## Abstract

Small-scale spatial variation in temperature can lead to localized changes in the index of refraction and can distort electro-optical (EO) signal transmission in ocean and atmosphere. This phenomenon is well-studied in the atmosphere, where it is generally called “optical turbulence”. Less is known about how turbulent fluctuations in the ocean distort EO signal transmissions, an effect that can impact various underwater applications, from diver visibility to active and passive remote sensing. To provide a test bed for the study of the impacts from turbulent flows on EO signal transmission, and to examine and mitigate turbulence effects, we set up a laboratory turbulence environment allowing the controlled and repeatable variation of turbulence intensity. The laboratory measurements are complemented by high resolution computational fluid dynamics simulations emulating the tank environment. This controlled Simulated Turbulence and Turbidity Environment (SiTTE) can be used to assess optical image degradation in the tank in relation to turbulence intensity, as well as to examine various adaptive optics mitigation techniques.

© 2017 Optical Society of America

## 1. Introduction

Underwater temperature and salinity microstructure associated with turbulence can lead to localized changes in the index of refraction (IOR) and can be a limiting factor in aquatic environments. These variations in the IOR can affect electro-optical (EO) signal transmissions that impact various applications, from diver visibility to active and passive remote sensing. The term “optical turbulence” is widely used in atmospheric optics to describe the analogous phenomenon of distortion of EO transmission due to variations in the IOR caused by changes of air temperature along the optical path. Underwater “optical turbulence” at sea was investigated in the 1970s by [1], who used this term to describe “small inhomogeneities in the index of refraction of seawater, their origins, and the effects they have on underwater optical systems”. More recently [2], looked at the effect of “light scattering on oceanic turbulence” with numerical studies compared to measurements in a small laboratory tank. Two recent field studies aimed at characterizing naturally-occurring “optical turbulence” in the aquatic environment highlight the difficulties associated with collecting concurrent data on optics and turbulence in the ocean [3, 4] or lakes [5]. Most often, temperature fluctuations are the dominating factor affecting the IOR [1], except in the case of strong freshwater or salt water influence, such as in river outflows or estuaries, or possibly in surface lenses generated by rainfall. In this study, we neglect the influence of salinity and instead focus on the effect of temperature. To quantify the scope of the impacts from turbulent flows on EO signal transmission in water, and to examine and mitigate turbulence effects, we set up a laboratory environment designed to be a testbed for repeatable optical experiments in a controlled turbulence setting, allowing the variation of turbulence intensity. This is a critical element for the study of underwater optical turbulence, as the cost associated with field experiments is high and the stochastic nature of turbulence complicates field efforts. The laboratory provides a measurement environment that is significantly simpler to control and less affected by external parameters than the field setting, such as a lake or open ocean, where particle scattering degrades the optical signal or platform motion can pollute the velocity data. The laboratory setup also allows us to vary turbulence intensity. This provides a “controlled turbulence environment” in terms of parameter space and a framework for repeatable experiments. Convective turbulence is generated in a classical Rayleigh-Bénard tank and the turbulent flow is quantified using a state-of-the-art suite of sensors that includes high-resolution Acoustic Doppler Velocimeter profilers, fast thermistor probes, as well as next-generation fiber-optics temperature sensors, and particle image velocimetry. The measurements are complemented by very high-resolution non-hydrostatic numerical simulations using computational fluid dynamics (CFD). The numerical simulations provide full fields of temperature and velocity and thus provide a better view of the large-scale flow field and distribution of turbulence parameters than could be gathered with the sparse laboratory measurements alone. Optical image degradation in the tank is also assessed in relation to turbulence intensity.

In this paper, we describe the “controlled laboratory turbulence environment” designed for the study of underwater “optical turbulence”, and quantify the turbulent flow conditions through measurements and numerical experiments.

## 2. Methods

We implemented a unique controlled turbulence environment that consists of a laboratory tank complemented by a high-resolution numerical model designed to emulate the laboratory setting, a so-called “numerical tank”. The combined setup has been termed the Simulated Turbulence and Turbidity Environment (SiTTE) for its ability to simulate a range of turbulence strengths and conditions.

#### 2.1 Laboratory setup

The laboratory tank is a modified acrylic water tank with optical windows with a 5m length and a height and cross-section of approximately 0.5m. This tank is unique in that it is outfitted with stainless steel plates at the bottom and top that can be temperature controlled (Fig. 1, left). This allows for the generation of classical convective Rayleigh-Bénard type turbulence, which is generated by heating and cooling the bottom and top, respectively. The strength of the convective turbulence in the tank is a function of the temperature difference between the top and bottom plates and can be characterized in terms of the Rayleigh number, defined as

Here, g is the acceleration due to gravity, α is the thermal expansion coefficient, ∆T is the temperature difference between the plates, d is the distance between the plates, ν is the kinematic viscosity, and D_{T}is the thermal diffusivity.

The Rayleigh number of the flow can be changed by changing the plate temperatures, and thus the turbulence intensity can be varied. In our experiments, Ra ranges from 1.5∙10^{10} to around 4∙10^{10}, corresponding to a temperature difference ∆T between the plates of 6K and 16K, respectively.

The turbulence in the tank is quantified by high-resolution Nortek Vectrino Profiler Acoustic Doppler Velocimeters (ADV) and fast thermistor probes (PME high-resolution conductivity-temperature (CT) probe) (Fig. 2, left). These instruments provide high-resolution velocity and temperature measurements, at 100 and 64Hz, respectively. Three Vectrino Profilers and two CT probes were mounted in the tank and collected time series of high-resolution velocity and temperature/conductivity for the subsequent estimation of turbulent kinetic energy dissipation rate ε and temperature variance dissipation rate χ. Data were collected at a sampling frequency of 100Hz with the Vectrino Profiler and at 64Hz with the PME temperature probes. To quantify the impact of turbulent fluctuations on optical signal transmission, turbulent kinetic energy dissipation rate ε and temperature variance dissipation rate χ were calculated from the velocity and temperature measurements via spectral fitting to Kolmogorov spectra (for velocity) and Batchelor spectra (for temperature) following techniques described in [6–10].

Turbulent kinetic energy dissipation rate ε and temperature variance dissipation rate χ were then compared to values obtained from the numerical simulations of convective turbulence in the tank and can subsequently be used to assess the impact on the optics and for the estimation of the optical turbulence coefficient C_{n}^{2} [4, 11, 12].

In addition to these point measurements of velocity and temperature, a state-of-the-art Particle Image Velocimetry (PIV) system, built by Dantec Dynamics Inc., was used to quantify the velocity fields and visualize the larger-scale flow in the tank [13]. The system provides measurements of two-dimensional planes of the flow in the convective tank, which can be compared to the numerical model. It also allows the calculation of turbulence statistics, including turbulent kinetic energy dissipation rates. The basic concept of a PIV system is to illuminate a seeded flow with a laser sheet and take quick successive image pairs with a CCD camera. Looking at correlations between particles (i.e., how much the particles have moved) between two successive images allows the user to calculate flow velocities. Figure 2 shows the experimental setup at SiTTE: the laser, the mirror directing the laser sheet into the tank at a 90 degree angle to the tank side wall to make a cross-section, as well as the CCD camera, a FlowSense EO 4M-41 with a sensor resolution of 2336 x 1752 pixel, pixel size 5.5 µm, and maximum frame rate at full resolution of 41 fps. The laser is a Litron ND:Yag laser, dual cavity, 135 mJ per cavity, with a 15Hz maximum frequency per cavity. Due to the slow velocities observed in the convective flow, even at high Rayleigh number, the flow was time-resolved and thus the sampling frequency was set to 10Hz. In the results reported here, the flow comparison was undertaken near the tank boundary, in part to understand the influence of boundary layers on the turbulence tank. The image on the left of Fig. 3 shows the PIV setup. The water in the tank was seeded with polyamide particles (50 µm diameter) at density of approximately 0.04 particles per pixel. The image on the right shows the focal plane and PIV field of view with the tank side boundary to the left of the PIV field of view. To calculate velocities, we employed the sophisticated Adaptive PIV algorithm provided within Dantec Dynamic Studio, which adjusts the size of the interrogation area locally to optimize for seeding density and velocity gradient variations. Here, the size of the interrogation area was allowed to range from 16 to 64 pixels with vectors calculated every 12 pixels. This yielded a vector spacing of 0.93mm for a total field of view of 180mm in the horizontal by 137mm in the vertical.

#### 2.2 Numerical tank

To complement the sparse laboratory measurements and better understand the large-scale flow field and temperature structure inside the laboratory tank, three-dimensional, very high-resolution, non-hydrostatic numerical simulations using CFD were performed. These simulations can provide full fields of temperature and velocity for the estimation of turbulence parameters and their impact on the optics. The combination of laboratory environment and numerical model provides a well-quantified framework for controlled repeatable experiments under various turbulence intensities.

The numerical tank was implemented in the open-source CFD code OpenFOAM using a Large-Eddy Simulation (LES) approach. In LES, the larger-scale eddies in the flow are explicitly resolved, while the scales smaller than the grid-size are modeled [14]. The traditional Smagorinsky model was chosen as the sub-grid scale model [15]. In LES, a larger portion of the turbulence spectrum is explicitly resolved than in the often used Reynolds-averaged Navier-Stokes (RANS) models (k-ε and others), which, while useful to predict turbulence parameters, do not resolve the smaller flow features and associated eddies. Direct Numerical Simulations (DNS) on the other hand, in order not to be computationally prohibitive for a domain as large as presented here, would be severely underresolved and thus suffer from excessive numerical diffusion. Since it is necessary to resolve the details of the flow and eddying characteristics in the temperature field, in addition to turbulence parameters, to be able to assess the effect on the optics, the LES approach is the preferred way to simulate the setup described in this paper.

Here, we present results from a very high-resolution, millimeter-scale simulation with a horizontal grid resolution of ∆x = ∆y = 5mm, and a vertical grid resolution of ∆z = 2.5mm, which corresponds to 20 million grid points in the 5m by 0.5m by 0.5m domain. Exploratory simulations at lower resolution (∆x = ∆y = ∆z = 1cm) were run on a modern, high-performance, dual six-core Linux desktop, whereas the production runs at the millimeter-scale resolution required High-Performance Computing resources at the DoD Supercomputing Resource Center, due to the high computational cost. A view into the laboratory tank and a corresponding model view is shown in Fig. 1. The model provides full velocity and temperature fields which can be verified using the laboratory measurements (Fig. 4).

#### 2.3 Impact on optical transmission

This paper focuses on presenting the SiTTE laboratory tank and measurement capabilities available to quantify the controlled turbulence in the tank. This controlled turbulence environment is designed to benefit the optics community interested in exploring optical turbulence properties and mitigation methods. Detailed studies of the optical conditions at SiTTE are beyond the scope of this paper and have been reported in [16, 17]. For the present paper, the velocity and turbulence data were simply put into the context of measurements of optical target clarity, by placing a high-speed imaging camera and active optical target, an iPad displaying optical resolution charts, at opposite ends of the tank, providing a path length of around 5m and optical attenuation length exceeding 20 under different scattering conditions by particles and turbulence. In the case presented here, the tank was filled with filtered tap water and particle scattering is secondary to the changes in the IOR due to temperature microstructure. High-definition video of an optical chart across the tank was taken during experiments and the images were assessed for image degradation. The optical chart used was an image on an iPad screen, the camera was a Casio EXILIM EX-F1, and the videos were shot in High-Definition (HD), with 30fps and resolution 1920 by 1080pixels. Note that the ADV and PIV require seeding of the water in the tank to collect meaningful velocity data, which affects water clarity. Hence, the video frames shown here were taken immediately preceding the seeding of the water, but after the tank had reached a steady-state with respect to convective turbulence (Fig. 5). Note that the effect of optical turbulence is more pronounced at the higher spatial frequencies, as predicted by SUIM [11].

To quantify the extent of image degradation from optical turbulence, an image quality metric, namely the Structural Similarity Index Method (SSIM) was applied [18]. The SSIM measures the similarity between two images, where one is considered to be of “perfect quality”. Results from applying the SSIM metric to the images collected at the different turbulence strengths are shown in Fig. 5, which show increased degradation with stronger optical turbulence, i.e., higher Rayleigh number (Fig. 6).

## 3. Results

The SiTTE laboratory tank allows the variation of plate temperature for a wide range of temperature differences (ΔT = 2^{◦}C to ΔT = 16^{◦}C). We focus here on presenting results for two cases of turbulence strength. The lower strength turbulence, corresponding to Rayleigh number Ra = 1.5 ∙ 10^{10} and a temperature difference between the plates of ΔT = 6K and the extreme turbulence case with Ra = 4 ∙ 10^{10} with the highest temperature difference we can achieve in the tank ΔT = 16K.

The optical impacts of these turbulence strengths are shown in Figs. 5 and 6. This impact on the optics is due to the changes in the IOR due to local temperature variation associated with turbulence. Figure 7 shows the numerical model representation of these temperature fields. The numerical simulations provide complete three-dimensional fields of temperature and velocity and a view of the overall circulation in the tank. These data serve to supplement the sparse laboratory measurements and are also used to guide experimental setup, including sensor placement and selection of optical paths for various applications. The simulations clearly show that the flow is characterized by convective plumes and strong vertical overturning and mixing (Fig. 7). The size and number of the convective cells that develop in the tank are a function of the tank dimensions, in particular the tank height, since the water rises and sinks and gets diverted once it reaches the solid boundaries at the top and bottom. With a tank of depth d = 0.5m and length L = 5m, we observe on the order of ten convective cells in our domain. In addition to the convective cells, a secondary circulation, namely in the cross-sectional direction, develops in the domain. Streamlines indicate this overturning and associated circulation, updrafts on one side of the tank near the center and downdrafts on the opposing side. (Fig. 8). These circulations can be visually confirmed in the laboratory when adding a tracer to the fully developed flow field, such as, for example, the seeding material needed to collect ADV and PIV data.

The model temperature fields can be used to calculate the IOR from the empirical relation described in [19]. This then allows an estimate of the disturbance encountered by an optical beam passing through the tank. Figure 9 shows that the IOR variation closely tracks the convective plumes and turbulent eddies seen in the temperature and velocity fields. Cross-sections of temperature taken halfway along the tank (at x = 2.5m) and at successive times also illustrate the circulation and variability associated with this dynamic system (Fig. 10). While the velocities associated with the turbulent flow are small, the velocity magnitude is on the order of 2 cm/s (Figs. 8, 9), the overturning and eddying still appears vigorous in terms of temperature microstructure and IOR fields (Fig. 10).

Using the data from the numerical model to quantify how the turbulence varies across the tank cross-section, we estimate the turbulent kinetic energy dissipation rate ε by calculating the energy spectrum in wavenumber space from velocity sections along x at each y-z-position (Fig. 11). The value of ε stays mostly within one order of magnitude across the tank, although there is a difference of about a factor of two between the two turbulence strengths examined. The variation near the boundaries, which is due to boundary layer effects can be expected, and is consistent with the cross-sectional circulation seen in the velocity field. This estimate of ε from the model, O(10^{−7}W/kg), is consistent with the laboratory results (see below). The pronounced difference in the optics between the two turbulence cases, as seen in Figs. 5 and 6, is not as obvious in the velocity field and associated turbulence parameters. This is not unexpected given the low maximum velocities of only about 2 cm/s in magnitude, which corresponds to a rather benign turbulence level in terms of mechanical turbulence.

Data from PIV measurements confirm this finding and illustrate that the main difference is seen in the length scales of the turbulent eddies. The higher, “extreme”, turbulence case shows smaller scales and qualitatively, the flow “appears” more chaotic. Instantaneous snap shots of vertical velocity comparing model and PIV show that the model accurately captures the velocity magnitude and flow field. Figure 12 shows vertical velocity from the PIV data (left), and on the same color scale, the vertical velocity from the CFD model (right). The model accurately captures the overall flow appearance and velocity magnitude, although it appears more benign than the laboratory data, due to the increased resolution in the PIV data. The PIV data has a resolution of about 0.93mm, the model has a horizontal resolution of 5mm and a vertical resolution of 2.5mm. The Kolmogorov microscale, corresponding to the inner scale of turbulence in the context of optical turbulence, is on the order of 2-3mm for this flow. The results confirm that our model predicts the correct velocity magnitude and flow behavior for a cross-section in the tank.

Figure 13 shows the same vertical velocity cross sections for the lower turbulence case. Note that these are instantaneous comparisons, and since turbulence is strongly varying, we do not expect the instantaneous comparison to be exactly the same, but rather focus on the overall flow behavior and average statistics. The flow magnitudes between laboratory and model data are comparable, as are the overall flow dynamics. The PIV data show some noise near the boundary, and for this turbulence strength, the flow scales in the model appear well resolved. Overlaying velocity vectors from the PIV fields shown in Figs. 12 and 13 on contours of vorticity further help to visualize the flow structure (Fig. 14).

These data verify that the numerical model predicts the correct flow behavior and velocities in the tank. Thus verified, and in the absence of comprehensive temperature measurements in the laboratory, the model can provide temperature fields for the characterization of optical turbulence impacts and to guide experimental setup. Figure 15 shows the temperature fields for the area near the tank boundary (PIV field of view) as predicted by the numerical model. The range of temperature variation is larger for the higher turbulence case, and the scales of the turbulent eddies are smaller. This is reflected in the much stronger effect on the optics of the higher turbulence case.

Examples of point measurements of velocity using the Vectrino Profiler ADV are shown in Fig. 16. The instrument collects data of a 3cm profile of velocity in the tank. The orientation of the instrument in the laboratory tank is shown in Fig. 2, it was aligned with the along axis of the tank and towards the side of the tank at center height. Comparing data from the Vectrino Profiler for the two turbulence cases show that, consistent with the PIV and numerical data, the maximum velocity magnitudes are on the order of 2cm/s for both cases. The Vectrino data is shown for all nine points from the Vectrino Profiler, which cover a horizontal sampling volume of ~3cm. Comparing the laboratory data to output from the numerical model from a similar location in the tank reveals that the variability time scales and velocity magnitudes are similar. Note that the Vectrino data is collected at a sampling frequency of 100 Hz, whereas the model data is subsampled every 5s, due to the storage requirements for the extreme amount of data generated by the model. The model time step is Δt = 0.01s, and select cases have been saved at this sampling frequency of 100 Hz for direct comparison with the optics and optical models. Those results are beyond the scope of this paper and will be reported in a separate publication.

To quantify the mixing in the tank and to validate that the turbulence conforms to the classical Kolmogorov theory of turbulence, we calculated energy spectra and turbulent kinetic energy dissipation rates ε from point measurements of velocity and from PIV data. We also estimated temperature variance dissipation rates χ from point measurements of temperature collected with high-resolution thermistors in the laboratory tank. These values were then compared to ε and χ calculated from the numerical experiments.

The numerical data compared well to the laboratory data and both conformed to the Kolmogorov spectrum of turbulence and the Batchelor spectrum of temperature gradients (Fig. 17). Consistent with the model results shown in Fig. 11, the turbulent kinetic energy dissipation rate ε calculated from the laboratory data is on the order of O(10^{−7} W/kg) for the experiments shown, and the Vectrino measurements do not show an increase in ε for the extreme turbulence case. The corresponding PIV data agree well with the numerical model and appear to resolve the difference in ε between the two turbulence cases, despite the limited frequency resolution in the inertial subrange of the PIV data. The calculation of turbulent kinetic energy dissipation rates from PIV data is strongly resolution dependent, which can result in large errors when using underresolved velocity gradients to estimate ε. The estimation of ε is improved when using the spectral curvefit method presented here [20]. This method still requires that enough of the inertial subrange of the spectrum is resolved in the PIV data, which can be a severe limitation, but is mitigated in our results due to the availability of Vectrino data and numerical model results. The numerical model acts to complement the PIV data: where the model does not well resolve the higher frequency portion of the inertial subrange, the PIV underresolves the larger scales, combined, a complete picture of the turbulence spectrum emerges. This is illustrated in Fig. 17. The numerical model fully resolves the lower frequency portion of the inertial subrange (light blue line, top left panel), while the PIV resolves well the higher frequency portion of the inertial subrange (cyan line) Since the shape of the spectrum in the inertial subrange is well predicted by Kolmogorov’s theory, we can connect the portions of both spectra which have a clear −5/3 slope, and we find an excellent agreement between model and PIV data. The gap in the inertial subrange of the spectra combined from model and PIV, between wavenumbers k = 100 rad/m to k = 500 rad/m and corresponding to length scales of about 6cm to 1cm, can thus be bridged using turbulence theory. Note that PIV spectra have limited frequency resolution and the low frequency portion of the spectrum, even if close to a −5/3 slope, may be influenced by aliasing and is inherently not well resolved. For these spectra, it is the higher frequency portion that resolves the inertial subrange. Conversely in the numerical model, the spectral resolution drops off in the higher frequency range, due to limitations imposed by numerical resolution on the spectral calculation.

Optical experiments at SiTTE dictate that the turbulence be resolved with high spatial and temporal resolution and accuracy. It is important to note in this context, that LES modeling explicitly resolves scales larger than the grid scale, while only the scales smaller than the grid size are parameterized. For grid resolutions close to that of the Kolmogorov microscale, as in the case presented here, this means that a significant portion of the inertial subrange of the energy spectrum is well resolved and that scales closer to the dissipative range of the turbulence spectrum are contained within the turbulence parameterization. This is also apparent in Fig. 17, where it is shown that the lower wavenumber portion of the inertial subrange is well resolved in the model. This resolution is sufficient for a robust estimate of the turbulence kinetic energy dissipation rate ε and, most importantly, the general flow characteristics of the turbulence. Increasing the model resolution to resolve the inertial subrange down the Kolmogorov microscale and beyond is close to computationally prohibitive for a domain size encompassing the entire tank and will have to be achieved by using subsets of the domain setup presented here. Despite resolution limitations inherent to the various methods and typical of the characterization of turbulent flow, our results show that both the large-scale and details of the flow and significant portions of the turbulence spectrum are very well characterized in our setup using various laboratory measurements and a high-resolution numerical model.

Calculating the temperature variance dissipation rate χ from both the laboratory and the numerical simulations also show a difference for different convective turbulence strengths. Since this method uses temperature gradient spectra to calculate χ, the estimates from the numerical simulations are strongly resolution dependent and, as indicated above, the numerical simulations do not fully resolve the smallest gradients and thus underestimate χ, when looking at model spectra alone. The model spectra conform to theory and follow well the theoretical Batchelor spectrum (Fig. 17), as well as the Kolmogorov spectrum of turbulence for a scalar (not shown). When combining the low-wavenumber portion of the model spectra with theory and laboratory measurements, the correct temperature variance dissipation rate can be inferred (Fig. 17, left bottom panel). The spectra also show that the larger scales and thus the three-dimensional temperature fields needed for the estimation of phase screens and IOR variations to study optical beam behavior are well resolved in the model.

## 4. Discussion

It has been shown that optical turbulence can be a limiting factor for EO signal propagation in the ocean. To provide a platform, where repeatable, controlled conditions can be realized, we developed and validated a unique setup, the Simulated Turbulence and Turbidity Environment (SiTTE). SiTTE combines a laboratory tank, turbulence measurements and high-resolution numerical simulations to provide a controlled turbulence environment in which to study the processes involved in optical turbulence. The goal was to develop an environment where turbulence levels can be controlled and fully characterized. This setup, which allows for repeatable experiments under precise conditions, provides an ideal platform for the testing of optical techniques to mitigate turbulence effects underwater.

To characterize the turbulence for various optical turbulence strengths, for subsequent use in studies investigating optical impacts, we performed experiments in the large Rayleigh-Bénard convective tank at SiTTE and complemented the laboratory data with numerical simulations using computational fluid dynamics.

The numerical model was able to accurately reproduce the turbulence fields observed in the laboratory tank. Quantitatively, the numerical simulations are consistent with the observed turbulent kinetic energy dissipation rate ε and temperature variance dissipation rate χ in the tank. The comprehensive fields from the numerical model can be used to calculate the variation in IOR along the tank and thus provide an estimate of the effect on an optical beam traversing the turbulence tank. This can be achieved through the use of phase-screen or other optical models and is the subject of ongoing work.

The laboratory and numerical data show that even for convective strength with dramatically different impact on the optics, the turbulent kinetic energy dissipation rates ε in the tank show only small changes. Since the effect on the optics is driven by changes in the IOR due to temperature variations, these results emphasize the importance of characterizing in detail the temperature distribution to assess the impact of the turbulent fluctuations on the optics, in addition to characterizing turbulence in terms of turbulent kinetic energy dissipation rate and the Kolmogorov spectrum.

Thus, it is particularly critical to accurately resolve the temperature fields. This can present a challenge in both the laboratory and the model, due to noise and resolution requirements, respectively. We show that in our setup, the temperature variance dissipation rates needed to calculate C_{n}^{2} are well characterized in the laboratory through the use of high-resolution thermistors, while the larger scale temperature fields and eddying flow characteristics can be described through the use of the high-resolution LES model, which has been verified with PIV data. The results and setup presented in this paper hence provide a detailed characterization of a unique controlled turbulence environment, which has the necessary resolution to assess the impact of Kolmogorov-type turbulence on underwater optics. This impact can be characterized through estimation of C_{n}^{2} using ε and χ from both laboratory data and numerical model, as well as through the use of phase screens from the numerical model.

Further work is ongoing to characterize the temperature fields in the tank down to the smallest gradients using increased model resolution and next-generation high-resolution fiber optics sensors [21, 22], as well as studying optical beam propagation using phase screens [23].

Our unique approach of integrating turbulence measurements using a suite of state-of-the-art sensors with computational fluid dynamics, which results in a controlled environment for the study of optical turbulence, can help advance our understanding of the processes involved in optical turbulence in ocean and atmosphere, provide guidance on how to mitigate the effects of turbulence impacts on underwater optical signal transmission, as well as on the use of optical techniques to probe oceanic processes.

## Funding

This project was supported by ONR/NRL base programs 73-4951/73-6892/73-1C04/73-1G38. Silvia Matt was in part supported by a National Research Council (NRC) Research Associateship and a Naval Research Laboratory Karles Fellowship.

## Acknowledgments

Numerical simulations were performed on resources provided by the Department of Defense Supercomputing Resource Centers operated by the DoD High Performance Computing Modernization Program. Katherine Simmers (SEAP) helped with 3D model visualizations. We thank Dr. Gero Nootz (NRC Postdoc at NRL) for help with the setup of PIV lab experiments. We also thank Drs. Danielle Wain, Cynthia Bluteau and Barry Ruddick for sharing their data processing routines. Dr. Sarah Woods contributed to the tank design and early instrumental setup. We are grateful to Dr. Joe Calantoni for allowing us the use of his Vectrino II instrument during exploratory experiments. Finally, we thank two anonymous reviewers for their comments, which improved the manuscript.

## References

**1. **G. D. Gilbert and R. C. Honey, “Optical turbulence in the sea,” Proc. SPIE **0024**, 49–56 (1971). [CrossRef]

**2. **D. J. Bogucki, J. A. Domaradzki, R. E. Ecke, and C. R. Truman, “Light scattering on oceanic turbulence,” Appl. Opt. **43**(30), 5662–5668 (2004). [CrossRef] [PubMed]

**3. **S. Matt, W. Hou, S. Woods, W. Goode, E. Jarosz, and A. Weidemann, “A novel platform to study the effect of small-scale turbulent density fluctuations on underwater imaging in the ocean,” Methods Oceanography **11**, 39–58 (2014). [CrossRef]

**4. **G. Nootz, E. Jarosz, F. R. Dalgleish, and W. Hou, “Quantification of optical turbulence in the ocean and its effects on beam propagation,” Appl. Opt. **55**(31), 8813–8820 (2016). [CrossRef] [PubMed]

**5. **W. Hou, S. Woods, E. Jarosz, W. Goode, and A. Weidemann, “Optical turbulence on underwater image degradation in natural environments,” Appl. Opt. **51**(14), 2678–2686 (2012). [CrossRef] [PubMed]

**6. **S. Matt, W. Hou, and W. Goode, “The impact of turbulent fluctuations on light propagation in a controlled environment,” Proc. SPIE **9111**, 911113 (2014).

**7. **H. Tennekes and J. L. Lumley, *A First Course in Turbulence* (MIT Press, 1972).

**8. **C. E. Bluteau, N. L. Jones, and G. N. Ivey, “Estimating turbulent kinetic energy dissipation using the inertial subrange method in environmental flows,” Limnol. Oceanogr. Methods **9**(7), 302–321 (2011). [CrossRef]

**9. **B. Ruddick, A. Anis, and K. Thompson, “Maximum likelihood spectral fitting: The Batchelor spectrum,” J. Atmos. Ocean. Technol. **17**(11), 1541–1555 (2000). [CrossRef]

**10. **J. Moum and J. Nash, “Mixing measurements on an equatorial ocean mooring,” J. Atmos. Ocean. Technol. **26**(2), 317–336 (2009). [CrossRef]

**11. **W. Hou, “A simple underwater imaging model,” Opt. Lett. **34**(17), 2688–2690 (2009). [CrossRef] [PubMed]

**12. **M. C. Roggemann and B. M. Welsh, *Imaging through Turbulence* (CRC Press, 1996).

**13. **S. Matt, W. Hou, W. Goode, and S. Hellman, “Velocity fields and optical turbulence near the boundary in a strongly convective laboratory flow,” Proc. SPIE **9827**, 98270F (2016).

**14. **P. Sagaut, *Large Eddy Simulation for Incompressible Flows* (Springer, 1998).

**15. **J. Smagorinsky, “General circulation experiments with the primitive equations. I. The basic experiment,” Month. Wea. Rev. **91**(3), 99–164 (1963). [CrossRef]

**16. **A. V. Kanaev, W. Hou, S. R. Restaino, S. Matt, and S. Gładysz, “Restoration of images degraded by underwater turbulence using structure tensor oriented image quality (STOIQ) metric,” Opt. Express **23**(13), 17077–17090 (2015). [CrossRef] [PubMed]

**17. **A. Kanaev, S. Gladysz, R. Almeida de Sá Barros, S. Matt, G. Nootz, D. Josset, and W. Hou, “Measurements of optical underwater turbulence under controlled conditions,” Proc. SPIE **9827**, 982705 (2016).

**18. **Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. **13**(4), 600–612 (2004). [CrossRef] [PubMed]

**19. **X. Quan and E. S. Fry, “Empirical equation for the index of refraction of seawater,” Appl. Opt. **34**(18), 3477–3480 (1995). [CrossRef] [PubMed]

**20. **D. Xu and J. Chen, “Accurate estimate of turbulent dissipation rate using PIV data,” Exp. Therm. Fluid Sci. **44**, 662–672 (2013). [CrossRef]

**21. **S. Matt, W. Hou, W. Goode, G. Liu, M. Han, A. Kanaev, and S. Restaino, “A controlled laboratory environment to study EO signal degradation due to underwater turbulence,” Proc. SPIE **9459**, 94590H (2015).

**22. **G. Liu, Q. Sheng, W. Hou, and M. Han, “Influence of fiber bending on wavelength demodulation of fiber-optic Fabry-Perot interferometric sensors,” Opt. Express **24**(23), 26732–26744 (2016). [CrossRef] [PubMed]

**23. **G. Nootz, NRC Research Associate at Naval Research Laboratory, 1009 Balch Blvd., Stennis Space Center, MS 39529, USA, and S. Matt, W. Hou and A. Kanaev are preparing a manuscript to be called ” Experimental and numerical study of underwater beam propagation in a Rayleigh–Bénard turbulence tank.”