Luottamuksellinen
Sivu 1
2/7/2008
Ninni Liukko and Timo Huttula
JY/BYTL
Local aquatic mixing scales
Based on water current measurements on R/V Aranda in July 1997
1. SITE AND MEASUREMENT DESCRIPTION
The measuring site was at the entrance to the Gulf of Finland (Fig. 1).
Fig. 1. The red sphere is pointing the measuring site at the entrance to the Gulf of Finland.
Water currents were measured with three instruments on board of R/V Aranda. The
vessel mounted ADCP with transducer/receiver unit mounted on the ship hull was
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supplemented with two other current meters. With these instruments it was possible to
measure the near surface layer (0-16 m), which is not covered by the vessel mounted
ADCP. The two meters were used during 24h intensive sampling periods. They were
moved vertically with cranes and winches. One bottom mounted upwards looking ADCP
was deployed to the first 24h monitoring site. It was collecting data during the entire
expedition.
In the ship on the starboard side near the bow an ultrasonic current meter (UCM50) by
Sensortec Ltd. was used to collect data at the depth of 0-9 m. The instrument utilises
three transducer-receiver pairs for collecting 3D current data. Current velocity and
direction is calculated from the differences in travel times between the sensors of each
pair. The measurement is fairly quick and the accuracy of this data very high. On the port
side the RCM9 by Aanderaa Instruments was used. It is a horizontal plane Doppler
current meter. It was used to collect data at the depths of 7-37 m. The instruments were
used outside the magnetic field of the ship and with such data integration periods that the
ship and crane movements were smoothed out.
The measurements were done in 16.-24.7.1997. The ADCP were measuring currents all
the time in 10 min intervals. The UCM50 and RCM9 were used during some about 12hour periods. For example, the UCM50 and RCM9 were used together without
significant breaks 19.7. 4:00-7:30, 21.7. 18:00-21:00, 22.7. 2:00-12:00 and 23.-24.7.
18:00-8:00.
2. RESULTS
The results from one measuring period, 2:00-12:00 22.7.1997, are presented.
2.1. Wind conditions
The wind direction varied 21.7. In the beginning of the 22.7. velocity measuring period
the direction was from south-east. It then turned to east, back to south-east and finally to
south-west at the end of the period. (Fig. 2).
The wind speed was very low (about 2 m/s) in the day before the measuring and also
during the mearuring period (2:00-12:00 22.7.) (Fig. 3).
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360
Wind direction (deg)
315
270
225
180
135
90
45
0
0:00
12:00
0:00
12:00
0:00
0:00
12:00
0:00
Fig. 2. Wind direction 21.-22.7.1997
Wind speed (m/s)
20
15
10
5
0
0:00
12:00
Fig. 3. Wind speed 21.-22.7.1997.
2.2. ADCP results
Current direction was to west and to north in the upper part of the water column and to
south-east in deeper layers according to the ADCP measurement (Fig. 4). The velocity
increased during the measuring period in the whole water column. In the depth of about
6-35 m the velocity was about 5 cm/s at first and increased to about 15 cm/s in the time
of 12. The highest velocities were in the uppermost layers (4-5m) at night and in the
depth of 35-50 m in the morning. Maximum velocities were about 17-19 cm/s. (Fig. 5).
Fig. 4. Current direction measured by the ADCP 2:00:08 – 12:00:08 22.7.1997. The Fig. shows
the depth of 4-50m (on the right: bin46 = 4m, bin44 = 6m, bin42 = 8m, … , bin3 = 2m and bin0 =
50m).
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Fig. 5. Current velocity measured by the ADCP 2:00:08 – 12:00:08 22.7.1997. The Fig. shows
the depth of 4-50m (on the right: bin46 = 4m, bin44 = 6m, bin42 = 8m, … , bin3 = 2m and bin0 =
50m).
2.3. UCM50 and RCM9 results
In the following the results of the UCM50 and the RCM9 current meters are presented
together after a linear interpolation of data in 0.5 h and 1 m intervals.
Temperature was 19-20 ºC in the surface layer and declined to about 3-4 ºC in the depth
of 35 m (Fig. 6). Velocity increased during the measuring period and was highest at
surface (30-35 cm/s) at the end of the period (Fig. 7). The direction of the highest
velocities in the morning was to west at surface and to north-west below 5 m depth. (Fig.
8 and 9).
0
20
-5
15
Depth (m)
-10
-15
10
-20
-25
5
-30
-35
02
04
06
08
10
12
0
Time (hh)
Fig. 6. Isotherms at 1 ºC intervals. Data interpolated (0.5 h and 1m intervals) from UCM50 and
RCM9 measurement data 22.7.1997.
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Depth (m)
0
-5
30
-10
25
-15
20
-20
15
-25
10
-30
5
-35
02
04
06
08
10
12
0
Time (hh)
-1
Fig. 7. Velocity level curves at 2 cm s intervals. Data interpolated (0.5 h and 1 m intervals) from
UCM50 and RCM9 measurement data 22.7.1997.
0
20
-5
15
Depth (m)
-10
-15
10
-20
5
-25
0
-30
-35
02
04
06
08
10
12
-5
Time (hh)
Fig. 8. North velocity level curves at 3 cm s-1 intervals. Data interpolated (0.5 h and 1 m intervals)
from UCM50 and RCM9 measurement data 22.7.1997.
0
20
-5
10
Depth (m)
-10
0
-15
-20
-10
-25
-20
-30
-30
-35
02
04
06
08
10
12
Time (hh)
Fig. 9. East velocity level curves at 3 cm s-1 intervals. Data interpolated (0.5 h and 1 m intervals)
from UCM50 and RCM9 measurement data 22.7.1997.
2.4. Scales of turbulence
The data interpolated from the original measuring data from UCM50 and RCM9 current
meters were used to calculate the Brunt-Vaisala requency (N), period length (Pw), and
Richardson number (Ri). Friction velocity (u*) was approximated and that was used to
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calculate the Dissipation energy (E), Buoyancy length scale (Lb), Batchelor scale (Ld) and
Kolmogorov scales.
The numbers were calculated for the measuring period with 0.5 hour intervals and for
depth layers 1-2 m, 8-9 m, 22-23 m and 33-34 m. The numbers were therefore calculated
for times 3:00, 3:30, 4:00, … , 10:00 and 10:30. These momentary values were averaged
for the whole period.
The results are shown in Table 1 and also in the following figures 10-19.
The results are not accurate, because salinity was not taken into account in density
calculations (we don’t have salinity data yet).
Table 1. Averages of calculated numbers for the period of 3:00-10:30 22.7.1997. Numbers are
calculated over the four depth layers shown in the first row.
BRUNT-VAISALA frequency N (rad
Period length Pw (s)
Richardson number Ri
Buoyancy length scale Lb (m)
Friction velocity appr u* (m s-1 )
Dissipation energy E (m2 s-3)
s-1)
Batchelor scale Ld
Kolmogorov length scale lm (m)
Kolmogorov length scale lm*2π (m)
Kolmogorov time scale tm (s)
Kolmogorov velocity scale vm (m s-1)
1-2 m
0.026
361.3
4036.2
0.38
0.006
7.27E-07
0.012
8-9 m
0.025
256.4
391.8
0.15
0.005
8.83E-07
0.008
22-23 m
33-34 m
0.016
396.7
32.8
0.17
0.004
1.4E-07
0.005
0.004
6839.3
5.1
5.47
0.006
6.91E-07
0.006
0.005
0.003
0.002
0.002
0.031
0.020
0.014
0.015
142.1
19.7
5.9
9.8
0.001
0.001
0.001
0.001
Brunt-Vaisala frequency and Wave period length
The Brunt-Vaisala frequency or buoyancy frequency (N) was calculated as N =
((g/ρ)*(dρ/dz))1/2, where g is 9.81 m s-2, ρ is density and z is depth. The wave period
length is then Pw = 2π/N.
The Brunt-Vaisala frequency is the frequency of the oscillation that results when the
density interface is displaced and then left to return to its rest position. The oscillation
spreads out as a moving internal wave.
The Brunt-Vaisala frequency was calculated over the depth of 1-2 m, 8-9 m, 22-23 m and
33-34 m and with 0.5 hour intervals and then averaged to cover the whole period (3:0010:30). The average value of N was 0.026 rad s-1 in the depth of 1-2 m and 0.004 rad s-1
in the depth of 33-34 m (Fig. 10). The period lengths are then 6 min for 1-2 m depth and
114 min for 33-34 m depth (Fig. 11).
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Brunt-Vaisala frequency N (rad s -1)
0.000
0.005
0.010
0.015
0.020
0.025
Depth layer
1-2 m
0.030
0.026
8-9 m
0.025
0.016
22-23 m
0.004
33-34 m
Fig. 10. Averages of Brunt-Vaisala frequency 22.7.1997 03:00-10:30 in different depth layers.
Period length Pw (s)
0
Depth layer
1-2 m
8-9 m
22-23 m
1000
2000
3000
4000
5000
6000
7000
8000
361.3
256.4
396.7
33-34 m
6839.3
Fig. 11. Averages of period length 22.7.1997 03:00-10:30 in different depth layers.
Richardson number
The Richardson number estimates the likelihood that internal waves in a density interface
will become unstable and break up into turbulence. Ri is a ratio between the buoyancy
forces and the shear force. If this ratio is greater than 0.25 waves of all wavelengths are
stable (Turner, 1973).
The Richardson number was calculated as Ri = N2/(du/dz)2, where N is the buoyancy
frequency and du/dz is the velocity gradient.
The average Richardson number was 4036 for depth 1-2 m and 5 for depth 33-34 m (Fig.
12). This suggests that the stratification in both cases was strong and that internal waves
were not breaking in these layers.
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Richardson number Ri
0
500
1000
1500
2000
2500
3000
3500
Depth layer
4500
4036.2
1-2 m
391.8
8-9 m
22-23 m
4000
32.8
33-34 m 5.1
Fig. 12. Averages of Richardson number 22.7.1997 03:00-10:30 in different depth layers.
Friction velocity
Friction velocity (u*) for depth layers were approximated so that u* ≈ le(du/dz), where le
is the length scale and du/dz is the velocity gradient. Calculation suggest that friction
velocity in depths 1-2 m and 33-34 m was 0.006 m s-1 and in depths 8-9 m and 22-23 m
0.005 m s-1 and 0.004 m s-1 respectively (Fig. 13). (These values are only rough
approximations, because the real friction velocity may change a lot with depth.)
-1
Friction velocity appr. u* (m s )
0.000
0.005
Depth layer
1-2 m
0.015
0.020
0.006
8-9 m
22-23 m
0.010
0.005
0.004
33-34 m
0.006
Fig. 13. Averages of approximated friction velocity 22.7.1997 03:00-10:30 in different depth
layers.
Dissipation of kinetic energy
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Dissipation of kinetic energy (E) was calculated with the approximated value of friction
velocity (u*): E= (u*)² (du/dz). E was found to be 7.3*10-7 in 1-2 m depth. In 22-23 m
depth it was only 1.4*10-7. (Fig. 14).
2
-3
Dissipation energy E (m s )
0.0000000
0.0000005
0.0000010
0.0000020
7.27491E-07
1-2 m
Depth layer
0.0000015
8.83088E-07
8-9 m
22-23 m
1.40022E-07
6.91034E-07
33-34 m
Fig. 14. Averages of approximated dissipation energy 22.7.1997 03:00-10:30 in different depth
layers.
Buoyancy length scale
The buoyancy length scale (Lb) is the size of the largest turbulent eddies. The largest
eddies occur when the inertial forces associated with the turbulence are about equal to the
buoyancy forces. This size is estimated from the turbulent energy dissipation rate E and
the buoyancy frequency N: Lb=(E/N³)1/2.
The buoyancy length scale was smaller than 0.4 m in 1-2 m, 8-9 m and 22-23 m depth
layers. These values are quite small when compared to the ocean, where the buoyancy
length scale may be about 10 m in the mixed layer and 1 m in the deep ocean or in
stratified regions (Mann & Lazier 1991). In 33-34 m depth Lb was found to be 5.5 m.
Buoyancy length scale Lb (m)
0
Depth layer
1-2 m
1
3
4
5
6
0.38
8-9 m
0.15
22-23 m
0.17
33-34 m
2
5.47
Fig. 15. Averages of buoyancy length scale 22.7.1997 03:00-10:30 in different depth layers.
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Batchelor scale for heat
Batchelor scale is the length scale of the smallest fluctuation of any property of diffusion
constant D and it is given by Ld = 2π (vD2/E)1/4, where v = 0.000001 m2 s-1 is the
coefficient of kinematic viscosity.
Batchelor scale for heat was calculated to be about 12 mm in 1-2 m and 5 mm in 22-23 m.
These values were calculated with the approximated values of E and they are in the range
of values for smallest temperature fluctuations (2-13 mm) suggested by Mann & Lazier
(1991).
Batchelor scale Ld (m)
0.000
0.003
0.006
0.009
Depth layer
8-9 m
33-34 m
0.015
0.012
1-2 m
22-23 m
0.012
0.008
0.005
0.006
Fig. 16. Averages of Batchelor scale 22.7.1997 03:00-10:30 in different depth layers.
Kolmogorov scales
The approximated kinetic energy dissipation value (E) was used when approximating
Kolmogorov scales. The Kolmogorov scales describe the dimensions of the smallest
possible eddies.
The Kolmogorov length scale was calculated as lm ≈ (v3/E)1/4, where v is the coefficient
of kinematic viscosity. In much of oceanographic literature this length is multiplied by 2π
(Mann & Lazier 1991). Both of these length scales are compared in figure 17. The
Kolmogorov length scale was highest in depth of 1-2 m and lowest in depth of 22-23 m
not depending on which one of the scales were used (Fig. 17).
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Kolmogorov length scale lm (m)
0.000
0.010
0.030
0.040
0.050
0.005
1-2 m
Depth layer
0.020
0.031
0.003
8-9 m
0.020
lm
lm*2pi
0.002
22-23 m
0.014
0.002
33-34 m
0.015
Fig. 17. Averages of approximated Kolmogorov length scale with and without the 2π-coefficient
22.7.1997 03:00-10:30 in different depth layers.
The Kolmogorov time scale, calculated tm = (v/E)1/2, was highest (142 s) in 1-2 m depth
and lowest (6 s) in 22-23 m depth (Fig. 18). The Kolmogorov velocity scale, vm = (vE)1/4,
was 0.0005-0.0007 m s-1 in each depth layer (Fig. 19).
Kolmogorov time scale tm (s)
0
30
Depth layer
1-2 m
33-34 m
90
120
150
142.1
8-9 m
22-23 m
60
19.7
5.9
9.8
Fig. 18. Averages of approximated Kolmogorov time scale 22.7.1997 03:00-10:30 in different
depth layers.
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-1
Kolmogorov velocity scale vm (m s )
0.000
Depth layer
1-2 m
8-9 m
22-23 m
33-34 m
0.001
0.002
0.003
0.004
0.005
0.0006
0.0006
0.0005
0.0007
Fig. 19. Averages of approximated Kolmogorov velocity scale 22.7.1997 03:00-10:30 in different
depth layers.
Literature
Mann K.H. & Lazier J.R.N. 1991. Dynamics of marine ecosystems. Biological-physical
interactions in the oceans. Blackwell Science, Inc., Cambridge, 432 p.
Turner J.S. 1973. Buoyancy effects in fluids. Cambridge University Press, Cambridge, 367 p.