Chinese Journal of Oceanology and LimnologyVol. 32 No. 1, P. 201-209, 2014http://dx.doi.org/10.1007/s00343-014-2078-x

Test and evaluation of a moored microstructure recorder*

TIAN Chuan (田川) 1 , ** , WANG Shuxin (王树新) 1 , GUAN Shoude (管守德) 2 , YANG Qingxuan (杨庆轩) 2 , XU Xiaoyang (徐霄阳) 3 1 School of Mechanical Engineering, Tianjin University, Tianjin 300072, China 2 Physical Oceanography Laboratory, Ocean University of China, Qingdao 266100, China 3 College of Engineering, Ocean University of China, Qingdao 266100, China

Received Apr. 18, 2012; accepted in principle May 31, 2012; accepted for publication Nov. 16, 2012 © Chinese Society for Oceanology and Limnology, Science Press, and Springer-Verlag Berlin Heidelberg 2014

Abstract A new moored microstructure recorder (MMR) is designed, developed, tested, and evaluated. The MMR directly measures the high-frequency shear of velocity fl uctuations, with which we can estimate the dissipation rate of turbulent kinetic energy. We summarize and discuss methods for estimating the turbulent kinetic energy dissipation rate. Instrument body vibrations contaminate the shear signal in an ocean fi eld experiment, and a compensating correction successfully removes this contamination. In both tank test and ocean fi eld experiment, the dissipation rate measured with the MMR agreed well with that measured using other instruments.

Key w ord : moored microstructure recorder (MMR); dissipation rate; turbulent kinetic energy; shear of velocity fl uctuations; compensating correction

1 INTRODUCTION

Long-term observation of ocean turbulent mixing is very important for improving oceanic numerical models or revealing the mechanism of ocean circulation variations (Munk and Wunsch, 1998; Sharples et al., 2001). Lueck et al. (1997) and Lueck and Huang (1999) developed autonomous dissipation measurement based on a moored instrument, which can autonomously measure velocity and temperature fl uctuations in the inertial sub-range using shear probes and FP07 thermistors. It was deployed in a swift tidal channel for eight days, and gave the spectrum of the turbulent kinetic energy (TKE) and estimated the TKE dissipation rate ɛ . Recently, Moum and Nash (2009) developed a simple, reliable, and affordable device (a moored temperature micro-structure recorder, χpod) that can measure ocean turbulence and be readily integrated into existing moorings or autonomous vehicles. They fi xed the χpods on a tropical atmosphere ocean (TAO) mooring at (0°, 140°W) and fi rst obtained the dissipation rate of temperature variance χ T and then the TKE dissipation rate ɛ at three depths over the range 30–90 m.

Our objective is to develop an abyssal moored microstructure recorder (MMR) that can directly measure the high-frequency shear of three-dimensional turbulent velocity fl uctuations, and fi nally obtain the TKE dissipation rate ɛ . We also expect the MMR to be readily integrated into abyssal moorings, which are intended to provide long-term observations of ocean mixing, internal waves and ocean circulation.

In this paper, we fi rst briefl y describe the basic confi guration of the MMR (Section 2), and then in Section 3 we introduce the procedures for estimating the TKE dissipation rate as well as a compensating correction to remove signal contamination from body vibrations of the instrument. To evaluate the performance of the MMR in fl uids, we conducted a tank test and an ocean fi eld experiment, results of

* Supported by the National Natural Science Foundation of China (Nos. 41006005, 40906004, 91028008, 40890153, 41176008, 41176010), the National High Technology Research and Development Program of China (863 Program) (No. 2008AA09A402), and the Program for New Century Excellent Talents in University (No. NCET-10-0764) ** Corresponding author: tianchuan_notc@163.com

202 CHIN. J. OCEANOL. LIMNOL., 32(1), 2014 Vol.32

which are presented in Sections 4 and 5, respectively. Conclusions follows in Section 6.

2 INSTRUMENT CONFIGURATION

For long-term turbulent mixing measurements, we designed and developed an MMR (Fig.1) and expected it to be readily integrated into a mooring system. To provide a stable platform free of body vibrations and reduce drag in fl uids, the main body of the MMR is designed like a wing tank, which is 2.8 m long with a mid-body diameter of 0.56 m, suffi ciently large to suppress body vibrations. To keep the axial direction ( x ) of the instrument always aligned with the mean fl ow direction, the instrument should rotate promptly in response to changes in the direction of the ambient current. Therefore, two wings are mounted at the rear of the body to provide the torque for rotation.

A shear probe is mounted on a conical end cap, which is attached to the front pressure case of the main body. To protect the shear probe from mechanical breakage without restricting the fl ow past the sensor, a guard ring is attached to the front of the body. The sampling frequency of the shear probe is 1 024 Hz. In the front pressure case, about 15 cm away from the shear probe, we have installed an orthogonal accelerometer and tilt transducer (MTi-28A53G35, Xsens Technologies BV) to monitor body vibrations and tilts (heading, pitch, and roll). Figure 1 shows the coordinate system in the MMR reference system. Three orthogonal accelerometers and tilts are all sampled at 100 Hz.

3 ESTIMATE OF THE TKE DISSIPATION RATE

3.1 Methods for estimating the TKE dissipation rate

Here we summarize the method for estimating the turbulent kinetic energy dissipation rate, on which

principle the MMR turbulence measurement is based. For isotropic turbulence with fully resolved

measurements of the shear of velocity fl uctuations ' /i ju x in the diffusive sub-range, the turbulent

kinetic energy dissipation rate ɛ can be computed as

' '

0

1 15 ( )d2 2

i i

j j

u uk k

x x

, (1)

where ν is the kinetic molecular viscosity, k is the wavenumber (in cycles per meter, hereafter cpm), and ψ ( k ) is the wavenumber spectrum of ' /i ju x The brackets denote a time average.

When measuring turbulence intensity at a fi xed point in the ocean, the shear probe directly measures the time derivative of velocity fl uctuations perpendicular to the axis of the instrument, which is the vertical velocity fl uctuation w , according to the MMR design. According to Taylor’s frozen fl ow hypothesis, the path component of the vertical velocity gradient w x can be estimated as

d 1 dd dxw wwx U t

, (2)

where U is the mean horizontal fl ow speed, and x is the alongpath direction, i.e., the same direction as the mean fl ow.

According to Eq.1, the TKE dissipation rate ɛ can be computed with w x . In practice, due to the limited sampling frequency of the shear probe, to estimate ɛ with this incompletely resolved spectrum we usually fi t the observed spectra over a limited bandwidth to an accepted universal form, that is, the theoretical Nasmyth spectrum. This is an iterative procedure as follows:

(1) Calculate the power spectrum ψ ( f ) of w x . (2) When the mean fl ow passes the mooring line,

the cable and instrument vibrate at a particular frequency associated with the shedding of the Karman vortex (Moum and Nash, 2009). The signal measured by the shear probe will be contaminated by the body vibration, so a compensating correction will be applied to eliminate the contamination, and the power spectrum of w x after correction is ψ ' ( f ). The reason and correction method will be discussed in detail in Section 3.2.

(3) Estimate the wavenumber spectrum ψ ( k ) via ψ ( k )= ψ ( f ) U . (3)

(4) The shear probe cannot be infi nitely small; therefore, the shear spectrum contains only a small fraction of the diffusive sub-range, with the highest wavenumbers almost always attenuated because of

x(Ax)

x′

x

y(Ay)

z(Az)

Heading

Roll

PitchShearprobe

Guardring

Wing

Fig.1 MMR and coordinate system in the MMR reference frame, denoted by x ( A x ), y ( A y ) and z ( A z )

Here heading, pitch and roll represent rotation angles about the z , y , and x axes, respectively.

203No.1 TIAN et al.: Test and evaluation of MTMI

the sensor response. We apply a shear probe response correction for ψ ( k ) at this step.

(5) Because only a small fraction of the diffusive sub-range is resolved by the measurement, estimating requires fi tting the observed spectra ψ obs ( k ) to the theoretical Nasmyth spectra ψ theory ( k ) over a limited bandwidth [ k min , k max ] (Moum and Nash, 2009):

max

min

max

min

obs

theory

15 ( )d2

15 ( )d2

k

k

k

k

k k

k k

. (4)

We set k min =1 and fi rst estimate ε based on an initial guess of k max =15. Then the Kolmogorov wavenumber k s can be estimated as follows:

3 1/41 ( / )

2sk . (5)

(6) Set k max = k s and recompute ε and k s using Eqs.4 and 5. This sequence is repeated and normally converges after two or three iterations.

Another common method for estimating the TKE dissipation rate ε uses the turbulence inertial sub-range. For a suffi ciently high Reynolds number (Lien and D’Asaro, 2006), the wavenumber spectrum of the velocity has the form

2/3 -5/3( )k k , (6)

where k is the wavenumber and α is the Kolmogorov constant (Tennekes and Lumley, 1972; Sreenivasan, 1995).

The acoustic doppler velocimeter (ADV) can measure high-frequency three-dimensional fl uid velocity. Therefore, using the velocity measurement from the ADV, we can estimate the turbulent kinetic energy wavenumber spectra and then the dissipation rate ε according to Eq.6 (Voulgaris and Trowbridge, 1998). Using this concept, we conducted an experiment in a tank to compare the MMR and ADV. Section 4 will describe the experiment in detail.

3.2 Removal of contamination from body vibration

To measure the turbulence intensity at a fi xed point, we tethered the MMR in a mooring with a cable. When the mean fl ow passes the mooring line, the cable and instrument vibrate at a particular frequency, the Strouhal frequency, which is associated with the shedding of the Karman vortex (Moum and Nash, 2009). The signal measured by the shear probe is contaminated with the body vibration, so a compensating correction should be applied to the

observed velocity shear spectrum to eliminate the contamination (Zhang and Moum, 2010).

Assuming the velocity shear signal to be s and the acceleration signal a , the compensating correction is as follows. First, the cross spectrum of signals s and a is estimated via

*sa ( ) ( ) ( )s aS F F , (7)

where ω is the angular frequency, F s ( ω ) is the Fourier transform of signal s , and the asterisk (*) represents a convolution.

The original spectrum of the shear signal s is ψ ss ( ω ) and that of the acceleration signal a is ψ aa ( ω ). Then, after the compensating correction, the spectrum ψ ss ( ω ) can be estimated as

2ss ss sa( ) ( )(1 ( ))c R , (8)

where

*

2 sa sasa

ss aa

( ) ( )( )

( ) ( )S S

R

. (9)

Due to Taylor’s frozen-fl ow hypothesis, using the spectrum ψ c ss ( ω ) after removing contamination from body vibration, the wavenumber spectrum can be estimated with Eq.3, and then the real TKE dissipation rate can be estimated with Eq.1.

4 TANK TEST

To evaluate the performance of the MMR in fl uids, we conducted a test in a tank to compare the TKE dissipation rate simultaneously observed with the MMR and ADV (Fig.2a). The tank was 30-m long, 0.6-m wide, and 1.0-m high. The maximum fl ow speed that can be driven by a water pump is about 0.4 m/s. During the test, the MMR was mounted on the bottom of the tank, and the shear probe was about 50 cm above the bottom without effects from the bottom boundary layer. The ADV was fi xed on the top of the tank and was designed to measure high-frequency velocity fl uctuations at the same depth but about 5 cm in front of the shear probe. The sampling frequency of the ADV was 64 Hz.

The test started at 17:30 UTC and ended at 19:30 UTC. During this time, the fl ow speed in the tank was initially about 0.22 m/s and then gradually increased to 0.3 m/s, and fi nally reached the maximum fl ow speed of about 0.36 m/s.

Using a 4-s segment of the velocity shear datasets collected by the MMR, we estimated the TKE dissipation rate ε MMR according to the method described in Section 3.1. Figure 3a shows the results.

204 CHIN. J. OCEANOL. LIMNOL., 32(1), 2014 Vol.32

Floata

b

c

Release

Anchor

MMR

Current meter

TD sensor

Fig.2 Design and close-up of the MMR in the tank test and ocean fi eld experiment a. Instrument test in the tank. The MMR was mounted on the bottom of the tank and the ADV was fi xed on the top of the tank. Positions of the MMR and ADV are indicated by green arrows; b. MMR when deployed in the Jiaozhou Bay; c. Mooring design of the ocean fi eld experiment. Details of the mooring system are given in the text.

10 1010-8

10-7

10-6

10-6

10-5

10-5

10-4

10-4

10-3

10-2

10-1

10

101

100 1001 000 0.1

ε estimated by MMR

k (cpm)

ε =1.30×10-6 W/Kg

a

k (cpm)

Φ (m

2 s-2/c

pm)

Ψ (s

-2/c

pm)

ε estimated by ADV

ε =1.28×10-6 W/kg

b

Fig.3 Estimate of the TKE dissipation rate ε from (a) MMR and (b) ADV In (a), the solid line represents the observed shear spectrum, the black dashed line is the theoretical Nasmyth spectrum, and the gray dashed line indicates k max . In (b), the solid line represents the observed TKE spectrum, and the black line is the theoretical spectrum indicating a slope of -5/3. The numbers at the lower left are the corresponding ε .

205No.1 TIAN et al.: Test and evaluation of MTMI

The observed velocity shear spectrum in Fig.3a fi ts well with the theoretical Nasmyth spectrum in the wavenumber band [ k min , k max ]. The TKE spectrum computed from a 30-s segment ADV measurement of velocity fl uctuations has a slope of -5/3 in the inertial sub-range (Fig.3b). Then we estimated ε ADV . The two independent estimates of ε in Fig.3 were sampled at about the same time, and the values of ε were nearly the same.

To eliminate the effect of low-frequency waves in the tank, estimates of ε MMR for every 4-s dataset were moving-averaged over 30 s (Moum and Nash, 2009). Figure 4 shows the values of ε determined with the MMR and ADV in the test. The values of ε MMR are very close to those of ε ADV . Both ε MMR and ε ADV increased with the gradually increasing fl ow speed U in the tank. For instance, the MMR-estimated mean TKE dissipation rate was about 2×10 -6 W/kg when U was 0.22 m/s. However, when U increased to 0.36 m/s, the estimated ε stabilized at about 6×10 -6 W/kg, which was three times larger.

In Fig.5, we directly compare the TKE dissipation rate ε at nearly the same time measured by the MMR and ADV independently. Overall, ε MMR agrees with ε ADV , and the root mean square error is about 6.5× 10 -8 W/kg. Nevertheless, we infer that ε MMR is a little larger than ε ADV , especially for low-speed with a larger bias of about 1.6×10 -7 W/kg. However, these biases are about 1–2 orders of magnitude smaller than the real values of ε , which is acceptable for turbulence measurements. In conclusion, the tank test indicates that the MMR can very accurately measure turbulence intensity in fl uids.

5 FIELD EXPERIMENT

5.1 Experimental design

To evaluate the performance of the MMR in the real ocean (Fig.2b), we conducted a comparison fi eld experiment in the Jiaozhou Bay, Qingdao from 06:30 UTC to 08:30 UTC on March 7, 2011. The water depth of the station was about 36 m. The weather was sunny and windless that day; therefore, the sea was fairly calm. In the fi eld experiment, the MMR was integrated in a mooring system (Fig.2c). We tethered the instrument body with two cables at the mid-body and fi xed it to the mooring line. Due to the mooring design, an Aanderaa Seaguard RCM current meter was about 1 m below the MMR and a temperature-pressure (TD) sensor (RBR-TD1060) was about 1 m above the MMR. Therefore, we could obtain the

depth of the MMR in the water and the ambient current passing the shear probe. We sampled the temperature and pressure at 1 Hz and sampled the current data at 1 min. Every 15 min, the MMR collected 14 min of velocity shear data, and fi nally we obtained 7 sets of valid data.

To compare the TKE dissipation rate measured with the MMR to that measured with other instruments, we continuously deployed and recovered a MSS60 profi ler to get microstructure profi les about 100 m away horizontally from the mooring site. Finally, we obtained 36 valid microstructure profi les. The sampling frequency of the MSS60 was 1 024 Hz, the

17:30 17:45 18:00 18:15 18:30 18:45 19:00 19:15 19:30

10-6

10-5

Time

ε (W

/kg)

Comparison of dissipation rate of TKE

U=0.22 m/s U=0.30 m/s U=0.36 m/s

MMRADV

Fig.4 Comparison of ε estimated with MMR (blue dots) and ADV (red dots) Flow speeds at different times between dashed lines are given at the top.

-6 -5.9 -5.8 -5.7 -5.6 -5.5 -5.4 -5.3 -5.2 -5.1 -5-6

-5.9

-5.8

-5.7

-5.6

-5.5

-5.4

-5.3

-5.2

-5.1

-5

logεMMR (W/Kg)

logε

AD

V+0

.03 (W

/Kg)

U=0.22 m/sU=0.30 m/sU=0.36 m/s

Fig.5 Scatter plot of ε MMR and ε ADV at different fl ow speeds The black dashed line indicates ε ADV = ε MMR . The shaded area indicates the mean standard deviations of ε MMR and ε ADV .

206 CHIN. J. OCEANOL. LIMNOL., 32(1), 2014 Vol.32

same as that of the MMR. By directly measuring the vertical component of the horizontal velocity gradient u z , we calculated the profi le of the TKE dissipation rate with the same analytical method as for the MMR (the method in Section 3.1), except that we substituted the instrument sinking velocity W for the background velocity U in Eq.2.

Figure 6 shows the horizontal fl ow speed, direction, and tilts of the MMR in the ocean during the fi eld experiment. The fl ow speed was initially about 0.37 m/s and then gradually decreased to about 0.18 m/s (Fig.6a). This gave us an excellent opportunity to investigate and evaluate the performance of the MMR for different fl ow speeds.

A major requirement when designing the instrument is that the shear probe points along the fl ow regardless of the various directions of the ambient current. Figure 6b shows the mean fl ow direction and the heading angle of the MMR. To simplify the comparison, the heading angle has been rotated by 180°. When the mean fl ow speed was large (larger than 0.3 m/s), the instrument was nearly aligned with the mean fl ow, indicating that the wing at the rear can provide suffi cient torque for rotation. When the mean fl ow speed decreased, the instrument deviated from the fl ow direction. However, the bias angle was

maintained within a range of 20°, which had little effect on the turbulence measurement. The pitch and roll of the MMR also changed in response to the variations of the current speed, i.e., with a larger deviation from zero at higher speeds. However, the maximum pitch was about 4° and maximum roll about 3° during the whole deployment time, which are considered generally insignifi cant to the turbulence measurement and can even be negligible (Lueck and Huang, 1999).

5.2 Removal of contamination from body vibration

When the mean fl ow passes the mooring line, it drives the cable and the MMR instrument body vibrates at the Strouhal frequency f s , which can be estimated as

f s = U /5 d , (10) where U is the mean fl ow speed and d is the diameter of the cable. When the mean fl ow was about 0.28 m/s, we estimated the frequency spectrum of the observed velocity shear w x and A x / U , A y / U , and A z / U resulting from instrument body vibrations. As shown in Fig.7, there are signifi cant energy peaks at about 5.7 Hz and 9.5 Hz, exactly corresponding to the Strouhal frequencies of the cable above ( d =10 mm) and below

0.1

0.2

0.3

0.4

Spee

d (m

/s) a

100

150

200

250

Hea

ding

(°)

b Flow directionHeading-180

-101234

c

Pitc

h (°

)

06:30 06:45 07:00 07:15 07:30 07:45 08:00 08:15 08:30-10

1

23 d

Rol

l (°)

Time

Fig.6 Current past the shear probe and tilts of the MMR a. Horizontal fl ow speed; b. Heading (solid curve; rotated 180°) and fl ow direction (dashed curve); c. Pitch; d. Roll.

207No.1 TIAN et al.: Test and evaluation of MTMI

( d =6 mm) the MMR when the mean fl ow was about 0.28 m/s. This means that the shear signal was apparently contaminated with instrument body vibrations. Therefore, a compensation correction should be applied before estimating the TKE dissipation rate.

According to the method introduced in Section 3.2, we selected a 4-s segment data as an example for removing instrument body vibrational contamination from the shear signal. Figure 8 compares wavenumber spectra and estimation of the TKE dissipation rate with and without the compensating correction. After the correction, the power peaks at the Strouhal frequencies were signifi cantly weakened and the observed wavenumber spectrum fi tted much better with the theoretical Nasmyth spectrum. The dissipation rate was 1.2×10 -6 W/kg before correction and 1.6×10 -7 W/kg after correction, an order of magnitude smaller. This implies that the instrument body vibrations signifi cantly contaminate the shear signal, and the compensating correction effectively removes this contamination.

5.3 Time series of ε and comparison

During the fi eld experiment, the fl uctuations of the MMR were small, derived from pressure measurement with the TD sensor, and the mean depth of the main body was about 22.0 m. We estimated the TKE dissipation rate profi le ε MSS60 from the MSS60 microstructure profi le using a method similar to that in Section 3.1. We depth-averaged ε MSS60 between

20.0 m and 24.0 m to compare with ε MMR (Fig.9). Therefore, the dissipation rates measured with the two instruments were simultaneous and at about the same depth but about 100 m apart horizontally.

Figures 9 and 10 indicate that the two independent estimates of ε are strongly correlated and have the same trend versus time; both gradually decrease with the weakening fl ow speed. Overall, ε MMR differs from ε MSS60 within a factor of 2, and the root mean square error relative to ε MSS60 is about 1.5×10 -8 W/kg, which is small compared with its mean value 3×10 -7 W/kg.

However, Fig.9 shows that ε MMR is larger than ε MSS60 to some extent, especially at very low fl ow speeds (Fig.10), similar to the results for the tank test (Figs.4 and 5). The probable reasons are: (1) Taylor’s frozen hypothesis may be not be suitable for low fl ow speed; (2) ε MMR and ε MSS60 were not observed at exactly the same time and depth, and were horizontally separated by a distance of about 100 m. Nevertheless, turbulence is inherently highly intermittent (Moum and Rippeth, 2009), which may be a source for the bias between the two independent estimates.

6 CONCLUSION We have discussed methods for estimating the

TKE dissipation rate. One method directly estimates the TKE dissipation rate in the diffusive sub-range using the sampled high-frequency shear of turbulent velocity fl uctuations. The other method is based on the -5/3 slope in the inertial sub-range. Both methods have been validated by moored or autonomous

1 10 10010-7

10-6

10-5

10-4

10-3

10-2

10-1

f (Hz)

Φ (s

-2/H

z)

Ax/UAy/UAz/Uwx

Fig.7 Frequency spectrum of w x (magenta), A x / U (black), A y / U (blue) and A z / U (red) Gray dashed lines indicate frequencies of 5.7 Hz and 9.5 Hz.

10 100 1000

Φ (s

-2/c

pm)

εnc=1.2×10-6 W/Kgεc=1.6×10-7 W/Kg

No correctionCorrection

10-6

10-8

10-4

10-2

100

k (cpm)

Fig.8 Comparison of wavenumber spectrum and estimate of dissipation rate before (blue) and after (red) the compensating correction The curves have the same meaning as in Fig.3a.

208 CHIN. J. OCEANOL. LIMNOL., 32(1), 2014 Vol.32

turbulence measurements (Lueck et al., 1997; Lien and D’Asaro, 2006). Using the fi rst method for the diffusive sub-range, we designed, developed, and tested an MMR. By measuring the high-frequency velocity shear of the vertical velocity fl uctuations, the TKE dissipation rate can be directly estimated with the MMR.

To test and evaluate the performance of the MMR, we fi rstly conducted a tank test, and the estimated TKE dissipation rate agreed well with that observed simultaneously with the ADV. Both increased with increasing fl ow speed. The root mean square error of ε MMR relative to ε ADV was about 6.5×10 -8 W/kg, which is 10–10 2 times smaller than its own value (O (10 -6 )), suffi ciently low for turbulence measurement. This test indicates that the MMR performs very well when the main body is fi xed in the tank, under which condition it is motionless relative to the mean fl ow.

To further evaluate the performance of the MMR, we conducted an ocean fi eld experiment in the Jiaozhou Bay. The observed ε MMR agreed well with the dissipation rate simultaneously measured with the MSS60 microstructure profi ler. The tilts of the instrument were too small (pitch, roll<4°) to affect the measurement. However, ε MMR was generally a little larger than the rates found with the ADV or MSS60, especially for low fl ow speed. Probable reasons were given in Section 5.3.

The ocean fi eld experiment showed that the instrument body vibrations could signifi cantly affect turbulence measurement in two ways:

(1) The body vibrations could directly contaminate

the observed velocity shear signal and, consequently, the wavenumber spectrum in the diffusive sub-range. This might also be a reason for the bias between ε MMR and ε ADV or ε MSS60 . Therefore, we introduced a compensating correction to remove the contamination and then estimate the TKE dissipation rate. We found that this correction signifi cantly increased the accuracy of ε .

(2) The fl ow speed past the shear probe is the vector sum of the background fl uid speed and the speed at which the instrument body moves because of the shedding of the Karman vortex. The instrument body vibration speed can be deduced from measurements using an accelerometer and tilt transducers. However, we found that the body vibration speed was small enough to make their effect on the measurement of ε imperceptible, similar to the results of Moum and Nash (2009).

This work is only a preliminary and brief introduction to the MMR. Evaluating the performance of the MMR in measuring ocean turbulent mixing continuously and over a long term in the abyssal ocean requires more comparative experiments for different fl ow speeds. These experiments are being or will be conducted in the near future.

7 ACKNOWLEDGMENT The authors thank the crews of R/V Dong Fang

Hong 2 for their help in the fi eld experiment.

References

Lien R-C, D’Asaro E A. 2006. Measurement of turbulent

06:30 06:45 07:00 07:15 07:30 07:45 08:00 08:15 08:307 March 2010

Comparison of the dissipation rate of TKE

MSS60MMR

ε (W

/Kg)

10-5

10-8

10-7

10-6

Fig.9 Comparison of the dissipation rates measured simultaneously with the MMR (blue) and MSS60 (red) at the same depth

-8 -7.8 -7.6 -7.4 -7.2 -7 -6.8 -6.6 -6.4 -6.2 -6-8

-7.8

-7.6

-7.4

-7.2

-7

-6.8

-6.6

-6.4

-6.2

-6

logεMMR(W/Kg)

logε

MSS

60+0

.1 (W

/Kg)

Fig.10 Scatter plot of ε MMR and ε MSS60 The black dashed line indicates ε MSS60 = ε MMR . The shaded area indicates the mean standard deviations of ε MMR and ε MSS60 .

209No.1 TIAN et al.: Test and evaluation of MTMI

kinetic energy dissipation rate with a lagrangian fl oat. J . Atmos . Oceanic Technol ., 23 : 964-976.

Lueck R, Huang D, Newman D, Box J. 1997. Turbulence measurement with a moored instrument. J . Atmos . Oceanic Technol ., 14 : 143-161.

Lueck R, Huang D. 1999. Dissipation measurement with a moored instrument in a swift tidal channel. J . Atmos . Oceanic Technol ., 16 : 1 499-1 505.

Moum J N, Rippeth T P. 2009. Do observations adequately resolve the natural variability of oceanic turbulence? J . Mar . Syst ., 77 : 409-417.

Moum J N, Nash J D. 2009. Mixing measurements on an equatorial ocean mooring. J . Atmos . Oceanic Technol ., 26 : 317-336.

Munk W, Wunsch C. 1998. Abyssal recipes II: energetics of tidal and wind mixing. Deep-Sea Res ., 45 : 1 977-2 010.

Sharples J, Moore C, Abraham E. 2001. Internal tide dissipation, mixing, and vertical nitrate fl ux at the shelf edge of NE New Zealand. J . Geophys . Res ., 106(C7) : 14 069-14 081.

Sreenivasan K R. 1995. On the universality of the Kolmogorov constant. Phys . Fluids , 7 : 2 778-2 784.

Tennekes H, Lumley J L. 1972. A First Course in Turbulence. MIT Press, Cambridge, Massachusetts, United States. 300p.

Voulgaris G, Trowbridge J H. 1998. Evaluation of the acoustic Doppler velocimeter (ADV) for turbulence measurements. J . Atmos . Oceanic Technol ., 15 : 272-289.

Zhang Y, Moum J N. 2010. Inertial-convective subrange estimates of thermal variance dissipation rate from moored temperature measurements. J . Atmos . Oceanic Technol ., 27 : 1 950-1 959.