Annual Journal
Journal of
of Hydraulic
Hydraulic Engineering,
Engineering, JSCE,
JSCE, Vol.54,
Vol.54, 2010, February
Annual
OBSERVATIO
OF TURBULE
CE CHARACTERISTICS
I
THE ŌTA RIVER USI
G ADV A
D HRCP
Mahdi Razaz 1, Prof. Kiyosi Kawanisi2
1
Member of JSCE, M. Eng., River and Coastal Engineering Laboratory, Dept. of Civil & Environmental Engineering,
Hiroshima University (1-4-1, Kagamiyama, Higashi-Hiroshima 739-8527, Japan)
2
Member of JSCE, Dr. of Eng., Associate Professor, Dept. of Civil & Environmental Engineering,
Hiroshima University (1-4-1, Kagamiyama, Higashi-Hiroshima 739-8527, Japan).
Acoustic Doppler Current Profilers (ADCP) and Velocimeters (ADV) have been increasingly used for
measuring small-scale processes involving turbulence in estuarine environments. A point at the center of
the Ōta Floodway, 2.8 km far from mouth, was selected to deploy an ADV and a HRCP (High-Resolution
ADCP) during 25 hours of Jan. 2009. Obtained data were despiked and analyzed in order to first examine
turbulence parameters calculated from HRCP data. Next, estimate TKE production and dissipation rates
from 1D spectra of vertical component of velocity w and using Kolmogorv’s -5/3 power law. Then,
redefine M-Y model parameters of proportionality constant B1 and stability function SM. Finally, intercompare HRCP and ADV in 3 reference levels of 0.03, 0.4, and 0.8 mab along with w-spectra and
turbulence energy spectra reveal that w’ is underestimated by HRCP which leads to lower dissipation
rates comparing to ADV. Also, longitudinal velocity fluctuations u’ of ADV are underestimated, as a
result streamwise Reynolds stress of ADV is less than that obtained from HRCP at bottom level.
Key Words: Acoustic Doppler effect, estuaries, tidal currents, turbulence, M-Y model, power spectrum
1. I
TRODUCTIO
To overcome the complexity caused by dynamic
natural elements e.g. tidal oscillation, river
discharge, wind driven waves, etc. instruments
referred to as pulse-to-pulse coherent Doppler sonar
have been developed. These instruments are able of
collecting data in situ with high quality throughout
water column and observation period. Backscattered
data can be translated into velocity components,
suspended sediment concentration (SSC), sound
speed in water, etc. These instruments have been
widely used by scientists to conduct various
measurements in complex flow fields, e.g. Hill et
al.1, Fugate and Friedrichs2, Muste et al.3, and
Kawanisi4.
Drawbacks of using instruments based on
acoustic pulse-to-pulse coherent sonar can be
divided into 2 main groups: a) intrinsic: issues in
converting raw backscattered wave data to
figures/numbers inside the instrument (e.g.
Lohrmann and Nylund5); b) extrinsic: ambiguities in
rendering raw collected data into applicable
knowledge such as SSC. At the present paper, by
processing backscatter data and applying necessary
corrections (e.g. Downing et al.6; Thorne et al.7; Hill
et al.1), raw backscatter data translated into vertical
profiles of velocity and SSC. HRCP analyzed data
will be reviewed and compared to the data acquired
by an ADV to focus on the latter problem with
intercomparing HRCP and ADV. According to
Voulgaris and Throwbridge8 ADV data are precise.
2. STUDY AREA
METHOD
A
D
OBSERVATIO
Ōta Floodway is the most-west branch of the Ōta
River with a length of nearly 9 km. It is a tidallydominated river and the maximum tidal range in an
extreme spring tide can reach 4 m close to the
mouth (Fig. 1). Fresh water inflow to the Ōta
Floodway is controlled by the Gion sluice gates that
are located in the bifurcation place. The Gion sluice
gates consist of 3 main gates that generally just one
of them is opened to provide a 32×0.3 m2 cross
section for spilling the flow into the Ōta Floodway.
From this cross section about 10% of flow in the
main branch of the Ōta River is diverted to the
floodway in normal days. However during the flood
event, the Gion sluice gates are opened as to divert
50% of total fresh water to the floodway.
In our observations we operated a commerciallyavailable HRCP: HR-AquaDopp and an ADV:
Vectrino +, both developed by NORTEK AS Co.
- 211 -
132.43
132.45
132.47
132.49
4 (a)
3
2
1
0
0.8
h (m)
132.41
34.45
σt (kg/m3 ) 999
(b)
z (m)
Gion Sluice Gates
Ti d a
l Co
mp
artm
ent
34.43
34.41
Observation
Point
0.4
0.0
Hiroshima City
34.37
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
z= 0.80 mab
z= 0.40 mab
0
2
4
6
z= 0.03 mab
10 12 14 16
8
Jan. 27
Jan. 28
Local Time (hr)
Fig. 2 Temporal variations of (a) water depth, (b) density (σt)
profile, and (c) instantaneous longitudinal velocity u.
VARIATIO
mainly near the upper and lower edges. These
erroneous areas may be a correspondence to the sign
reversal of the streamwise Reynolds shear stress
−u ′w′ around the end of ebb, a consequence of
unreliable stress estimations, or HRCP limitations in
highly stratified flow. The gray stripe indicates the
lower low water in which HRCP transducers were
dried out. In Fig. 3(a) variations of the longitudinal
Reynolds shear stress −u ′w′ in depth is plotted.
Hereafter symbols ↑ and ↓ stands for approximate
HWS and LWS time in figures, respectively. Over
the observation period | u′w′ | is relatively low.
According to Fig. 3(a), this variable reaches its peak
values just before and after lower low water slack
(LWS). Referring to Fig. 2(c) reveals that
l ongi t udi nal Reynol ds s t r es s and vel oci t y
0.8
(a)
_ u ' w ' (cm 2 /s 2 )
(b)
(c)
-3.75
3.75
log10 PS (cm3 /s 2 )
-0.5
0.0
log10 K M (cm 2 /s)
-3.0
2.0
0.6
z (m)
However mean velocity collected by the ADV and
ADCP are assumed to be identical (Stone and
Hotchkiss9), there are uncertainties about fluctuating
part of measured velocity by ADCPs mainly
because of low time resolution, their relatively large
sampling volumes, and using 3 or 4 separated beams
that move away from each other as the beam length
increases. In order to measure velocity profile
precisely, the HRCP was installed down-looking as
the transducers were 1 m above the bed (mab). To
prevent device from being shaken by currents it was
fixed on a special frame. Data was collected at 1.0
Hz sampling rate and 2.0 cm cell depth. Blanking
distance was set to 5 cm. To measure the turbulence
just near to the bed we deployed the ADV with a
synchronized compass/tilt in about 8 cm far from
the bed that its beams intersect in approximately 50
mm far from the center of sampling volume. Every
20 minutes location of the ADV was changed so as
to measure velocity components in 0.03, 0.40, and
0.80 mab. A Conductivity/Temperature/Depth
(CTD) probe developed by Alec Electronics Co. was
casted every 30 minutes to check salinity and
density profiles in 10 cm depth-triggered mode. The
observation fulfilled over 25 hours of 27-28 Jan.
2009 using described instruments in a point that is
located 2.8 km far from the river mouth at the center
of the river (Fig. 1). Water depth, salinity and
velocity variations in observation time-span are
shown in Fig. 2.
0.4
0.2
0.0
0.8
0.6
z (m)
Fig. 1 Map of the observation point.
3. DEPTH-TIME
TURBULE
CE
(c)
14 16 18 20 22
0 0.5 1 km
0.4
0.2
0.0
0.8
0.6
OF
z (m)
34.35
1025
0.2
u (m/s)
34.39
0.6
0.4
0.2
Depth-time variation of turbulence parameters
averaged over 5-minute intervals estimated from
HRCP data are shown in Fig. 3. Areas with absolute
white color denote the omitted erroneous data
0.0
16
18
20 22
0
2
4
6
Jan. 27
8
10
Jan. 28
12
14 16
Local Time (hr)
Fig. 3 Depth-time distributions of (a) Reynolds stress, (b)
shear production, and (c) eddy viscosity.
- 212 -
Ri
log10 (K M )
K M (cm 2 /s)
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Jan. 28
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Fig. 4 Temporal variations of (a) local gradient Richardson
number, (b) vertical eddy viscosity and (c) scatter plot
of KM variations as a function of Ri-1 in 0.8 (●), 0.4
(○), and 0.03 mab (▼).
component u are in phase. Since TKE shear
production Ps is a function of Reynolds stress, it is
expected to find the highest magnitudes of Ps at the
same time as Reynolds stress (Fig. 3(b)). Fig. 3(c)
exhibits spatiotemporal variations of eddy viscosity
coefficient KM that is a function of Ps and means
velocity gradients; hence it is in proportion with Ps
and or −u ′w′ . Magnitudes of KM in the second tide
were generally higher than those in the first tide;
especially, after the lower LWS all over the flood
duration KM was high. During the first ebb and
particularly in LWS, KM had very small values near
the bottom, corresponding to weak near-bedgenerated turbulence.
Stratification of the river bottom layer is taken
into account by plotting Richardson number Ri
obtained from the HRCP data. In Fig. 4(a) dash line
denotes the critical value of ¼. Ri in the near-bottom
layer rarely exceeds ¼ and in floods lowest
Richardson numbers are noticeable, while large
values of Ri could be found in the upper layer in
slack waters particularly in HWS. Fig. 4(c) suggests
that KM and Ri-1 are in good agreement.
Rates of TKE production and dissipation are
plotted in Figs 5 and 6. Selected sections are marked
by dash lines in Fig. 2(a). We used Kolmogorov’s
-5/3 power law to describe 1D kinetic energy
density as a function of energy dissipation ε.
0.8
z (m)
0.6
0.4
0.2
0.0
(b) LWS
(a) Ebb
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Buoyant production Pb is estimated assuming
KM=KH, where KH is the vertical eddy diffusivity. As
it is expected to observe larger magnitudes of shear
production Ps before and after of LWS, uppermost
values of shear production are discernible in the
second LWS near the bed and in the following flood
with around 0.4 and 1 cm2/s3, respectively (Fig. 6).
Although during the first tide buoyant production
rate Pb is insignificant, in the following ebb and
flood in about 0.7 mab outstanding magnitudes of
this variable can be seen. Since rate of energy
dissipation is often less than Pb+Ps except in the
HWS according to the HRCP data set, we cannot
assume a continuous local balance between TKE
production and dissipation. In order to confirm the
method and hardware applied to obtain TKE
production and dissipation rates, we conducted
short-term measurements in a laboratory flume
using the same HRCP. Results notify an acceptable
compliance between kinetic energy production and
dissipation. This imbalance is reported by Kawanisi4
and confirmed in our previous study at the same
point (Razaz et al.10). Such an imbalance that was
studied by Satcey et al.11) may stem from unsteady
state of flow during tidal phases or underestimation
of w’ by HRCP (Fig. 15).
Vertical eddy viscosity KM as a function of qlm at
0.03, 0.4 and 0.8 mab for the ebb and flood phase is
plotted in Fig. 7. q is the turbulence energy and lm
refers to the mixing length. Apparently KM and qlm
are in good proportion, and if we accept that
turbulent mixing length in M-Y model l is equal to
lm, ratio of KM/qlm represents the amount of M-Y
stability function SM. From proportionalities shown
in Fig. 7 it is inferred that during flood SM≈0.22
which is slightly greater than that in the ebb.
Kawanisi4 calculated the highest value of SM=0.29
during flood. In our previous observation SM
calculated as 0.25. All these signify that SM in M-Y
model which is calculated under neutral condition,
is not valid here because under unstratified
equilibrium conditions Gulperin et al.12 function
gives SM=0.39, while highest SM in flood, when
stratification is negligible, is less than 0.3.
Fig. 8 is the scatter diagram of dissipation ε
against q3/lm. In M-Y model B1=16.6, though here
B1 is outstandingly larger, particularly near the bed.
Very small dissipation rates obtained from the
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Turbulent Velocity Parameters (Jan. 27)
-40-20 0 20 40 -15-10 -5 0 5 10 0.0 0.2 0.4 0.6
Turbulent Velocity Parameters (Jan. 28)
Fig. 5 Typical profiles of turbulence energy production and
dissipation rate: 10Ps (○), 10Pb (●), and 10ε (▲).
Fig. 6 Typical profiles of turbulence energy production and
dissipation rate: 10Ps (○), 10Pb (●), and 10ε (▲).
0
1
2 -1 0 1 2 3 4 -2-1 0 1 2 3 4 -0.2 0.0 0.2 0.4
- 213 -
K M (cm 2 /s)
3.0
æ
25 z= 0.4 mab
æ
æ æ
ql m
2.5 z= 0.03 mab
qæl m ææææ æ ææ
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=
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K Mæ æ ç æ
15
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l
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0.5
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0.0 æ ç
0 ç
0
2
4
6
8
10 0 20 40 60 80 100
2
qlm (cm /s)
qlm (cm 2 /s)
HRCP data are responsible for these extraordinary
high values. If we accept ε=Pb+Ps, then B1 could be
roughly estimated as 70 by replacing ε with Pb+Ps
in Fig. 9. According to this figure and the way B1 is
calculated, it is proposed that ε is underestimated
from HRCP data by an order of 10, averagely.
Kawanisi4 calculated this constant about 40
assuming ε=Ps. Also, we already calculated this
constant about 40 assuming ε=Ps. Also, we already
calculated this constant as 55 under the same
assumption. These results recommend a higher
value for B1 instead of the original value.
4. I
TERCOMPARI
G PERFORMA
CE
OF HRCP A
D ADV
(1) Turbulence parameters
In this section we will try to compare key
turbulence parameters at 3 reference levels of 0.03,
0.4 and 0.8 mab obtained from analyzing raw data
collected by the ADV and HRCP. In the following
figures, U= (u2+v2)1/2; u, v, and w are longitudinal,
transverse, and vertical components of velocity,
respectively; prime sign denotes variation from the
mean value; and “−” stands for averaging over
time. Absolute values of longitudinal and vertical
velocity fluctuations can be defined as
( )
1/2
( )
1/2
σu = u′2 ,σw = w′2 , respectively.
10 1
10 0
10 -1
10 -2
10 -4
0.8
10 -2
10 -3
2 3
ε (cm /s )
æ
çæ
B =235
B =703
B =3110
10 -1
0.6
:0.8 mab
ç :0.4 mab
:0.03 mab
æ
Fig. 8 Scatter diagram of energy dissipation rate against q3/lm.
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: Flood
: Ebb
over the observation length. In 0.4 mab, difference
between measurements of the two sensors increases
to its maximal, while in 0.8 mab we can observe less
disparity. This pattern can be observed in other
turbulence statistics variations. In Fig. 11 ratio of
σu/u*, u* is the shear velocity, is plotted. Mean nearbed value for ADV is around 3 and rises to 7 for
HRCP data.
Considering Fig. 12 reveals that value of σw/σu
didn’t change noticeably with distance from bed for
both sensors. Mean values of this ratio for the ADV
data is about 0.48 and for the HRCP estimated as
0.28 for each of three reference levels. Concerning
Figs. 10, 11, and 12 it can be inferred that σu and σw
are underestimated by ADV and HRCP, respectively.
Also, inspecting u-spectra of ADV data reveals that
they are saturated at 0.2 Hz. This frequency is too
high under field scale considerations.
Variations of ratio of longitudinal Reynolds
stress to the turbulence energy are plotted in Fig. 13.
Mean values of this parameter doesn’t show
remarkable changes related to depth. In general,
estimations from ADV data are 70% larger than that
from HRCP. Finding largest magnitudes in slack
waters, suggests that inactive and effectively
irrotational part of turbulence is larger as cited in
Bradshaw15 . Inactive part of turbulence doesn’t
produce any shear stress and is determined by the
turbulence in the outer layer. This inactive motion is
generated as a result of density interface in water
column that acts like a free surface and suppresses
the vertical movement of eddies. Mean value of
ADV data set is about 0.08, while for the HRCP
data set is half of that. Assuming l= lm, it is inferred
that | u′w′ | / q2 = SM2 . According to Stacey et al.11
equivalency of l and l m in stratified turbulent
boundary layer is acceptable. From this method,
averaged values of SM over the observed period are
z (m)
q3 / lm (cm 2 /s 3 )
Values of plotted variables according to Mellor
and Yamada13 in a neutral equilibrium boundary
layer are defined as: σu/u*≈2, σw/σu≈0.5, and | u′w′ |
/q2≈0.15. On the other hand, Nezu and Nakagawa14
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. Fig. 10 shows
temporal variations of the streamwise Reynolds
stress RS over the observation period. Best
convergence between HRCP and ADV data can be
recognized near the bed, where RSADV= 0.83 RSHRCP
10 3
10 2
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30 z= 0.8 mab
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2
25
.
=0
20
Kç Mæ æççæ æ ç
ql m
15
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0
50
100
150
qlm (cm 2 /s)
Fig. 7 Relation between qlm and KM in different levels and tidal phases.
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0.4
0.2
0.0
0 40 80 120
B1
Fig. 9 Vertical profile of constant B1.
- 214 -
q 3 / lm
:
10 1 ε
q 3 / lm
:
Pb + Ps
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16 18 20 22
Jan. 27
0
1/ 2
z= 0.8 mab
z= 0.4 mab
σu / u ' w '
U ' w ' (cm 2 /s 2 )
10 2
10 10
10
10 -1
10 -2
z= 0.03 mab
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Local Time (hr)
10 12
Jan. 28
14 16
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0.6
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Jan. 28
Local Time (hr)
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Jan. 27
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Local Time (hr)
8
10
Jan. 28
12
14
16
Fig. 11 Comparison between evaluated σu/ | u′w′ |1/ 2 acquired
from HRCP data (○) and ADV data (●).
u ' w' / q 2
σw / σu
Fig. 10 Comparison between streamwise Reynolds stresses
acquired from HRCP data (○) and ADV data (●).
12
8
4
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4
12
8
4
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0.20
0.15
0.10
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0 2 4 6 8 10 12
Jan. 28
Local Time (hr)
14 16
Fig. 12 Comparison between evaluated σw/σu acquired from
HRCP data (○) and ADV data (●).
Fig. 13 Comparison between evaluated | u′w′ | /q2 acquired
from HRCP data (○) and ADV data (●).
approximately 0.2 and 0.28 using HRCP and ADV
data, respectively.
In this part, dissipation calculated from 1D
spectra of w-component will be discussed. As shown
in Fig. 16, HRCP dissipation rate is less than
production rate except in short times. ADV
dissipation rate in 0.03 mab is smaller than in 0.8
mab, however it seems to be overestimated in 0.4
mab. The larger values of dissipation and turbulence
statistics in 0.4 mab can be a consequence of
boundary effects. In spite of setting nominal
(Power) Spectral density functions or simply the
(power) spectra of turbulence energy q2 as measured
by the ADV and HRCP sensors are examined here.
The spectra from whole observation time span in 3
reference levels are presented in Fig. 14, in which f
represents the sampling rate of each sensor. These
spectra are computed by Fast-Fourier Transform
(FFT) method (He16). Evidently, both sensors have
the same energy level except in near-bed level.
While the ADV waves carry no energy in
frequencies less than 5 × 10-1 Hz, this limit is
extended to 5×10-2 Hz for the HRCP. It is unknown
to us why the energy of ADV spectrum dropped
down in 0.03 mab. As another comparison between
the HRCP and ADV we examine the 1D spectra of
vertical component of velocity w. In particular the
spectra represented in Fig. 15 belong to flood phase
when velocity fluctuations are remarkable. These
spectra illustrate that ADV turbulence velocity
spectra contain more energy than that of HRCP.
HRCP w-component contains quite less fluctuations
rather than ADV data. In addition, mean value of
wHRCP is smaller than that of ADV at the same
intervals. This problem intensifies with distance
from bed. For both sensors there is no sudden
change in the slope indicating that the noise floor is
approached. Spectra of both ADV and HRCP decay
at relatively high f values with a -5/3 rolloff all the
way up to half of sampling frequency.
(3) Dissipation
velocity of ADV to 0.1, 0.3 or 1 m/s which are
attributed to weak spots at 46; 20; 8, 20 cm far
from boundary, respectively, it seems that
boundary effect is yet considerable in 0.4 mab.
εHRCP is smaller than εADV as a result of lower energy
range of w-spectra at the same frequency span.
Unfortunately, we cannot estimate Ps from ADV
data accurately, since number of observed points in
the water column is not enough to produce a reliable
velocity distribution. However, laboratory tests
conducted in a flume using the same HRCP resulted
in equivalence of dissipation and production of TKE.
Hence, we may assume that turbulent nature of flow
in tidal rivers causes some disabilities in the HRCP.
4. CO
CLUSIO
105
z=0.8
z=0.8
104
Eq 2 (cm 2 /s)
(2) Spectral Characteristics
10
3
ADV
(Vectrino+)
z=0.4
z=0.4
z=0.03
102
101
100
10-1
HRCP
(AquaDopp)
10 -1
10 0
10 1
f (Hz)
Fig. 14 Power spectrum of turbulence energy computed from
HRCP and ADV data at 3 reference levels.
- 215 -
10 -2
z=0.03
Ew (cm 2 /s)
10 1
z=0.03, 27 Jan. 20:20
z=0.4, 27 Jan. 8:40
Vectrino+
101
10 0
10
-1
10
-2
z=0.8, 27 Jan. 10:00
101
Vectrino+
100
100
10 -1
AquaDopp
10 -3 10 -2 10 -1 10 0
10 1
10
Vectrino+
10 -1
AquaDopp
-2
10 -3 10 -2 10 -1 10 0
f (Hz)
10 1
10
AquaDopp
-2
10 -3 10 -2 10 -1 10 0
10 1
Fig. 15 Power spectra of w-component in 3 different level and tidal phase.
ε , Ps,HRCP + Pb ,HRCP (cm 2 /s)
Examining spatiotemporal variations of
longitudinal Reynolds shear stress reveals that
just before and after lower LWS this variable
increases to its absolute peak values. However
in flood time Reynolds stress stays in relatively
high levels. Subsequently, TKE production rate
and vertical eddy viscosity that are a function of
Reynolds stress are augmented at the same time
as Reynolds stress. Because other factors such
as velocity gradients and turbulent mixing
length affect the latter two variables, their
spatiotemporal variations don’t exactly follow
Reynolds stress fluctuations. During HWS/LWS
flow becomes highly stratified especially in
upper layers. Maximum stability function found
to be 0.23 which is quite less that Gulperin’s
function12 result in unstratified equilibrium
conditions. This means the assumption of
neutral conditions in M-Y model for estimating
stability function is invalid. According to the
HRCP result, TKE production and dissipation
rates are not equal except in HWS that Ps is in
its lowest rates. It seems that dissipation is
underestimated by an order of 10 from the
HRCP data that leads to outstanding magnitude
of B1. Comparing turbulence statistics together
with u- and w-spectra reveals that u’ and w’ are
underestimated by ADV and HRCP,
respectively. Streamwise Reynolds stress of
ADV, except at bottom level, is larger than that
of HRCP. As a result, σw/σu and σu/u*
measurements are divergent for both
instruments. However, SM values of both
sensors are in good agreement.
Finally, plotting spectra of turbulence energy
102
1010
10-1
10-2
10
10 -3
10 -4
10 10
10 -1
10 -2
10
10 -3
10 -4
10 -5
10 1
10 -1
10 -3
10 -5
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6
Local Time (hr)
8
10 12 14 16
Jan. 28
Fig. 16 Temporal variations of TKE production obtained from
HRCP data (●) and dissipation rate estimated from HRCP (○)
and ADV data (▼).
and w-component reveals the difference
between energy density of ADV and the HRCP.
Lower energy of HRCP w-component spectra
can explain the underestimation of Reynolds
stress and dissipation rates.
More studies could help to reveal more
precise differences between these two sensors.
REFERE
CES
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(Received September 30, 2010)
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