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Abstract
This study simulated the generation and evolution of saltwater turbulence within a water tank. By pouring fresh water over saltwater in the tank, a layer of saline water with a fixed gradient was created. Convective turbulence was then formed by heating the bottom of the tank. The temperatures at different heights were measured using eight thermocouples; thus, the average temperatures and temperature fluctuations at different heights were calculated. The salinity profile was obtained by moving a conductivity probe up and down to measure the conductivity. Two-dimensional light intensity grayscale images were recorded after transmitting a collimated laser beam through the water tank, after which the normalized variance and power spectra of the light intensity fluctuations at different heights were calculated. The results showed that the saltwater in the tank could be divided by height into two layers, namely, the mixed layer and entrainment zone, according to the profiles of the average temperature and average salinity under the experimental conditions. Different portions of the images showed different characteristics. The part corresponding to the saltwater mixed layer was similar to that corresponding to the mixed layer in the fresh water experiment. However, a two-peak structure was observed in the curve of the normalized light intensity spectrum calculated from the grayscale values in the part corresponding to the bottom of the entrainment zone, whereas a two-peak structure was not found in the light intensity fluctuation spectrum corresponding to the mixed layer. According to the refractive index fluctuation spectrum model, one peak was due to temperature fluctuations, and the other peak was due to salinity fluctuations. It can be concluded that the salinity contribution to the refractive index fluctuation in the entrainment zone was larger than that in the mixed layer. Moreover, spectral analysis showed that in the saltwater, the inner scale of turbulent temperature fluctuation was approximately 1.9 mm, while the inner scale of turbulent salinity fluctuation was approximately 0.1 mm. These findings will be helpful for us to understand the microstructural characteristics of seawater turbulence and guide the implementation of optical transmission experiments in seawater.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High-temperature and high-salinity ocean currents reach depths of 200-400 m when entering low-temperature and low-salinity regions of the ocean. As a result, the salinity and temperature in the lower layer become higher than those in the upper layer [1,2]. This phenomenon also occurs near the ocean surface [3], introducing convection and turbulence. The diffusion of both heat and salt from the lower layer to the upper layer causes random fluctuations in the saltwater refractive index, and the diffusion velocity depends on the motion of the fluid. Similar to phenomena observed in the atmosphere, turbulent effects such as scintillation and refraction are generated when laser beams propagate through turbulent saltwater [4].
The small-scale characteristics of turbulence have a significant effect on scintillation; those characteristics in saltwater, especially fluctuations in the temperature and salinity, are usually obtained by measuring the refractive index and conductivity. A large amount of work has been conducted on the fluctuations in the refractive index of saltwater. An example of this research includes characterizing density fluctuations by measuring the refractive index to obtain the fluctuations in the density spectrum and the extent of its inertial sub-range [5]. However, due to limitations encountered when measuring the conditions of seawater, the spatial resolution of the obtained data is low, and information about the inner scale, an important parameter affecting the scintillation [6,7] of turbulent salinity fluctuations, cannot be obtained.
Therefore, it is necessary to carry out seawater measurements based on the scintillation of light beams. To date, theoretical studies have proposed numerous parameters, including the scintillation index, refractive index structure constant, dissipation rate, temperature variance dissipation rate and Kolmogorov microscale [8,9]. Subsequently, after a theoretical analysis of the scintillation of light beams propagating through turbulent saltwater, the scintillation indices of plane and spherical light waves and of a Gaussian beam propagating through weakly turbulent, clear ocean water were revealed [10]. Researchers have also studied the intensity characteristics and coherence properties of Gaussian beams propagating in clear turbulent oceans via numerical calculations [11].
To simplify the real conditions of marine environments, laboratory methods are often used to study the characteristics of marine turbulence [12–14]. Turbulence with a low Reynolds number has been produced in the laboratory by mechanically stirring the water at a fixed distance from the interface either in one layer or in both layers [15]. Theoretical analysis has also focused on the influence of seawater turbulence on the propagation of light, and measurements of this effect in the laboratory have been performed [16].
The microstructural characteristics of saltwater turbulence and its effect on light propagation are usually limited to theoretical studies and numerical simulations, while experimental measurements with a fine resolution are rarely reported. Laboratory simulations are greatly advantageous, as the conditions are controllable; thus, experiments can be repeated [17]. Accordingly, we created turbulence in the laboratory with a convection water tank. In the second section, Descriptions of the equipment and methods employed during our experiment are provided in the second section, after which the results of our experimentation are given, followed at last by a discussion of our findings and our conclusions.
2. Experiments and methods
The experiment was conducted in a rectangular water tank, as shown in Fig. 1. The size of the water tank was 1500 mm*1500 mm*600 mm, as shown in part A in Fig. 1. The tank was surrounded by four 10 mm thick transparent glass plates; this design minimizes the effects of the surrounding glass plates on the central flow field of the tank. To reduce the dissipation of heat, 3 cm thick sponges were attached to the outer wall of the glass; however, to facilitate the acquisition of measurements, some parts were remained transparent. A 1450 mm × 1450 mm × 60 mm oil tank was placed at the bottom of the water tank to provide the requisite heat (depicted by part B in Fig. 1). Thirty-nine electric heating tubes were evenly placed in the oil tank, which was then filled with transformer oil characterized by a good insulation performance and a low thermal expansion coefficient. To compensate for the expansion of the transformer oil during heating, an auxiliary oil tank was connected to the bottom tank (depicted by part C in Fig. 1). The heating power of the bottom tank was adjustable with a maximum value of 39 kW. In this way, an indirect heating method was adopted in which the oil was heated by electric heating tubes and the water in the water tank was heated by the oil. This method ensured a uniform heat distribution along the bottom surface of the tank. In a single experiment, the heterogeneity of the base plate temperature was approximately within 0.5°C.
Fig. 1 A. tank frame, B. heating tank, C. auxiliary tank, D. thermocouple sensor, E. vertical rod for fixing the thermocouple sensor, F. small vehicle on a track along the top of the tank, G. vertically moving conductivity sensor driven by a stepper motor (not shown in the figure), H. computer for collecting data and controlling the experiment, I. initial spot, J. receiving screen, K. CCD camera for recording the light intensity.
During the experiment, a sodium chloride solution with a fixed concentration at room temperature was poured into the water tank until the saltwater height reached approximately 12 cm (therefore, the saltwater depth at the beginning of each experiment was different). Then, a piece of foam board with a uniform hole distribution was placed on top of the saltwater. Then, fresh water at room temperature was carefully poured over the board, after which the fresh water seeped into the water tank through the holes in the foam plate. After the water in the tank reached a stationary state (which took approximately 30 minutes), a visible salinity gradient was formed at heights of 10-15 cm. The bottom tank was then heated to drive heat convection within the water tank, thereby simulating the appearance and evolution of saltwater turbulence.
The saltwater temperature was measured with 8 thermocouple thermometers (depicted by part D in Fig. 1) with a separation of 3 cm in the vertical direction. These thermocouples are specially designed; the size of the sensing component of the thermocouple is approximately 0.5 mm, and the time constant is approximately 0.03 s. The 8 thermocouples were fixed on a vertical rod (depicted by part E in Fig. 1) connected to a small vehicle (depicted by part F in Fig. 1) that could move horizontally to measure temperatures at different positions. In our experiment, the vehicle was fixed to reduce motion-induced interference within the flow field. The thermocouple measurement error was within 0.01°C, and the frequency response was greater than 5 Hz. The measured temperature data were collected by a computer (depicted by part H in Fig. 1) with a sampling frequency of 25 Hz, and the temperature data were averaged every 50 s to obtain a temperature profile.
A 547 A conductivity probe [18] (depicted by part G in Fig. 1) was mounted to the end of a computer-controlled rod moving only in the vertical direction at a speed of 0.02 m/s. A laser pointer attached to the rod and two photoresistors fixed at different heights assisted the computer control a stepper motor and accurately decided the position of the conductivity probe. The sampling frequency is 25 Hz and the measurement accuracy of the probe is better than 95%. A correction method was applied to the conductivity data to reduce the lag error attributable to the large lag coefficient of the probe. The hysteresis coefficients of the sensors were measured before conducting the experiments. The conductivity was corrected by subtracting (adding) the product of the hysteresis coefficient, conductivity gradient and vertical sensor speed as the sensor moved downward (upward); the details of this procedure can be found in Appendix A. Profiles were obtained after each round trip of approximately 50 s. Conductivity data were used to calculate the brine concentration; the details of this calculation are available in Appendix B.
The main optical instruments used in this experiment consisted of a collimated beam system and an optical charge-coupled device (CCD) camera. The He-Ne laser beam was expanded twice and then collimated once by the collimated beam system (not shown in Fig. 1) into a circular collimated beam with a spot diameter of 200 mm (depicted by part I in Fig. 1) and a divergence of approximately 1 marc, which could be approximately regarded as a plane wave. The collimated light beam entered from one side of the water tank, passed through the turbulent flow field in the tank, and then exited from the other side of the tank before finally reaching the receiving screen, upon which a circular spot was created, as depicted by part J in Fig. 1. Absorption and scattering were not considered in this study. The distance between the entering side of the tank and the screen was 2000 mm, which was composed of 1500 mm in the tank and 500 mm in the air, as shown in Fig. 1b. The spot was measured by a CCD camera (5.2 μm × 5.2 μm, 60 dB, 256 grayscale, and 1024 × 1280 pixels, as depicted by part K in Fig. 1). The spot image collected by the computer was a 256-grayscale image with a resolution of 1024 × 1280 pixels. Two spatial resolutions of the spot captured by the CCD camera were established as 21 pixel/mm and 55 pixel/cm with focal lengths of 35 mm and 12 mm and view angles of 49° and 13°, respectively. We experimentally determined the relationship between the grayscale value of the image and the intensity of the light by changing the aperture of the lens, the results of which revealed a strong linear relationship between the grayscale value and light intensity. However, the CCD camera exhibited dark current shot noise and detector saturation; hence, during the experiment, the CCD aperture was set appropriately. The average grayscale value of the image was approximately 80. According to the experimental results, dark current and circuit noise appeared with a grayscale value of approximately 7 on average.
3. Experiment results
To obtain the saltwater turbulence characteristics, a total of 18 experiments were carried out, among which 3 were without salt and 15 were with salt. The thickness of the saltwater layer in the experiments ranged from 5 to 15 cm. In 2 of the 15 experiments with salt, a stable temperature stratification appeared. The initial salinity gradient was in the range of 1.5~8 g/(kg·cm), and the initial temperature gradient was 0~6°C/cm. Among all 15 experiments, the temperature and salinity profiles were similar, and the interface between the saline water and fresh water exhibited the same optical characteristics. Therefore, the results of one of the experiments are given below.
3.1 Temperature and salinity profiles
Figure 2 shows the acquired profiles of the mean salinity (Fig. 2a), mean temperature (Fig. 2b), and temperature variance (Fig. 2c). Since the sensor used to acquire the salinity measurements was approximately 50 mm in length and there was a 20 mm gap near the bottom of the water tank during its vertical movement, no data were recorded below a height of 55 mm from the bottom of the tank. Profiles at two different moments, one at the beginning and at a state of fully developed turbulence, are given in Fig. 2.
Fig. 2 Average salinity profiles (a), average temperature profiles (b), and temperature variance profiles (c) at different moments. The figures on the figures are the moments corresponding to the profile measurements.
As shown in Fig. 2a, the salinity initially decreased with the height and was very low above 160 mm. Upon heating after 2843 s, the salinity below 100 mm was constant, and the salinity above 100 mm decreased with the height with a gradient of approximately 3.0 g/(kg•cm). Compared with measurements taken at the beginning of the experiment, the salinity at the bottom of the tank decreased while the salinity at 100 mm increased due to the upward diffusion of the salinity attributable to the convection in the water tank. According to the current measurement results, it can be estimated that the salinity diffusion coefficient was approximately 1.7 × 10−8 m2/s, which is greater than one order of magnitude larger than the molecular diffusion coefficient [19]. Details of the calculation method can be found in Appendix C. As shown in Fig. 2b, the temperature changed little with the height at the beginning of the experiment; then, after the initiation of heating along the bottom, the temperature below 100 mm remained constant, while a visible temperature gradient was maintained above 100 mm. As the heating progressed, the entire temperature profile showed an overall increase, indicating heat transfer from the bottom to the top and a gradual increase in the temperature gradient above a height of 100 mm. At 2800 s, the temperature gradient was approximately 2.0 °C/cm. According to the current measurement results, the thermal diffusivity at heights above 100 mm was approximately 2 × 10−6 m2/s [19], which is one order of magnitude larger than the molecular thermal conductivity coefficient and two orders of magnitude larger than the aforementioned salinity diffusion coefficient. From the temperature fluctuation variance profile given in Fig. 2c, the temperature variance was initially less than 5 × 10−4 °C2; after the heating had continued for 2800 s, the temperature fluctuation variance showed a maximum of 0.1 °C2 both at the bottom of the water tank and at a height of 130 mm and a minimum at a height of 100 mm.
3.2 Temperature fluctuation spectrum
To further analyze the saltwater turbulence characteristics, the measured temperature fluctuations and power spectra of the temperature fluctuations at five positions, namely, P1 (at a height of 10 mm), P2 (40 mm), P3 (70 mm), P4 (100 mm), and P5 (130 mm), as shown in Fig. 2c, are given in Fig. 3. The temperature sequence consisting of a total of 2048 points at three heights during 2800-2881.92 s is shown in Fig. 3a, from which it is evident that the temperature fluctuation intensity at P1 was large; many small spikes appeared on the timing curve, and the temperature change over a short period was more than 1 °C. However, the temperature fluctuations at P2, P3 and P4 were not strong, and the temperature remained unchanged at 39.9 °C; as the height increased, the total heat transferred upward gradually decreased. P4 was located at the bottom of the gradient layer, where the turbulence was very weak. Therefore, the temperature at position P4 at 2840 s fluctuated little. From the P4 temperature sequence, a large temperature decrease of approximately 0.4 °C can be seen at 2860 s; this temperature drop was caused by the downward movement of the upper, colder fluid to the position of P4. The sharp decrease in the temperature at P4 was not observed at either P2 or P3, because P4 was situated at the bottom of the gradient layer, while P2 and P3 were located in the upper part of the mixed layer. Meanwhile, the temperatures at P1 and P5 slowly rose. The temperature fluctuation intensity at P5 was large; however, although the temperature did fluctuate, the temperature curve does not exhibit many fine changes. At 2800 s, there was a strong temperature gradient in the fluid near the probe. When the lower fluid with a higher temperature reached P5, the measured temperature at P5 increased. A downward force was applied to the fluid with a higher temperature and higher salinity after it rose into the layer with a lower salinity, causing that fluid to move downward, thereby entraining the colder water with a lower salinity and weaker turbulence downwards at the same time. After this mixing, the temperature at P5 gradually increased, and the salinity also increased. The process that occurred at P5 is similar to the entrainment at the bottom of the real atmospheric boundary layer [20]. Therefore, in this paper, we call the lower part of the temperature profile (or the salinity profile) the mixed layer (ML) and the upper part with a larger temperature gradient and a larger salinity gradient the entrainment zone (EZ).
Fig. 3 Temperature measurements from the thermocouple sensors at five different heights The points P1, P2, P3 P4, and P5 close to the curve denote the positions where the curves were obtained (see Fig. 2c). The colors for the curves for P1, P2, P3, P4 and P5 in the left panel are black, dark yellow, dark cyan, red and blue, respectively. S in (b) denotes the power spectrum density of temperature fluctuation, σT2 denotes temperature fluctuation variance, and f-5/3 represents the asymptotic kolmogorov scaling.
An autoregressive (AR) power spectral density estimation method was applied to obtain the temperature power spectral density [21], as shown in Fig. 3b, which illustrates the power spectra of the temperature sequences shown in Fig. 3a. It can be seen that P1, P2, P3 and P4 exhibit ranges that satisfy a −5/3 power law, but the temperature sequence measured at P5 hardly showed any characteristics that satisfy such a power law, and its spectral curve was steeper than a slope of −5/3. Additionally, P1 exhibited a low energy at low frequencies, while P4 and P5 had higher energies in the same frequencies. This outcome is also evident in the timing curve in Fig. 3a. P1 contained many small-scale fluctuations, while the fluctuations at P4 and P5 were larger in scale. These features are very similar to those of the temperature fluctuations in pure water.
3.3 Spot features
The initial collimated beam could be regarded as a plane wave propagating through the saline medium and irradiating the receiving screen, upon which the beam creates a spot with a grayscale light intensity, as shown in Fig. 4a. The grayscale value is proportional to the brightness of the beam. The normalized variance β of the horizontal pixel grayscale value of every 21 adjacent rows in the circular spot can be calculated and can be considered as the value at the height corresponding to the middle row. The normalized variance β is thus defined as,
where I is the grayscale value of the pixel, which is proportional to the light intensity, and the overbar denotes a spatial average. Therefore, the value of β calculated by Eq. (1) is the scintillation index [4]. The resulting curve of the scintillation index as a function of the height is shown in Fig. 4b. According to optical propagation theory [4], the refractive index structure constant along the path of transmission can be obtained from the scintillation index and can usually be used to characterize the intensity of turbulence.Fig. 4 Image obtained on the receiving screen after the laser beam was transmitted through saline turbulence (a). Profile of the scintillation index calculated from the fluctuations in the light intensity at different heights (b). There are two white rectangles in (a): the upper box denotes the position for Fig. 5(a), and the lower box denotes the position for Fig. 6(a).
As shown in Fig. 4a, the brightness distributions at different heights exhibit different characteristics. In the lower part of the spot, the brightness distribution is similar to that of the spot caused by temperature fluctuations in fresh water. Additionally, bright and dark stripes appear in this area, and large bright spots appear at their intersections. However, the features of the upper part of the spot are completely different from those of the lower part, where the temperature gradient is larger; a higher-resolution image of the upper part of the spot is shown in Fig. 5a. Correspondingly, a higher-resolution picture for the lower part are shown in Fig. 6a.
Fig. 5 High-resolution spot (a) and spectral densities of the intensity fluctuations (b) obtained after a laser beam passes through the entrainment layer. The label “Hori” represents the normalized power spectrum calculated from the horizontal lines of the picture, and the label “Vert” represents the normalized power spectrum calculated from the vertical columns of the image. The spatial scale 5mm is shown in (a).
Fig. 6 High-resolution spot (a) and spectral densities of the intensity fluctuations (b) obtained after a laser beam passes through the mixed layer. The spatial scale 5mm is shown in (a).
As the temperature fluctuation spectra in the previous section suggest, similar to the classification of atmospheric boundary layers, brine turbulent layers can also be divided into a mixed layer and an entrainment zone according to the scintillation index profile.
Figure 4b shows a profile of the normalized intensity variance, which is proportional to the refractive index structure constant [4,22,23]. From Figs. 2 and 4, the mixed layer evidently exhibits a rate of decline proportional to z-4/3, which is in accordance with the general law that refractive index structure constants vary with the height in an actual atmospheric mixing layer [24]. The scintillation index rapidly decreases above 100 mm. After the light beam passes through the mixed layer, the intensity fluctuation of the light spot is similar to that in fresh water and exhibits a clear striped structure representative of obvious isotropic characteristics. The entrainment layer lies at a height between 100 mm and 160 mm. After the light beam passes through the lower part of the entrainment layer, a very fine grayscale distribution appears in the light spot; in contrast to the striped structure appearing in the spot generated by the mixed layer, only slight intensity fluctuations appear in the upper part of the spot. In the upper part of the entrainment layer, large, bright and dark stripes are observed. The fluctuation range of the normalized intensity variance is on the same order of magnitude as that of the scintillation caused by temperature fluctuations in fresh water.
3.4 Intensity spectrum
To further analyze the characteristics of the light intensity fluctuations in the middle of the spot shown in Fig. 4a, Fig. 5 illustrates the light intensity fluctuations with a higher resolution and the corresponding light intensity fluctuation spectra.
Figure 5a shows a higher-resolution image (with a resolution of 21 pixels/mm) of the spot corresponding to the upper white rectangle in Fig. 4a. In Fig. 5a, some darker stripes with very blurry, feathery edges are observed that are different from the stripes with edges that are usually evident in fresh water turbulence [22]. The power spectra of the light intensity fluctuations were calculated in Fig. 5a, and they are shown in Fig. 5b. The abscissa is the spatial wavenumber, and the ordinate is the normalized intensity fluctuation spectral density, i.e., multiplied by the spatial frequency and then divided by the variance. The two curves in Fig. 5b are the horizontal and vertical fluctuation spectral densities; they are very close to each other, indicating that the light intensity fluctuations are isotropic. As is also shown in Fig. 5b, the curves have two peaks at 0.21 mm−1 and 3.6 mm−1. Based on the previous results of light propagation in a water tank containing fresh water, the inner scale of the turbulence has an effect on the light propagation [22]. Recently proposed models of refractive index fluctuation spectra in turbulent ocean water show that there are two peaks in the refractive index power spectrum corresponding to the inner scales of the temperature and salinity [25–27]. According to our previous water tank simulation results and numerical simulation results, the reciprocal of the peak wave number of the normalized intensity fluctuation spectrum is approximately 2.5 times the inner scale of turbulence [22]. The corresponding scales for the two peaks of the two spectral curves in Fig. 5b are 1.9 mm (1/0.21 mm−1/2.5 = 1.9 mm) and 0.1 mm, which are far less than the inner scale of thermal convection turbulence in a water cell by Kulikov [17]. Using the light intensity fluctuations shown in Figs. 5a and 5b, the variance of the light intensity caused by fluctuations in the salinity was estimated using the spectral analysis method, resulting in a value of approximately 10% of the total variance. This outcome also proves that the variance of the light intensity fluctuations caused by salinity fluctuations was far smaller than that caused by temperature fluctuations in fresh water.
Similar to the general characteristics of temperature fluctuations in fresh water, the intensity fluctuation below 100 mm shows only one peak. For comparison, we analyzed the intensity fluctuation at a height of 60 mm (corresponding to the lower white rectangle in Fig. 4a) and the corresponding power fluctuation spectrum in the same way. Figure 6a, which has a resolution of 21 pixels/mm, shows some bright stripes with very sharp edges. The power spectra of the light intensity fluctuations in Fig. 6a were calculated, and they are shown in Fig. 6b. The two asymptotic slopes for the low and high wavenumbers are approximately κ and κ-5.5/3, which are similar to the results that Pawar and Arakeri obtained for the intensity spectra of a laser propagating though buoyancy-driven turbulence [28]. Unlike Fig. 5b, a double-peak structure does not appear in the power spectrum curves in Fig. 6b. This phenomenon indicates that the contributions of salinity fluctuations to the density field fluctuations in the mixed layer are less those in the entrainment layer.
4. Discussion and conclusion
A convective water tank can be used to simulate the evolution of saline turbulence. Pouring fresh water over saltwater creates a visible salinity gradient. Convection turbulence appeared after heating the bottom of the tank, where the temperature and salinity fluctuated. After heating the bottom of the tank for a period of time, the saltwater in the tank could be divided into two layers with different characteristics. Due to the thorough mixing of fluids in the lower layer caused by thermal convection, the average temperature and average salinity of the fluid in the lower layer did not change with the height; we called this layer the mixed layer. The temperature and salinity of the fluid in the upper layer gradually decreased with the height, and the fluid density decreased with the height overall. After the saltwater in the lower layer rose to the upper layer, an entrainment process formed similar to the top of the atmospheric boundary layer, and thus, we called this layer the entrainment layer. The variance of the temperature fluctuations in the mixed layer gradually decreased with the height and reached a minimum at the top of the mixed layer. The variance of the temperature fluctuations was larger in the entrainment layer. The temperature fluctuation spectra showed that the temperature fluctuations in the mixed layer followed a classic −5/3 power law, while the temperature fluctuations in the entrainment layer did not.
To study the fine-resolution structure of saltwater turbulence, we transmitted a collimated laser beam through turbulent brine and obtained two-dimensional grayscale images of the brightness distribution on a receiving screen. The intensity of the turbulent flow over the transmission path could be determined by the normalized variance of the grayscale intensity of the received spot. Accordingly, the grayscale information associated with the fine-resolution structure of the turbulent flow field was obtained by analyzing the grayscale power spectrum.
The light intensity spectrum was also analyzed. The influence of the salinity on the refractive index was not seen in the fluctuations of the light intensity when the laser beam passed through the brine medium in the mixed layer. When the light beam passed through the brine medium in the lower part of the entrainment layer, an influence of the salinity on the refractive index could be observed.
Since no measurements of the salinity fluctuations were acquired, a profile of the salinity fluctuations was not obtained. Judging from the current experimental results, the temperature fluctuations are the weakest at the lower part of the entrainment layer, and the contribution of the salinity fluctuations is represented by the light intensity fluctuations, indicating that the salinity fluctuations in the entrainment layer are relatively large. To some extent, these results confirm the power spectrum of seawater refractivity fluctuations in terms of the temperature spectrum and salinity spectrum [25,26]. Of course, this conclusion requires further measurements for verification.
Appendix A
For a conductivity probe moving upward, the sampled conductivity Cu can be regarded as,
where Cz is assumed to be the true conductivity value at the height z, λ is the hysteresis coefficient, v is the velocity of the conductivity probe and Gu is the conductivity gradient, which can be calculated from Cu. Similarly, for a probe moving downward, the sampled conductivity Cd can be regarded as,Thus, based on Eqs. (2) and (3), a corrected conductivity profile can be calculated as,Appendix B
To retrieve the saline concentration from the conductivity, a simple relationship between the saline concentration and conductivity was obtained experimentally, as given in Eq. (5),
where the units of S are g/kg and the units of C are mS/cm. For example, when C = 40 mS/cm, S = 19.0 g/kg.Appendix C
The diffusion coefficients K can be calculated from the measurements as follows,
where is the salinity gradient, is the time rate of change of the salinity, and h is the upper limit height of the traverse (approximately 160 mm in Fig. 2).Funding
National Natural Science Foundation of China (NSFC) (41475012, 61475105, and 61471003).
Acknowledgments
We also thank five anonymous reviewers for their constructive and helpful comments.
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