figs.
7-11. Numbers in each figure is referred to as the
tidal phase displayed in Fig. 2(a). Hereafter, letter
“A” denotes the first half of the semi-diurnal tide
and “B” the second in figures. In Figs. 7(a)-(d)
vertical distributions of mean streamwise velocity
are illustrated. During LWS (3A), tidal straining can
be recognized. In flood and ebb time, velocity
profile was logarithmic.
Reynolds shear stress is plotted in Fig. 8.
Strong turbulent event led to large Reynolds stresses
(2A) that evaluated 2.5 times as large as that
produced during flood (4B). In calmer conditions, e.g.
HWS and second ebb, low values of | u′w′ | are
detectable. In flood time despite faster current speed,
flow regime is not so turbulent in comparison with
first ebb. During LWS as a result of stratification,
baroclinic pressure gradient and tidal straining
Reynolds shear stress reduced.
- 196 -
(a)
z (m)
0.5
0.4
0.2
0.0
-1 0
1
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8 12
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- 20 -10
4
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-4 -3 - 2 -1 0 1 -1
_ u ' w ' (cm 2 /s 2 )
4B
4A
3B
0.0 0.4 0.8 1.2
0
Fig. 8 Vertical profiles of local shear stress in (a) HWS, (b) ebb,
(c) LWS, and (d) flood.
(a)
0.5
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-8 -6 -4 -2 0 2 -20 0 20 40 60 80 2 0 2 4 6
K M (cm 2 /s)
0 5 10 15 20
Fig. 9 Vertical profiles of vertical eddy viscosity in (a) HWS,
(b) ebb, (c) LWS, and (d) flood.
(a)
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0 2 4 6 8 -0.2 0.0 0.2 0.4
Ri
0.4
Fig. 10 Vertical profiles of local Richardson number in (a)
HWS, (b) ebb, (c) LWS, and (d) flood.
(a) Aug. 22 00:34 (b) Aug. 22 03:20 (c) Aug. 22 07:06 (d) Aug. 22 10:01
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10 20 30 0 4 8 12
Turbulent Velocity Variables
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0 10 20 30
Fig. 11 Typical profiles of turbulent velocity variables: 100
| u′w′ | /q2 (○), σu/ | u′w′ |1/ 2 (●), and 100σw/σu (▲).
(a) Aug. 22 00:34 (b) Aug. 22 03:20 (c) Aug. 22 07:06 (d) Aug. 22 10:01
0.5
0.4
z (m)
Vertical eddy viscosity KM as a function of qlm
at 0.02 and 0.26 mab for the ebb and flood phase is
plotted in Fig. 13. It seems that KM and qlm are in
proportion, and if we accept that l=lm then the ratio
(c)
(b)
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Fig. 7 Vertical profiles of mean streamwise velocity in (a)
HWS, (b) ebb, (c) LWS, and (d) flood.
7. PARAMETERS OF M-Y MODEL
0.3
0.1
z (m)
In Fig. 9 vertical distributions of vertical eddy
viscosity is plotted. During the first HWS (1A) KM
was notably large between 0.1 to 0.3 mab, though
shear production rate was not high throughout the
water column. In the first ebb (2A) magnitude of Ps
was increasing as it goes further from bottom which
leads to the vertical eddy viscosity increment with a
constant rate. During LWS, especially second one
(3B) we have different gradients of KM with different
signs. Such a phenomenon can be described as: in
high stratification (Ri>0.5-0.7) buoyant production
may cause vertical transfers of momentum and heat
occur against their mean gradient (Komori et al.8)).
As shown in Fig. 10, Ri was excessively high in
LWS/HWS that shows a highly-stratified and stable
flow. In contrast with the first ebb (2A) during the
following flood (4A) magnitude of KM is quite low
and almost constant throughout the water column.
Considering Figs. 6(c) and 11 indicates that
variations of SM were in accordance with tidal phase,
i.e. during the ebb peak values of SM was in onset of
the first ebb SM=0.43. It seems that over the LWS
tidal straining affected SM; in other tidal phases
stability function looks stable throughout water
column. Stacy et al.9) found that SM varies from
about 0.3 near the bed to 0.1 in above the stratified
layer. σu/ | u ′w′ |1/ 2 didn’t change noticeably except in
LWS. Ratio of vertical velocity fluctuations to
streamwise fluctuation varied comparably with tidal
phase: largest values can be detected in flood and
ebb times. Studies of Komori et al.8) showed: σw/σu
decreases slightly as stratification shifts from neutral
to weakly stable condition and then increases as Ri
rises. Correspondingly, here on Aug. 22 07:06 it can
be seen that in stable condition more vertical
motions than horizontal motions occurred, when the
Ri was high.
Rates of TKE production and energy
dissipation ε are illustrated in Fig. 12. We applied
Kolmogoroff’s -5/3 power law to describe 1D
kinetic energy density as a function of energy
dissipation, e.g. Kawanisi1). Pb is estimated from Eq.
(9) assuming KM=KH. Peak magnitude of Ps in the
flood phase was 0.15 cm2/s3. Buoyant production
rate Pb was negligible. Thus, Rate of energy
dissipation is larger than Pb+Ps; so we cannot
assume a local balance of TKE. Such an imbalance
is reported by Kawanisi1) and also was studied by
Stacy et al.9).
0.3
0.2
0.1
0.0
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0.1 0.0 0.1 0.2 0.3 -2 -1 0
10 Ps , _10 Pb , ε (cm 2 /s3 )
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1 0.0 0.5 1.0 1.5
Fig. 12 Typical profiles of turbulent energy production and
dissipation rate: 10Ps (○), 10Pb (●), and ε (▲).
- 197 -
K M (cm 2 /s)
6 z= 0.02 m
ç
ç
5
l
4
3çç5 q m çç çç
.
0
= ç
ç
3
K M ççç
ç ç
ql m
2
æ ç
= 0.26
1 æææçæææææççæææççæææçææççæç çç ç K M
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0
0
5
10
15
qlm (cm 2 /s)
REFRENCES
ç
60 z= 0.26 m
l
50
.36qç m ç
0
=
ç
40
KM ç
30
æ
çç
çç
æ æ
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l
20
ç ç
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0.21q m
ææ
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10 çææçæçææçæçææçææææææææææææææ
KM =
ç
ç
ç
ææ
ç
æ
ç
ç
ç
æææ
ææ
0 æçççççç
0
50
100
150
qlm (cm 2 /s)
1) Kawanisi, K.: Structure of turbulent flow in a shallow tidal
estuary, J. of Hydraulic Engineering, ASCE, 130(4),
pp.360-370, April 2004.
2) Mellor, G.L., and Yamada, T.: Development of a turbulence
closure model for geophysical fluid problems, Rev,
Geophys. Space Phys.,Vol. 20(4), pp.851-875, 1982.
3) Stone, M. C., and Hotchkiss, R. H.: Evaluating
q 3 / lm (cm 2 /s3 )
Fig. 13 Relation between qlm and KM in ebb (○) and flood (●).
103
102
101
100
ç
ç
çç
çç ç
ç
ç ç ç
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ç ççç ç
ç çç çç
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æ ææ
10-1
100
101
2 3
ε (cm /s )
æ
ç
velocity measurement techniques in shallow streams,
q 3 lm 8.90
ε = 0.95
102
Fig. 14 Scatter diagram of energy dissipation rate against q3/lm
at 0.02 (○) and 0.26 mab (●).
of KM/qlm will represent the amount of M-Y stability
function SM. Referring to Fig. 6(c) supports that
stability function in ebb should be larger than that in
flood. Proportionality shown in Fig. 13 suggests
SM=0.35. Kawanisi1) calculated the highest value of
SM= 0.29 during flood. Both of these signify that the
SM in M-Y model which is calculated under neutral
condition is not valid here because under
unstratified equilibrium conditions SM=0.39
(Gulperin et al.10)).
Fig. 14 is the scatter diagram of ε which is
estimated from u-spectra against q3/lm at 0.02 and
0.26 mab. In M-Y model B1=16.6, though here
in0.02 mab B1=8.9. Kawanisi1) calculated this
constant about 40 assuming ε=Ps.
J. Hydraulic Research, Vol.45(6), pp. 752–762, 2007.
4) Kawanisi, K., Tsutsui, T., Nakamura, S., and Nishimaki, H.:
Influence of Tidal Range and River Discharge on Transport
of Suspended Sediment in the Ohta Flood-way, J.
Hydrosciences and Hydraulic Engineering, Vol. 24(1), May,
pp.1-9, 1996.
5) Cao, Z., Pender, G., and Meng, J.: Explicit Formulation of
Shields Diagram for Incipient Motion of Sediment, J.
Hydraulic Engineering, ASCE, Vol.132(10), pp.1097-1099,
2006.
6) Nezu, I. and Nakagawa, H.: Turbulence in open-channel
flows, Balkema, Rotterdam, The Netherlands, 281, 1987.
7) Bradshaw, P., Inactive motion and pressure fluctuations in
turbulent boundary layers, J. Fluid Mech., Vol. 30, pp.241258, 1967.
8) Komori, S.,Ueda, H., Ogino, F.,and Mizushima, T.:
Turbulence structure in stably stratified open-channel flow,
J. Fluid Mechanics, Vol. 130, pp.13-26, 1983.
9) Stacy, M.T., Monismith, S.G., and Burau, J.R., Observation
of turbulence in a partially stratified estuary, J. Phys.
Oceanogr., Vol.29, pp.1950-1970, 1999.
10) Gulperin, B., Kantha, L., Hassid, S., and Rosati, A.: A
quasi-equilibrium turbulent energy model for geophysical
flows, J. Atmos. Sci., Vol.45(1), pp.55-62, 1988.
8. CONCLUSIONS
Turbulent parameters in the bottom layer of
Ohta Floodway were investigated. Examining
critical and current induced shear stress indicates
that no resuspension happens in the observation site.
A high turbulent current at the first ebb deeply
affected the results: Largest values of | u′w′ | and Ps
was detected in ebb time, however KM reached its
peak during flood. During HWS/LWS flow became
highly stratified especially in upper layers. σu/u*
found to be about 3 showing no relation with tidal
phase. Least values of | u′w′ | /q2 were observed in
relatively slack waters that means inactive and
effectively irrotational part of turbulence was larger
during LWS and HWS. Stability function in M-Y
model SM calculated as approximately 0.2 in flood
and 0.35 in ebb. Constant B1 evaluated as 8.9 which
is less than previous studies as a result of high
imbalance in TKE production and dissipation. This
imbalance implies that for estimating turbulent
parameters equality of production and dissipation
rates is unreliable.
- 198 -
(Received September 30, 2009)