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). 360 315 ) g

e 270 d ( 225 n o i t

c 180 e r i

d 135

d n

i 90 W 45 0 0:00 12:00 0:00 12:00 0:00

Fig. 2. Wind direction 21.-22.7.1997

20

) 15 s / m (

d

e 10 e p s

d n i 5 W

0 0:00 12:00 0:00 12:00 0:00

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 2 0 - 5 - 1 0 1 5

) - 1 5 m (

h 1 0 t - 2 0 p e D - 2 5 5 - 3 0 - 3 5 0 0 2 0 4 0 6 0 8 1 0 1 2 T i m e ( h h ) Fig. 6. Isotherms at 1 ºC intervals. Data interpolated (0.5 h and 1m intervals) from UCM50 and RCM9 measurement data 22.7.1997. 0 - 5 3 0 - 1 0 2 5

) - 1 5 m 2 0 (

h t - 2 0 p 1 5 e D - 2 5 1 0 - 3 0 5 - 3 5 0 0 2 0 4 0 6 0 8 1 0 1 2 T i m e ( h h ) Fig. 7. Velocity level curves at 2 cm s-1 intervals. Data interpolated (0.5 h and 1 m intervals) from UCM50 and RCM9 measurement data 22.7.1997.

0 2 0 - 5 1 5 - 1 0

) - 1 5 1 0 m (

h t - 2 0 p

e 5 D - 2 5 - 3 0 0 - 3 5 - 5 0 2 0 4 0 6 0 8 1 0 1 2 T i m e ( h h ) 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 2 0 - 5 1 0 - 1 0

) 0 - 1 5 m (

h t - 2 0 p - 1 0 e D - 2 5 - 2 0 - 3 0 - 3 5 - 3 0

0 2 0 4 0 6 0 8 1 0 1 2 T i m e ( h h ) 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 2 0

- 1 0 1 5

) - 2 0 m (

h 1 0 t p e - 3 0 D

5 - 4 0

0 0 2 0 4 0 6 0 8 1 0 1 2 T i m e ( h h ) 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 - 1 0

6 . 5 ) - 2 0 m (

h 6 t p e - 3 0 D 5 . 5

- 4 0 5

4 . 5 0 2 0 4 0 6 0 8 1 0 1 2 T i m e ( h h ) Fig. 11. Salinity level curves at 0.25 __ intervals. Data interpolated (0.5 h and 1 m intervals) from CTD data 22.7.1997. 0 1 0 0 6

- 1 0 1 0 0 5

) - 2 0 1 0 0 4 m (

h t p e - 3 0 1 0 0 3 D

- 4 0 1 0 0 2

1 0 0 1 0 2 0 4 0 6 0 8 1 0 1 2 T i m e ( h h ) 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) Period length (s) 0.000 0.020 0.040 0.060 0 200 400 600

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 m m ( (

r 15-16

r 15-16 e e y y a a 17-18

17-18 l l

h h t t p p 19-20 19-20 e e D D 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 03:00- 10:30 in different depth layers.

0 6 0 0

- 5 5 0 0

- 1 0 4 0 0 )

m - 1 5 (

h 3 0 0 t p e - 2 0 D 2 0 0 - 2 5 1 0 0 - 3 0

0 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 T i m e ( h h ) 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

1-2 14565 120 3-4 15342 21009 5-6 3972 701 7-8 1259 2092 9-10 159

11-12 2542 224

) 13-14 20913

m 1376 (

r 15-16 224

e 787 y

a 463

l 17-18

h 683 t

p 19-20 131 e 89 D 21-22 134 183 23-24 326 211 25-26 104 74 27-28 57 63 29-30 358 30 31-32 48 68 33-34 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) 0.000 0.002 0.004 0.006 0.008 0.010

1-2

3-4

5-6

7-8

9-10

11-12

) 13-14 m (

r 15-16 e y a 17-18 l h t

p 19-20 e

D 21-22

23-24

25-26

27-28

29-30

31-32

33-34

Dissipation energy (m2 s-3) 0.0000000 0.0000025 0.0000050

1-2

3-4

5-6

7-8

9-10

11-12

) 13-14 m (

r 15-16 e y a 17-18 l h t

p 19-20 e

D 21-22

23-24

25-26

27-28

29-30

31-32

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 1 0 0 1

- 5 0 . 8 - 1 0

) 0 . 6

m - 1 5 (

h t p e - 2 0 D 0 . 4

- 2 5 0 . 2 - 3 0

0 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 T i m e ( h h ) 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 1E-15 max 6.86541E-05 average 7.17731E-07 St dev 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 1/2 the buoyancy frequency N as follows: Lb = (E/N³) .

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). Buoyancy length scale (m) 0.00 0.25 0.50 0.75 1.00

1-2

3-4

5-6

7-8

9-10

11-12

) 13-14 m (

r 15-16 e y a

l 17-18 h t p 19-20 e D 21-22

23-24

25-26

27-28

29-30

31-32

33-34 Batchelor scale (m) 0.00 0.01 0.02 0.03 0.04

1-2

3-4

5-6

7-8

9-10

11-12

) 13-14 m (

r 15-16 e y

a 17-18 l

h t

p 19-20 e

D 21-22

23-24

25-26

27-28

29-30

31-32

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.

3 1/4 The Kolmogorov length scale was calculated as lm ≈ (v /E) , 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).

1/2 The average Kolmogorov time scale, calculated as tm = (v/E) , 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) Kolmogorov length scale (m) 0.00 0.02 0.04 0.06 0.08 0.10 0.00 0.02 0.04 0.06 0.08 0.10

1-2 1

3-4 3

5-6 5

7-8 7

9-10 9

11-12 11

) 13-14 13 ) m m ( (

r 15-16

r 15 e e y y a a

l 17-18 17 l

h h t t p 19-20 p 19 e e D 21-22 D 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 time scale (s) Kolmogorov velocity scale (m s-1) 0 50 100 150 200 0.000 0.001 0.002 0.003

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 m m ( (

r 15-16

r 15-16 e e y y a a

l 17-18

l 17-18

h h t t p 19-20 p 19-20 e e D 21-22 D 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

360 315 )

g 270 e d ( 225 n o i t 180 c e r i

d 135

d n

i 90 W 45 0 0:00 12:00 0:00 12:00 0:00

Fig. 21. Wind direction 23.-24.7.1997.

20

) 15 s / m (

d e

e 10 p s

d n i 5 W

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 2 0 - 5 - 1 0 1 5

) - 1 5 m (

h 1 0 t - 2 0 p e D - 2 5 5 - 3 0

- 3 5 0 1 8 2 0 2 2 2 4 0 2 0 4 0 6 0 8 T i m e ( h h ) 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 2 5 - 5 - 1 0 2 0 )

m - 1 5

( 1 5

h t - 2 0 p

e 1 0 D - 2 5 - 3 0 5 - 3 5 0 1 8 2 0 2 2 2 4 0 2 0 4 0 6 0 8 T i m e ( h h ) 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 1 0 - 5 5 - 1 0 )

m - 1 5 0 (

h t - 2 0 p

e - 5 D - 2 5 - 3 0 - 1 0 - 3 5 - 1 5 1 8 2 0 2 2 2 4 0 2 0 4 0 6 0 8 T i m e ( h h ) 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 - 5 1 0 - 1 0

) 0

m - 1 5 (

h t - 2 0 p e - 1 0 D - 2 5 - 3 0 - 2 0 - 3 5

1 8 2 0 2 2 2 4 0 2 0 4 0 6 0 8 T i m e ( h h ) 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 2 0

- 1 0 1 5

) - 2 0 m (

h 1 0 t p e - 3 0 D

5 - 4 0

0 1 8 2 0 2 2 2 4 0 2 0 4 0 6 0 8 T i m e ( h h ) Fig. 29. Isotherms at 1 ºC intervals. Data interpolated (0.5 h and 1m intervals) from CTD data 23.-24.7.1997. 0 7 . 5

- 1 0 7

) - 2 0 6 . 5 m (

h t p e - 3 0 6 D

- 4 0 5 . 5

5 1 8 2 0 2 2 2 4 0 2 0 4 0 6 0 8 T i m e ( h h ) 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 1 0 0 6

- 1 0 1 0 0 5

) - 2 0 1 0 0 4 m (

h t p e - 3 0 1 0 0 3 D

- 4 0 1 0 0 2

1 0 0 1 1 8 2 0 2 2 2 4 0 2 0 4 0 6 0 8 T i m e ( h h ) 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) Period length (s) 0.000 0.020 0.040 0.060 0 100 200 300 400 500 600 700 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

15-16 m m ( (

r r

e 17-18 e 17-18 y y a a l l

19-20 19-20 h h t t p p 21-22 21-22 e e D D 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 1 0 0 0

- 5 9 0 0 8 0 0 - 1 0 7 0 0

) - 1 5 m

( 6 0 0

h t

p - 2 0 5 0 0 e D - 2 5 4 0 0 3 0 0 - 3 0 2 0 0 - 3 5 1 0 0 2 2 2 4 0 2 0 4 0 6 0 8 T i m e ( h h ) 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 10000 20000 30000 1-2 24 437 3-4 76 453 5-6 340 138 7-8 206 2211 9-10 4870 5008 11-12 5500 7570 13-14 7787 7488 ) 15-16 6928 m (

4450 r

e 17-18 3316

y 3946 a l

19-20 3801 h

t 19068

p 21-22 15707 e 14113 D 23-24 1285 1245 25-26 6110 1514 27-28 1872 1742 29-30 26208 11319 31-32 4738 3977 33-34 4667 3 35-36 5 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 Friction velocity (m s-1) Dissipation energy (m2 s-3) 0.00 0.01 0.02 0.03 0.04 0.00000 0.00001 0.00002 0.00003 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 15-16 m m ( (

r r e

e 17-18 17-18 y y a a l l

19-20 19-20 h h t t p p 21-22 21-22 e e D D 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 1 0 0 1

- 5 0 . 8 - 1 0

) - 1 5 0 . 6 m (

h t

p - 2 0 e

D 0 . 4 - 2 5

- 3 0 0 . 2

- 3 5 0 2 2 2 4 0 2 0 4 0 6 0 8 T i m e ( h h ) 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

Buoyancy length scale (m) Batchelor scale (m) 0 1 2 3 4 5 0.00 0.01 0.02 0.03 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 ) ) 15-16 15-16 m m ( (

r r e

e 17-18 17-18 y y a a l l

19-20 19-20 h h t t p p 21-22 21-22 e e D D 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 Kolmogorov length scale (m) Kolmogorov length scale (m) 0.00 0.02 0.04 0.06 0.08 0.10 0.00 0.02 0.04 0.06 0.08 0.10 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 ) 15-16 m m ( (

r r

e 17-18 e 17-18 y y a a l l

19-20 19-20 h h t t

p 21-22 p 21-22 e e D 23-24 D 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 time scale (s) Kolmogorov velocity scale (m s-1) 0 100 200 300 400 500 600 0.000 0.001 0.002 0.003 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 )

m 15-16 m ( (

r r e 17-18 e 17-18 y y a a l l

19-20 19-20 h h t t p 21-22 p 21-22 e e D 23-24 D 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.