Ocean Turbulence Denoising and Analysis Using a Novel EMD-Based Denoising Method

Abstract

Ocean turbulence measurement in the wild sea has contributed significantly to improving our understanding of ocean mixing processes. Restricted by observation instruments and methods, the measured turbulence signal contains much information about the marine energy evolution mixed with a large amount of noise. Aiming at eliminating noise in deep sea exploration, a novel EMD-based (empirical mode decomposition) denoising method was designed. In this method, the collected ocean turbulence signal is first decomposed using EMD algorithm to obtain the intrinsic mode functions (IMFs). Then, the correlation coefficient between each IMF and the raw turbulence shear as well as the accelerations signal is calculated, which is taken as vibration reference signal. Finally, search for the proper IMF that has the following features (i) the correlation coefficient with the raw shear is larger than that with the accelerations signal; (ii) maximum difference exists between two adjacent correlation coefficients with the accelerations. IMFs that have these features are searched for signal reconstruction to realize the denoising of non-stationary turbulence. Turbulence signals collected with a self-designed autonomous reciprocating turbulence observation profiler (ARTP) deployed in the South China Sea (SCS) are used to validate the effectiveness and feasibility of the novel denoising method. Through comparison with the Nasmyth theoretical spectrum, the results show that the denoising method can not only effectively remove the noise component, but also maintain the detail characteristics of the effective turbulence signal under high noise, which offers a good theoretical foundation for the analysis of the ocean turbulent characteristics and energy evolution.

1. Introduction

Turbulence in the ocean enhances the mixing of materials and momentum by creating small-scale variance that increases gradients across which molecular diffusion acts [1]. At small scales, turbulence influences the ocean circulation and ecosystems by enhancing the transport of heat and nutrients within the water column and thus controls the ocean overturning circulation at a wide range of temporal and spatial scales [2,3]. As ocean turbulence is unsteady and irregular, much effort has gone into improving people’s understanding of energy exchange in the marine environment [4]. Oceanic turbulence measurements are mainly made to assess the dissipation rate of turbulence kinetic energy (TKE), which not only help understanding the turbulence energy evolution process and global climate change, but also strengthen the prediction system of marine climate and disasters [5,6].

High accurate turbulence data is the basis to analyze turbulence mixing characteristics. Typically, micro-structure is used for fluctuations associated with small-scale turbulence. Turbulence is analyzed by measuring velocity fluctuations at dissipation scales using shear probes, or temperature fluctuations measured with thermistors [7]. By mounting the shear probe or thermistors on different ocean observation platforms, they can produce abundant turbulence data. However, to measure a few centimeters of turbulence micro-structure in the open sea is quite difficult due to its inherent chaotic, unsteady and unpredictable characteristics, as well as the tough experiment environment. The collected turbulence data is inevitably polluted by various noises, such as instrument mechanical vibrations, high frequency electronic noise, and environment noise (usually wind and sea waves or the collision of the probes) [8]. It can be known from the analysis that the limitations and difficulties of all conventional instruments are mechanical vibrations, rather than the electronics used to amplify the probe signals [9]. So, a relatively stable platform and efficient denoising method can better help obtain high-precision turbulence data, which will lay foundation for further analysis.

Oceanic turbulence measurements have been taken for about a hundred years since the pioneering work [10,11]. According to the demands of turbulence detection, the development of ocean turbulence measurements is closely related to the development of ocean observation instruments. According to the different trajectories, turbulence observation instruments can be divided into various categories. The earliest measurements were carried out with horizontal towed profilers. As the variations in the ocean are predominantly vertical, and these kinds of profilers are quite unstable. Turbulence data obtained in this way are seriously contaminated [12]. By the late 1960s, most turbulence measurements were conducted with vertical profilers. Under the gravity and buoyancy from brushes, the vertical profiler can descend at a uniform speed, which is simpler and less susceptible to contamination. The limitations are the insufficient sampling over long periods of time and within large spaces. In addition, these profiles need too much manpower involved [13]. The viability of long-term and autonomous measurement of turbulence was demonstrated by the moored instrument TAMI. These profilers rely on the ambient current to ensure the turbulence past its sensors. Although being able to collect long enough turbulence data, the moored instruments still have limitations as they can only collect turbulence data at fixed underwater positions [14]. In the 1990s, autonomous underwater vehicles (AUVs) and gliders were put into service for environmental measurements. These profilers are self-propelled and controlled by an on-board computer. The major concern is the mechanical vibrations produced by the AUV or glider’s motor and fin actuators. In addition, many AUVs and gilders are not much longer than the largest eddies in the dissipation range of velocity fluctuations (≈1 m) [15,16]. Other new approaches such as VMP-X (vertical microstructure profiler—eXpendable) are mainly improved based on the above technologies [17]. In this paper, a self-designed profiler will be reported. The biggest characteristic is that the profiler is not fixed at a certain depth but sinks and rises repeatedly in a very long range of depths, which can provide data over a long time period and varied vertical turbulence.

In order to obtain enough accurate turbulence data, both instruments and denoising methods are developing. So far, researchers have proposed different methods to improve the accuracy of the collected data. The most common method includes the low-pass filter based on the fast Fourier transform (FFT) and the wavelet transform denoising method, but these methods are not very suitable for unsteady turbulence signals [18,19]. Based on the features of the collected signals from different sensors, frequency response transfer function and the cross-spectrum denoising method are developed [20]. However, these two methods are only good at eliminating the vibration noise. Recently, some methods for signal denoising schemes have been introduced that are based on empirical mode decomposition (EMD), which was originally developed to process nonstationary and nonlinear data, such as experimental turbulence records [21,22]. Through adaptively decomposing the noisy signal into a set of intrinsic mode functions (IMFs) ordered by frequency, EMD has been further applied successfully to a variety of physical systems. The key benefits of using EMD are automaticity and fully data adaptivity. Through the selection of the appropriate IMFs based on the correlation coefficients with three-axis accelerations for reconstruction, a novel turbulence denoising method based on EMD will be introduced. With that, we can achieve the optimal estimation of the observation spectrum and the dissipation rate of TKE.

The outline of this paper is as follows. The turbulence observation instrument and deployment are introduced in Section 2. Based on the analysis of the correlation between turbulence shear and the three-axis acceleration, Section 3 mainly presents the EMD-based turbulence denoising method and proper IMF selection criteria in detail. This part also gives the process to calculate the dissipation rate of TKE based on the denoised signal. Sea data collected with the self-designed turbulence profiler are used to verify the validity of the new denoising method. The results are shown and discussed in Section 4. Conclusion remarks are finally given in Section 5.

2. Turbulence Observation Instrument and Deployment

In order to realize the measurement over a long time period and wide space, the autonomous reciprocating turbulence observation profiler (ARTP), mainly designed to conduct up and down reciprocating motion along the moored cable, was used. ARTP can measure ocean turbulence velocity shear, three-axis acceleration, ocean temperature, current speed and other ocean environment parameters, which can meet the standard of ocean turbulence analysis.

Based on the design of bilateral symmetry, the ARTP, with a total length of 1.6 m, consists of two separate pressure cabin linked by the mounting bracket (shown in Figure 1a). The core components of the ARTP include the shear probe, pressure cabin, the buoyancy-driven elements, the control and acquisition board, and the battery. On the top left of the ARTP, there are two orthogonal shear probes with the sampling frequency set to 1024 Hz to measure the cross-stream velocity fluctuations contained. The CTD (conductivity–temperature–depth) used to record the real-time water conductivity, temperature and the underwater depth of the profiler was mounted on the top right. The three-axis accelerometers with the sampling frequency set to 120 Hz were housed in the pressure cabin by a righthand cartesian coordinate to monitor the status of the instrument under the seawater. Signals measured with the three-axis accelerometers include acceleration information on three direction and attitude information by heading (rotation around the z axis and ranging from −180 to 180), pitch (rotation around the y axis and ranging from −90 to 90) and roll (rotation around the x axis and ranging from −180 to 180). The buoyancy-driven elements are used to ensure the ARTP achieves reciprocate profiling motion. By changing the oil volume of the hydraulic bladders, ARTP can adjust the relationship between buoyancy and gravity, which realize the up and down reciprocating motion. The control and acquisition board are used to control the buoyancy-driven device and store the collected signals. The voltage output of the sensors was digitized by 16-bit A/D conversion and finally stored in a storage card. The whole ARTP is powered by battery.

The main structure and whole observation platform of the ARTP is shown in Figure 1. The whole turbulence observation platform includes the following five parts (shown in Figure 1b). Except the core part of the ARTP, the float groups were designed to provide buoyancy and ensure the stability of the whole system. Two groups of CTD sensors are used to collect the environment parameters in different positions. The two retainers are tied one meter away from the CTD sensors and strong enough to support the full weight of ARTP, even through the inertial force by the high speed movement. The two retainers can stop the motion of ARTP to control it, reciprocating up and down between them. Under the combined effect of the float groups and the anchor block, the whole system underwater can keep a vertical state. When the observation finished, the acoustic release receives the control signal and releases the anchor block, then the whole observation platform ascends to the sea surface under the effect of buoyancy.

The whole observation platform with the ARTP was deployed in the north of the SCS (South China Sea) at (20°55.49′ N 118°09.83′ E). The depth of this ocean area is about two thousand meters, which meets the requirements of sea trial. The field test location of the observation platform is shown in Figure 2. According to the observation range limitation of the two retainers, the ARTP’s motion range is approximately ranged from 500 m to 1500 m under the seawater.

3. Methodology

3.1. Correlation Analysis of the Collected Signal

The turbulence micro-structure shear, which can be related to turbulence levels, was measured with the shear probes. The two shear probes were oriented at ${90}^{\circ }$ to each other, so as to provide for orthogonal components of the ocean turbulence. The shear probe consisted of a piezoelectric ceramic beam and a voltage $E_p$ was produced as the beam sense the turbulence shear force: $E_p=\widehat{s}Wu$, where $\widehat{s}$ is the probe sensitivity (provided by the manufacturer after calibration), $W$ is the velocity of the sensor transported by ARTP through the water column, and $u$ is the cross-axial velocity fluctuation produced by the water current transverse to the direction of the shear probe. The shear signal $\partial u/\partial z$ was given by [23]:

$$\frac{\partial u}{\partial z}=\frac{1}{W}\frac{\partial u}{\partial t}=\frac{1}{\widehat{s}{W}^2}\frac{d{E}_p}{dt}$$

(1)

When shear probes are used to conduct measurements in the open sea environment, the vehicle motion and vibration may have a large effect on the shear force. Then the measured signal consists of the turbulence shear response to the shear force and the vibration noise, which is typically estimated with the signal collected by the three-axis accelerometers.

The measured accelerations include an inertial component and a gravitational component. The inertial components (denoted as dynamic accelerations) are used to describe the vibration of the instrument and can be separated from the gravity signal with independent pitch and roll information:

$$\mathrm{Accz} = {\hat{\mathrm{a}}}_{\mathrm{z}} + \mathrm{g} \cos \mathsf{\theta }\mathrm{os}\mathsf{\theta }\phi$$

(2)

where the angles $\mathsf{\theta }$ and $\phi$ are the vehicle pitch and roll, which also obtained from the three-axis accelerometers. $g$ is the acceleration of gravity, and ${\widehat{\mathrm{a}}}_{\mathrm{z}}$ is the vertical inertial acceleration in the body frame. Similarly, the signals from the axial and athwartship are $\mathrm{Accx}{\widehat{\mathrm{a}}}_{\mathrm{x}}+\mathrm{g}\sin \mathsf{\theta }$ and $\mathrm{Accy}={\widehat{a}}_y+\mathrm{g}\sin \phi$, respectively.

To obtain high accurate turbulence shear, the core is to remove the contamination to the shear signals by subtracting all coherent signals from the dynamic accelerations. Assume the measured shear can be expressed as:

$$S=\widehat{S}+h_i\ast a_i$$

(3)

where $S$ is the measured shear from the probe, $\widehat{S}$ represents the true uncontaminated environmental shear and $a_i$ represent the component of acceleration with $i=1, 2, 3$, which corresponds to the shear. The weight value $h_i$ represents the “transfer” of acceleration into the shear signal and the asterisk ($\ast$) denotes a convolution. Also, we assume that vehicular motions and vibrations are statistically independent of the environmental turbulence ($\overline{\widehat{S}{a}_i}=0$). According to the above definition, our objective is to obtain the portion of the measured shear that is not coherent with the measured accelerations.

3.2. Process of the EMD-Based Denoising Method

Real and effective turbulence signals are the basis for analysis of turbulence mixing characteristics. So, separating the desired signal from the noise is a common, but important, question in turbulence signal processing. In this work, we use the acceleration measurements to minimize the contamination of the collected shear by vehicular motions and vibrations.

First, the measured raw turbulence signal $S(t)$ is decomposed into a finite number n of intrinsic mode functions (IMFs) that represents different time scales and frequency from high to low using the EMD method [24]:

$$S(t)={\displaystyle \sum _{\mathrm{j}=1}^{n}im{f}_{\mathrm{j}}}(t)+r_n(t)$$

(4)

IMFs can be expressed as $im{f}_{\mathrm{j}}(t)={\mathrm{A}}_{\mathrm{j}}(t)\cos {\mathsf{\Phi }}_{\mathrm{j}}(t)$, where ${\mathrm{A}}_{\mathrm{j}}(t)$ and ${\mathsf{\Phi }}_{\mathrm{j}}(t)$ represent the amplitude and phase of the jth mode, respectively. Each IMF is characterized by a time-dependent ${\omega }_{\mathrm{j}}(t)$ and a typical time scale can be obtained by averaging over the whole time interval.

Even with suitable properties to deal with nonstationary and nonlinear data, EMD still cannot resolve signal from noise in the most complicated cases, for instance, when the signal is nonlinear while the noise has the same time scale as the signal. In this situation, their separation becomes impossible. Nevertheless, EMD offers a totally different approach to data decomposition, it is equivalent to a kind of orthogonal decomposition to a great extent. Based on this characteristic, we can conclude that in the obtained IMFs, the invalid IMFs related to the vibration noise are poorly orthogonal to the original signal but highly orthogonal to the accelerations. Hence, the correlation with the accelerations is good. So, the selection principle based on the correlation coefficient between IMF component and accelerations is used to judge the authenticity of obtained IMF component, and then remove the invalid component. To avoid the real IMF with small amplitude being removed, all IMF and the measured accelerations are normalized. In addition, to ensure the effectiveness of the IMF, the correlation coefficients between IMF component and raw turbulence shear are also calculated. The correlation coefficients between the decomposed IMFs and the measured signal are obtained as [25]:

$$r_{\mathrm{j}}=\frac{c(1,2)}{\sqrt{c(1,1)*c(2,2)}}=\frac{{\displaystyle \sum _{\mathrm{j}=1}^{n}im{f}_{\mathrm{j}}}(t)X_i(t)}{\sqrt{{\displaystyle \sum _{\mathrm{j}=1}^{n}im{f}_{\mathrm{j}}^2}(t){\displaystyle \sum _{\mathrm{j}=1}^n{X}_i{}^2}(t)}}$$

(5)

where c is the covariance matrix of matrix [$X(t), IMF$] $\mathrm{j}=1, 2, \cdots n$ and n is the number of IMFs. $X_i(t)$ represents the measured three-axis accelerations (i = 1, 2, 3) or turbulence shear (i = 1, 2). Then, the calculated correlation coefficients of each component are normalized:

$${\lambda }_i=u_i/\max (u_i),(i=1, 2, \cdots , \mathrm{m})$$

(6)

Find the two groups of adjacent coefficients with the acceleration that has the maximum difference, the IMF components before the selected coefficients are regarded as proper components. Compare the correlation coefficients of these IMF to ensure the correlation coefficients with the raw shear is larger than that with the accelerations signal and obtain the valid IMFs. Finally, based on the valid IMFs to reconstruct and obtain the real signal.

Assuming the isotropic turbulence, the dissipation rate of TKE is calculated with the reconstructed turbulence shear signal using spectral integration [26]:

$$\epsilon =7.5\nu \overline{{\left(\frac{\partial u}{\partial z}\right)}^2}=7.5\nu {\displaystyle {\int }_{k_{\min }}^{k_{\max }}\mathsf{\Phi }(k)dk}$$

(7)

where ∂u/∂z is the reconstructed vertical shear and Φ(k) is the wavenumber spectrum of the shear signal, ν is the coefficient of viscosity, u is the fluid velocity and z is vertical coordinate.

Based on the above analysis, the main steps of the novel EMD-based denoising method are as follows:

Step 1:

Preprocessing the observed original turbulent shear voltage and converting it into physical turbulent shear signal $S(t)$. Use low-pass filter to remove the high frequency electronic noise.

Step 2:

Calculate the dynamic accelerations and re-sample the dynamic accelerations to ensure the frequency is the same as that of the turbulence shear.

Step 3:

Decompose the raw shear signal as well as the accelerations using EMD method and obtain the IMF components of each layer and the remainder.

Step 4:

Calculate and normalize the correlation coefficient between the obtained IMFs and the raw shear as well as the accelerations. Select the two adjacent coefficients with the acceleration signal that has the maximum difference. Compare the correlation coefficients of these IMF to ensure the coefficients with the raw shear is larger than that with the accelerations signal and obtain the valid IMFs.

Step 5:

Reconstruct the turbulence shear signal based on the valid IMF component and obtain the denoised turbulence shear signal $\widehat{S}(t)$.

Step 6:

Based on the reconstructed $\widehat{S}(t)$ to calculate the wavenumber spectrum and the dissipation rate of TKE.

The flow chart of the new method to calculate the dissipation rate of TKE is given in Figure 3. The correlation coefficient between each IMF component and accelerations are calculated to remove the vibration noise coherent with the accelerometers data. In addition, to ensure the IMFs are effective, the correlation coefficients between the sensitive IMFs and raw shear are also calculated. From the view of signal orthogonal correlation, we select the valid IMFs that are highly orthogonal to raw shear and lowly orthogonal to accelerations as the vibration noise. Based on the reconstructed signal, calculate the wavenumber spectrum and compare it with the standard Nasmyth theoretical spectrum to evaluate the denoising effect of the new method.

4. Result and Analysis

4.1. Analysis of the Raw Collected Signal

In the field test, the ARTP is programmed to reciprocate between 530 m and 1510 m under the deep sea. According to the movement mode of the ARTP, the whole process in one vertical can be divided into three stages: acceleration upwards under the pressure of internal hydraulic bladder, uniform motion under the combined inertial force of buoyancy and gravity, and deceleration under the resistance and friction. The measured turbulence shear in acceleration stage is greatly affected by vibration of instrument power device, which should be focused on denoising. According to the CTD measurements, the rising velocity and depth of the whole process are shown in Figure 4. During the uniform upwardly rising process, the velocity is range from 0.3 m/s to 0.4 m/s and the mean velocity is about 0.34 m/s, which meet the requirement for measuring the deep sea turbulence.

Turbulence shear signals are measured from two orthogonal shear probes equipped on the ARTP and accelerations are collected with the three-axis accelerometer. One of the shear probes was broken during the field test, so we only processed the turbulence shear from one shear probe. The obtained turbulence shear and accelerations are shown in Figure 5. Here we show the acceleration stage and the uniform motion stage.

The samples in Figure 5a are the time series of the collected turbulence shear. The instrument samples the time derivative of the shear probe signals, which are converted to the along-flow gradients of velocity (∂u/∂x) using the measured current speed for this record. The shear signal sample contains contamination from the instrument motions and vibrations, which obscures the true environmental shear signal in the time domain. From Figure 5a we can see that the signal collected in the acceleration stage is much bigger than the signal obtained in the uniform motion stage, which should be analyzed in detail. Motions and vibrations of the observation instrument are revealed by the three-axis accelerometer records in Figure 5b. It also can be seen that the accelerations change obviously around 1150 m under the deep sea. The heading, pitch and roll reveal that the observation instrument is stable enough to collect the ocean turbulence signal.

To further analyze the correlation between the turbulence shear and accelerations, we transform the two kinds of signals into frequency domain using FFT, where frequency spectra can give considerable information on the quality of the data. The comparison between the shear frequency spectra and the accelerations frequency spectra is presented in Figure 6.

It is obvious that the shear power spectra and acceleration spectra have high consistency between 2 cpm (vertical line) and 7 cpm. This effectively reflects that the vibration of the moored system (represented as acceleration signals) seriously affects the measured turbulence shear signal.

4.2. Signal Processing Using the EMD-Based Denoising Method

The noise is removed with the EMD-based denoising method and the correlation coefficient, as described above. In the field test, the ARTP collected different profiles from the deep sea. Here, the shear signal sample processed is 3 min long in acceleration stage and the corresponding velocity U = 0.35 m/s. The velocity components ∂u/∂x are decomposed using the EMD method. All the IMF modes have different mean frequencies and time scales. The comparison of the velocity shear signal and the nine IMF modes, as well as the residue are shown in Figure 7.

In Figure 7, each IMF modes has its own time scales and frequencies. IMF1–IMF9 represent the different parts of the original ocean turbulence shear signal with the frequency from high to low. The time scales of the nine IMF modes become larger as the orders increase, while the frequency and amplitudes become smaller. The variation tendency of IMF1 is the most similar to the original shear signal and the residue only represents the general trend. The correlation coefficients of IMF components and raw shear, as well as accelerations, are shown in Figure 8.

In Figure 8, it can be seen before IMF5, the IMF has a strong correlation with the raw shear while the IMF5–IMF7 have the strong correlation with the accelerations. The maximum difference exists around IMF5, namely, the first four IMFs can be considered the proper components. Then, coefficients with acceleration and the raw shear of the selected four IMFs are compared to ensure the IMFs are strongly correlated with the raw shear. In this sample, the four IMFs are all valid and will be used to reconstruct the shear signal. The comparison of the reconstructed shear and raw shear signals is shown in Figure 9.

4.3. Denoising Effectiveness Evaluation of the EMD-Based Denoising Method

Finally, calculate the turbulence shear spectrum based on the reconstructed shear signal and transform it into a wavenumber domain under Taylor’s frozen turbulence hypothesis [27]. Typically, the Nasmyth theoretical spectrum is used as the standard spectrum to evaluate the denoising effectiveness [28]. Here, the effectiveness of the EMD-based denoising method is compared with the traditional cross-spectrum denoising method and both of the two denoised spectra are compared with the Nasmyth theoretical spectrum, which are shown in Figure 10. In Figure 10, the three solid curves are the observed spectra, respectively, where the green curve is the raw shear spectrum, the golden one is the spectrum after being corrected with the denoising method proposed in this paper, and the brown one shows the spectrum after being processed with the traditional cross-spectrum denoising method. The black dashed curve is the Nasmyth theoretical spectrum, and the blue solid triangle represents the cut-off wavenumber.

Compared with the traditional cross-spectrum denoising method, the observed spectrum, corrected with the EMD-based denoising method, better eliminates the noise spike and the corrected spectrum is fairly smooth between 2 and 7 cpm, which means the low wavenumber noise apparent in the raw shear spectrum is removed more effectively. Also, the spectrum shape agrees much more closely with the Nasmyth theoretical spectrum up to 50 cpm. The wavenumber spectra are integrated to the cutoff wavenumber to calculate the dissipation rate of TKE (Equation (7)) and the dissipation rate of the TKE computed with the reconstructed shear signal using the EMD-based denoising method drops near an order of magnitude compared to the raw measured data, which provides reliable and effective data for the further analysis of turbulence characteristics.

The results show that the novel EMD-based denoising method can effectively take advantage of the correlation coefficient between each IMF component and the accelerations, as well as the raw shear, to eliminate the invalid IMFs, which effectively suppress the low frequency vibration component in the original signal. The novel EMD-based denoising method is also applied to one whole profile collected using the ARTP, and the calculated dissipation rate of TKE from the raw shear and the clean shear are compared in Figure 11. Compared with the dissipation rate of TKE computed with the raw shear, the results obtained from the reconstructed shear drop by different orders of magnitude, which provides a reliable and effective data foundation for the further analysis of the turbulence characteristics and turbulence evolution.

5. Conclusions

Based on the analysis of the vibration noise characteristics in the observed turbulence shear signal, an EMD-based turbulence denoising method is proposed to eliminate the vibration noise component. The main contributions of the proposed EMD-based turbulence denoising method are summarized as follows.

(I)

To obtain the detailed characteristics of the turbulence signal, the EMD method is applied. Through calculating the correlation coefficient between each IMF and the accelerations, as well as the raw shear, the turbulence denoising shear is reconstructed based on the valid IMFs component. In the research of turbulence, an empirical spectrum of velocity fluctuations, derived by Nasmyth in wavenumber domain, is used as standard spectrum to evaluate the quality of the observed spectrum. By comparing with the Nasmyth spectrum, the results show that the EMD-based denoising method can effectively and reliably eliminate vibration noise. Furthermore, the denoising effectiveness is better than the cross-spectrum denoising method.

(II)

The denoising turbulence signals can well improve the accuracy of the turbulence data for the further research of the turbulence characteristics. The dissipation rate of turbulence kinetic energy (TKE) as a key parameter to describe the turbulence characteristic is also calculated in wavenumber domain from the measured turbulence velocity fluctuations.

The proposed EMD-based denoising method is effective in eliminating vibration noise, which improves the accuracy of turbulence shear signal and can supply effective turbulence signal to analyze the turbulence mixing characteristics. Meanwhile, based on the estimated dissipation rate of TKE, the heat flux can be further analyzed in future work.