Ninni Liukko and Timo Huttula
19.2.2008
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 as part of
EU-MAST-project coordinated by Finnish Marine Institute. The ship was firmly
anchored with four anchors (two from prow and two from stern) and ship swinging was
minimized to few meters.
The vessel mounted ADCP with transducer/receiver unit mounted on the ship hull was
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 current measurements were done in 16.-24.7.1997. The ADCP were measuring
currents all the time in 10 min intervals. The UCM50 and RCM9 profile measurements
were done during some about 12-hour periods. Measuring a vertical profile took about 45
minutes and after that the next profile was started in about 20 minutes time. Therefore, in
a fixed depth measurements were done about once in an hour. For example, the UCM50
and RCM9 were used together without longer 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 22.7.1997
The results from the first measuring period, 22.7.1997 2:00-12:00, are presented in this
chapter.
2.1. Wind conditions
The wind direction varied 21.7. In the beginning of the velocity measurement period 22.7
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 measurement period
and also during the measurement period (2:00-12:00 22.7.) (Fig. 3).
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 at the end.
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 figure shows
the depth 4-50 m (on the right: bin46 = 4m, bin44 = 6m, bin42 = 8m, … , bin3 = 2m and bin0 =
50m).
Fig. 5. Current velocity measured by the ADCP 2:00:08 – 12:00:08 22.7.1997. The figure shows
the depth of 4-50 m (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. Interpolation and
figures were done with the Matlab software.
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.
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. CTD results
CTD profiles were measured with intervals of about an hour. Temperature, salinity and
density were measured. The CTD data was also interpolated for the curve level figures
(Figs. 10-12).
The isotherm figure based on the interpolated CTD data and the isotherm figure based on
the interpolated RCM9 and UCM50 data are slightly different. The figure based on
RCM9 and UCM50 shows some oscillation that are not seen in the CTD figure. This
suggest that the oscillation is not necessarily real, but caused by the interpolation and
different measuring time in different depths. (Fig. 6 and 10).
0
20
Depth (m)
-10
15
-20
10
-30
5
-40
02
04
06
08
10
12
0
Time (hh)
Fig. 10. Isotherms at 1 ºC intervals. Data interpolated (0.5 h and 1m intervals) from CTD data
22.7.1997.
0
7.5
7
Depth (m)
-10
6.5
-20
6
-30
5.5
-40
02
5
04
06
08
10
12
4.5
Time (hh)
Fig. 11. Salinity level curves at 0.25 __ intervals. Data interpolated (0.5 h and 1 m intervals) from
CTD data 22.7.1997.
Depth (m)
0
1006
-10
1005
-20
1004
-30
1003
-40
1002
02
04
06
08
10
12
1001
Time (hh)
Fig. 12. Density level curves at 0.25 __ intervals. Data interpolated (0.5 h and 1 m intervals) from
CTD data 22.7.1997.
2.5. Scales of turbulence
The data interpolated from the original measurement 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 calculate the Dissipation energy (E), Buoyancy length scale (Lb), Batchelor scale (Ld)
and Kolmogorov scales.
The interpolated CTD density data were used for calculations.
The numbers were calculated for the measuring period with 0.5 hour intervals and for 33
depth layers: 1-2 m, 2-3m, 3-4m, … , 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.
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 average Brunt-Vaisala frequency was highest in the depth of 5-6 m, where the
average wave period length was shortest (147 s ≈ 2 min 27 s). The lowest Brunt-Vaisala
frequency and the longest period length (527 s = 8 min 47 s) was in depth 30-31 m. (Fig.
13).
The level curves for period length were also drawn for the discussed time period (Fig. 14).
The longest waves seem to have occurred in the mid depths (11-17 m) and in the deepest
measured layers (25-34 m). The shortest waves then have occurred in the uppermost ten
meters depth and in the depth 20-25 m.
Brunt-Vaisala frequency (rad s -1)
0.020
0.040
0
0.060
1-2
1-2
3-4
3-4
5-6
5-6
7-8
7-8
9-10
9-10
11-12
11-12
13-14
13-14
Depth layer (m)
Depth layer (m)
0.000
Period length (s)
15-16
17-18
19-20
200
400
600
15-16
17-18
19-20
21-22
21-22
23-24
23-24
25-26
25-26
27-28
27-28
29-30
29-30
31-32
31-32
33-34
33-34
Fig. 13. Averages of Brunt-Vaisala frequency (left) and Period length (right) 22.7.1997 03:0010:30 in different depth layers.
0
600
-5
500
Depth (m)
-10
400
-15
300
-20
200
-25
100
-30
03
04
05
06
07
Time (hh)
08
09
10
0
Fig. 14. Period length level curves at 50 s intervals 22.7.1997 according to calculations based on
interpolated UCM50 (velocity), RCM9 (velocity) and CTD (density) data.
Richardson number
The Richardson number estimates the likelihood that internal waves in a density interface
will become unstable and break up into turbulence. It 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 highest (1,536,663) in depth 10-11m and lowest (30)
in 30-31 m depth (Fig. 15). This suggests that the stratification in both cases was strong
and that internal waves were not breaking in these layers.
Richardson number
0
10000
20000
30000
14565
1-2
120
15342
3-4
21009
5-6
7-8
9-10
Depth layer (m)
11-12
3972
701
1259
2092
159
2542
224
13-14
15-16
17-18
19-20
21-22
23-24
25-26
27-28
29-30
31-32
33-34
20913
1376
224
787
463
683
131
89
134
183
326
211
104
74
57
63
358
30
48
68
64
Fig. 15. Averages of Richardson number 22.7.1997 03:00-10:30 in different depth layers. The
value for depth 10-11m is 1,536,663.
Friction velocity and dissipation of kinetic energy
Friction velocity (u*) for depth layers were approximated so that u* ≈ le(du/dz), where le
is the length scale (here layer depth) and du/dz is the velocity gradient. Dissipation of
kinetic energy (E) was calculated with the approximated value of friction velocity (u*): E
= (u*)² (du/dz).
Calculation suggest that the average friction velocity was highest in 30-31 m depth and
quite high also in 6-8 m depth. Also the dissipation energy is highest in these depths. The
friction velocity and dissipation energy values were lowest in 16-19 m depth.
Friction velocity (m s -1)
Dissipation energy (m 2 s-3)
0.0000000
1-2
1-2
3-4
3-4
5-6
5-6
7-8
7-8
9-10
9-10
11-12
11-12
13-14
13-14
15-16
17-18
19-20
21-22
Depth layer (m)
Depth layer (m)
0.000 0.002 0.004 0.006 0.008 0.010
0.0000025
0.0000050
15-16
17-18
19-20
21-22
23-24
23-24
25-26
25-26
27-28
27-28
29-30
29-30
31-32
31-32
33-34
33-34
Fig. 16. Averages of approximated friction velocity (left) and dissipation energy (right) 22.7.1997
03:00-10:30 in different depth layers.
Level curves for dissipation energy were also calculated for the whole period (Fig. 17).
The scale of the dissipation energy was very wide and therefore the level curves in figure
17 show only variation between 10-7 and 10-6 m2 s-3. Though the figure shows that the
highest dissipation energy values occurred mostly in the uppermost and in the deepest
depth layers.
-6
x 10
1
0
-5
0.8
Depth (m)
-10
0.6
-15
-20
0.4
-25
0.2
-30
03
04
05
06
07
Time (hh)
08
09
10
0
Fig. 17. Dissipation energy level curves at 2*10-7 m2 s-3 intervals 22.7.1997 according to
calculations based on interpolated UCM50 (velocity), RCM9 (velocity) and CTD (density) data.
The variation scale is from 1*10-15 to 6.8*10-5 m2 s-3.
min
max
average
St dev
1E-15
6.86541E-05
7.17731E-07
3.73815E-06
Buoyancy length scale and Batchelor 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 as follows: Lb = (E/N³)1/2.
The average value of the buoyancy length scale was highest (0.84 m) in 30-31 m depth
and lowest (0.05 m) in 5-6 m depth (Fig. 18). 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).
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 = 10-6 m2 s-1 is the coefficient of
kinematic viscosity.
The average Batchelor scale for heat was highest (0.034 m) in 10-11 m depth. In the other
layers the average values were smaller than 0.015 m. The range of values for smallest
temperature fluctuations for ocean is 2-13 mm as suggested by Mann & Lazier (1991).
Most of the average values therefore fit to this range. (Fig. 18).
Batchelor scale (m)
Buoyancy length scale (m)
0.25
0.50
0.75
0.00
1.00
1-2
1-2
3-4
3-4
5-6
5-6
7-8
7-8
9-10
9-10
11-12
11-12
13-14
13-14
15-16
17-18
19-20
Depth layer (m)
Depth layer (m)
0.00
0.01
0.02
0.03
0.04
15-16
17-18
19-20
21-22
21-22
23-24
23-24
25-26
25-26
27-28
27-28
29-30
29-30
31-32
31-32
33-34
33-34
Fig. 18. Averages of Buoyancy length scale (left) and Batchelor scale for heat (right) 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 forms are compared in figure 19. The average
Kolmogorov length scale was highest in depth of 10-11 m not depending on which one of
the forms were used (Fig. 19).
The average Kolmogorov time scale, calculated as tm = (v/E)1/2, was highest (2010 s =
33.5 min) in 10-11 m depth (Fig. 20). The average Kolmogorov velocity scale, vm =
(vE)1/4, was 0.0005-0.0007 m s-1 in each depth layer (Fig. 20).
Kolmogorov length scale (m)
0.02
0.04
0.06
0.08
Kolmogorov length scale (m)
0.10
0.00
1-2
1
3-4
3
5-6
5
7-8
7
9-10
9
11-12
11
13-14
13
15-16
17-18
19-20
21-22
Depth layer (m)
Depth layer (m)
0.00
0.02
0.04
0.06
0.08
0.10
15
17
19
21
23-24
23
25-26
25
27-28
27
29-30
29
31-32
31
33-34
33
Fig. 19. Averages of Kolmogorov length scale without (left) and with the 2π coefficient (right)
22.7.1997 03:00-10:30 in different depth layers.
Kolmogorov velocity scale (m s -1)
Kolmogorov time scale (s)
50
100
150
200
0.000
1-2
1-2
3-4
3-4
5-6
5-6
7-8
7-8
9-10
9-10
11-12
11-12
13-14
13-14
15-16
17-18
19-20
21-22
Depth layer (m)
Depth layer (m)
0
0.001
0.002
0.003
15-16
17-18
19-20
21-22
23-24
23-24
25-26
25-26
27-28
27-28
29-30
29-30
31-32
31-32
33-34
33-34
Fig. 20. Averages of Kolmogorov time scale (left) and Kolmogorov velocity scale (right)
22.7.1997 03:00-10:30 in different depth layers. The time scale for depth 10-11m is 2010s.
3. RESULTS 23.-24.7.1997
3.1. Wind conditions
360
Wind direction (deg)
315
270
225
180
135
90
45
0
0:00
12:00
0:00
12:00
0:00
Fig. 21. Wind direction 23.-24.7.1997.
Wind speed (m/s)
20
15
10
5
0
0:00
12:00
0:00
12:00
Fig. 22. Wind speed 23.-24.7.1997.
3.2. ADCP results
Fig. 23. Current direction measured by the ADCP 23.-24.7.1997 22:00:08 – 08:00:08. The figure
shows the depth 4-50 m (on the right: bin46 = 4m, bin44 = 6m, bin42 = 8m, … , bin3 = 2m and
bin0 = 50m).
Fig. 24. Current velocity measured by the ADCP 23.-24.7.1997 22:00:08 – 08:00:08. The figure
shows the depth 4-50 m (on the right: bin46 = 4m, bin44 = 6m, bin42 = 8m, … , bin3 = 2m and
bin0 = 50m).
3.3. UCM50 and RCM9 results
0
20
-5
15
Depth (m)
-10
-15
10
-20
-25
5
-30
-35
18
20
22
24
02
Time (hh)
04
06
08
0
Fig. 25. Isotherms at 1 ºC intervals. Data interpolated (0.5 h and 1m intervals) from UCM50 and
RCM9 measurement data 23.-24.7.1997.
0
25
Depth (m)
-5
-10
20
-15
15
-20
10
-25
-30
5
-35
18
20
22
24
02
Time (hh)
04
06
08
0
Fig. 26. Velocity level curves at 2 cm s-1 intervals. Data interpolated (0.5 h and 1 m intervals)
from UCM50 and RCM9 measurement data 23.-24.7.1997.
0
10
-5
5
Depth (m)
-10
-15
0
-20
-5
-25
-10
-30
-35
18
20
22
24
02
Time (hh)
04
06
08
-15
Fig. 27. 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 23.-24.7.1997.
0
10
-5
Depth (m)
-10
0
-15
-20
-10
-25
-30
-20
-35
18
20
22
24
02
Time (hh)
04
06
08
Fig. 28. 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 23.-24.7.1997.
3.4. CTD results
0
20
Depth (m)
-10
15
-20
10
-30
5
-40
18
20
22
24
02
Time (hh)
04
06
08
0
Fig. 29. Isotherms at 1 ºC intervals. Data interpolated (0.5 h and 1m intervals) from CTD data
23.-24.7.1997.
Depth (m)
0
7.5
-10
7
-20
6.5
-30
6
-40
5.5
18
20
22
24
02
Time (hh)
04
06
08
5
Depth (m)
Fig. 30. Salinity level curves at 0.25 __ intervals. Data interpolated (0.5 h and 1 m intervals) from
CTD data 23.-24.7.1997.
0
1006
-10
1005
-20
1004
-30
1003
-40
1002
18
20
22
24
02
Time (hh)
04
06
08
1001
Fig. 31. Density level curves at 0.25 kg m-3 intervals. Data interpolated (0.5 h and 1 m intervals)
from CTD data 23.-24.7.1997.
3.5. Scales of turbulence
Brunt-Vaisala frequency and wave period length
Brunt-Vaisala frequency (rad s -1)
0.020
0.040
0
0.060
1-2
1-2
3-4
3-4
5-6
5-6
7-8
7-8
9-10
9-10
11-12
11-12
13-14
13-14
Depth layer (m)
Depth layer (m)
0.000
Period length (s)
15-16
17-18
19-20
21-22
100 200 300 400 500 600 700
15-16
17-18
19-20
21-22
23-24
23-24
25-26
25-26
27-28
27-28
29-30
29-30
31-32
31-32
33-34
33-34
35-36
35-36
Fig. 32. Averages of Brunt-Vaisala frequency (left) and Period length (right) 23.-24.7.1997
21:30-08:00 in different depth layers.
0
1000
-5
900
800
-10
Depth (m)
700
-15
600
-20
500
-25
400
300
-30
200
-35
22
24
02
Time (hh)
04
06
08
100
Fig. 33. Period length level curves at 50 s intervals 23.-24.7.1997 according to calculations based
on interpolated UCM50 (velocity), RCM9 (velocity) and CTD (density) data. Maximum value
was 2012 s.
Richardson number
Richardson number
0
1-2
3-4
5-6
7-8
9-10
11-12
Depth layer (m)
13-14
15-16
17-18
19-20
10000
24
437
76
453
340
138
206
2211
4870
5008
5500
7570
7787
7488
6928
4450
3316
3946
3801
21-22
23-24
1285
1245
25-26
20000
19068
15707
14113
6110
1514
1872
1742
27-28
29-30
26208
31-32
33-34
35-36
30000
4738
3977
4667
3
5
11319
8853
Fig. 34. Averages of Richardson number 23.-24.7.1997 21:30-08:00 in different depth layers.
Friction velocity and dissipation of kinetic energy
Dissipation energy (m 2 s-3)
Friction velocity (m s -1)
0.01
0.02
0.03
0.00000
0.04
1-2
1-2
3-4
3-4
5-6
5-6
7-8
7-8
9-10
9-10
11-12
11-12
13-14
13-14
Depth layer (m)
Depth layer (m)
0.00
15-16
17-18
19-20
21-22
0.00001
0.00002
0.00003
15-16
17-18
19-20
21-22
23-24
23-24
25-26
25-26
27-28
27-28
29-30
29-30
31-32
31-32
33-34
33-34
35-36
35-36
Fig. 35. Averages of approximated friction velocity (left) and dissipation energy (right) 23.24.7.1997 21:30-08:00 in different depth layers.
-6
x 10
1
0
-5
0.8
Depth (m)
-10
0.6
-15
-20
0.4
-25
0.2
-30
-35
22
24
02
Time (hh)
04
06
08
0
Fig. 36. Dissipation energy level curves at 2*10-7 m2 s-3 intervals 23.-34.7.1997 according to
calculations based on interpolated UCM50 (velocity), RCM9 (velocity) and CTD (density) data.
The variation scale is from 9*10-15 to 4*10-4 m2 s-3.
Buoyancy length scale and Batchelor scale
Batchelor scale (m)
Buoyancy length scale (m)
1
2
3
4
0.00
5
1-2
1-2
3-4
3-4
5-6
5-6
7-8
7-8
9-10
9-10
11-12
11-12
13-14
13-14
15-16
17-18
19-20
21-22
Depth layer (m)
Depth layer (m)
0
0.01
0.02
0.03
15-16
17-18
19-20
21-22
23-24
23-24
25-26
25-26
27-28
27-28
29-30
29-30
31-32
31-32
33-34
33-34
35-36
35-36
Fig. 37. Averages of buoyancy length scale (left) and Batchelor scale for heat (right) 23.24.7.1997 21:30-08:00 in different depth layers.
Kolmogorov scales
0.04
Kolmogorov length scale (m)
0.02
0.04
0.06
0.08
0.10
0.00
1-2
1-2
3-4
3-4
5-6
5-6
7-8
7-8
9-10
9-10
11-12
11-12
13-14
13-14
15-16
17-18
19-20
21-22
Depth layer (m)
Depth layer (m)
0.00
Kolmogorov length scale (m)
0.02
0.04
0.06
0.08
0.10
15-16
17-18
19-20
21-22
23-24
23-24
25-26
25-26
27-28
27-28
29-30
29-30
31-32
31-32
33-34
33-34
35-36
35-36
Fig. 38. Averages of Kolmogorov length scale without (left) and with (right) the 2π coefficient
23.-24.7.1997 21:30-08:00 in different depth layers.
Kolmogorov velocity scale (m s -1)
Kolmogorov time scale (s)
100
200
300
400
500
600
0.000
1-2
1-2
3-4
3-4
5-6
5-6
7-8
7-8
9-10
9-10
11-12
11-12
13-14
13-14
15-16
17-18
19-20
21-22
Depth layer (m)
Depth layer (m)
0
0.001
0.002
0.003
15-16
17-18
19-20
21-22
23-24
23-24
25-26
25-26
27-28
27-28
29-30
29-30
31-32
31-32
33-34
33-34
35-36
35-36
Fig. 39. Averages of Kolmogorov time scale (left) and Kolmogorov velocity scale (right) 23.24.7.1997 21:30-08:00 in different depth layers.