Simulation study on light propagation in an isotropic turbulence field of the mixed layer Renmin Yuan,1,* Jianning Sun,2 Tao Luo,1 Xuping Wu,1,3 Chen Wang,1 and Chao Lu1,4 1

Key Laboratory of the Atmospheric Composition and Optical Radiation, CAS, School of Earth and Space Sciences, University of Science and Technology of China, Anhui, 230026, China 2 School of Atmospheric Sciences, Nanjing University, Jiangsu, 210093, China 3 School of Mathematics and Physics, Anhui Jianzhu University, Anhui, 230601, China 4 Shenzhen National Climate Observatory, Guangdong, 518040, China * [email protected]

Abstract: Water tank experiments and numerical simulations are employed to investigate the characteristics of light propagation in the convective boundary layer (CBL). The CBL, namely the mixed layer (ML), was simulated in the water tank. A laser beam was set to horizontally go through the water tank, and the image of two-dimensional (2D) light intensity fluctuation formed on the receiving plate perpendicular to the light path was recorded by CCD. The spatial spectra of both horizontal and vertical light intensity fluctuations were analyzed, and the vertical distribution profile of the scintillation index (SI) in the ML was obtained. The experimental results indicate that 2D light intensity fluctuation was isotropically distributed in the cross section perpendicular to the light beam in the ML. Based on the measured temperature fluctuations along the light path at different heights, together with the relationship between temperature and refractive index, the refractive index fluctuation spectra and the corresponding turbulence parameters were derived. The obtained parameters were applied in a numerical model to simulate light propagation in the isotropic turbulence field. The calculated results successfully reproduce the characteristics of light intensity fluctuation observed in the experiments. ©2014 Optical Society of America OCIS codes: (010.1300) Atmospheric propagation; (010.1330) Atmospheric turbulence.

References and links 1. 2. 3. 4.

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961). R. J. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88(03), 541–562 (1978). L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE, 2005). J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, and F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21(6), 929–948 (1986). 5. L. Y. Cui, B. D. Xue, X. G. Cao, J. K. Dong, and J. N. Wang, “Generalized atmospheric turbulence MTF for wave propagating through non-Kolmogorov turbulence,” Opt. Express 18(20), 21269–21283 (2010). 6. R. Z. Rao, S. P. Wang, X. C. Liu, and Z. B. Gong, “Turbulence spectrum effect on wave temporal-frequency spectra for light propagating through the atmosphere,” J. Opt. Soc. Am. A 16(11), 2755–2762 (1999). 7. R. B. Stull, An Introduction to Boundary Layer Meteorology (Kluwer Academic, 1988). 8. M. Kelly and J. C. Wyngaard, “Two-dimensional spectra in the atmospheric boundary layer,” J. Atmos. Sci. 63(11), 3066–3070 (2006). 9. R. J. Hill, “Review of optical scintillation methods of measuring the refractive-index spectrum, inner scale and surface fluxes,” Waves Random Media 2(3), 179–201 (1992). 10. D. Peng, Y. Xiuhua, Z. Yanan, Z. Ming, and L. Hanjun, “Influence of wind speed on free space optical communication performance for Gaussian beam propagation through non Kolmogorov strong turbulence,” J. Phys. Conf. Ser. 276, 012056 (2011). 11. F. Beyrich, J. Bange, O. K. Hartogensis, S. Raasch, M. Braam, D. van Dinther, D. Graef, B. van Kesteren, A. C. van den Kroonenberg, B. Maronga, S. Martin, and A. F. Moene, “Towards a validation of scintillometer measurements: the LITFASS-2009 Experiment,” Boundary Layer Meteorol. 144, 83–112 (2012). 12. J. W. Deardorff, G. E. Willis, and B. H. Stockton, “Laboratory studies of the entrainment zone of a convectively mixed layer,” J. Fluid Mech. 100(01), 41–64 (1980).

#206000 - $15.00 USD (C) 2014 OSA

Received 6 Feb 2014; revised 2 Mar 2014; accepted 10 Mar 2014; published 19 Mar 2014 24 March 2014 | Vol. 22, No. 6 | DOI:10.1364/OE.22.007194 | OPTICS EXPRESS 7194

13. M. F. Hibberd and B. L. Sawford, “Design criteria for water tank models of dispersion in the planetary convective boundary-layer,” Boundary Layer Meteorol. 67, 97–118 (1994). 14. R. Yuan, X. Wu, T. Luo, H. Liu, and J. Sun, “A review of water tank modeling of the convective atmospheric boundary layer,” J. Wind Eng. Ind. Aerodyn. 99(10), 1099–1114 (2011). 15. A. S. Gurvich, M. A. Kallistratova, and F. E. Martvel, “An investigation of strong fluctuations of light intensity in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20(7), 705–714 (1977). 16. V. A. Kulikov, M. S. Andreeva, A. V. e. Koryabin, and V. I. Shmalhausen, “Method of estimation of turbulence characteristic scales,” Appl. Opt. 51(36), 8505–8515 (2012). 17. A. Maccioni and J. C. Dainty, “Measurement of thermally induced optical turbulence in a water cell,” J. Mod. Opt. 44(6), 1111–1126 (1997). 18. J. Zhang and Z. Y. Zeng, “Statistical properties of optical turbulence in a convective tank: experimental results,” J. Opt. 3(4), 236–241 (2001). 19. Z. B. Gong, Y. J. Wang, and Y. Wu, “Finite temporal measurements of the statistical characteristics of the atmospheric coherence length,” Appl. Opt. 37(21), 4541–4543 (1998). 20. R. Yuan, School of Earth and Space Sciences, University of Science and Technology of China, Anhui, 230026, China, and J. Sun are preparing a manuscript to be called ” Simulation study on light propagation in an anisotropic turbulence field of the entrainment zone.” 21. G. K. Batchelor, “Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity,” J. Fluid Mech. 5(01), 113–133 (1959). 22. R. J. Hill and S. F. Clifford, “Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation,” J. Opt. Soc. Am. A 68(7), 892–899 (1978). 23. C. H. Gibson and W. H. Schwarz, “The universal equilibrium spectra of turbulent velocity and scalar fields,” J. Fluid Mech. 16(03), 365–384 (1963). 24. H. L. Grant, B. A. Hughes, W. M. Vogel, and A. Moilliet, “The spectrum of temperature fluctuations in turbulent flow,” J. Fluid Mech. 34(03), 423–442 (1968). 25. H. M. Dobbins and E. R. Peck, “Change of refractive index of water as a function of temperature,” J. Opt. Soc. Am. A 63(3), 318–320 (1973). 26. R. Frehlich, “Effects of global intermittency on laser propagation in the atmosphere,” Appl. Opt. 33(24), 5764–5769 (1994). 27. R. J. Hill and J. H. Churnside, “Observational challenges of strong scintillations of irradiance,” J. Opt. Soc. Am. A 5(3), 445–447 (1988). 28. J. M. Martin and S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27(11), 2111–2126 (1988). 29. S. J. Caughey and S. G. Palmer, “Some aspects of turbulence structure through the depth of the convective boundary layer,” Q. J. R. Meteorol. Soc. 105(446), 811–827 (1979). 30. R. Yuan, J. Sun, K. Yao, Z. Zeng, and W. Jiang, “A laboratory simulation of the atmospheric boundary layer analyses of temperature structure in the entrainment zone,” Chin. J. Atmos. Sci. 26, 773–780 (2002). 31. J. C. Kaimal, J. C. Wyngaard, D. A. Haugen, O. R. Cote, Y. Izumi, S. J. Caughey, and C. J. Readings, “Turbulence structure in convective boundary-layer,” J. Atmos. Sci. 33(11), 2152–2169 (1976). 32. F. Beyrich and S. E. Gryning, “Estimation of the entrainment zone depth in a shallow convective boundary layer from sodar data,” J. Appl. Meteorol. Climatol. 37(3), 255–268 (1998). 33. T. Luo, R. Yuan, X. Wu, and S. Deng, “A new parameterization of temperature structure parameter in entraining convective boundary layer,” Opt. Commun. 281(23), 5683–5686 (2008). 34. P. Stoica and R. L. Moses, Introduction to Spectral Analysis (Prentice-Hall, 1997).

1. Introduction Theoretically, two-dimensional (2D) or three-dimensional (3D) spectra are usually adopted to describe the behavior of light propagation in turbulent mediums, for example, the refractive index spectra for weak-fluctuation [1], the precise spectra model [2], and von Karman spectral form of refractive index fluctuation spectra [3]. Based on the turbulent medium wave propagation equation, Tatarskii deduced the 2D expressions of light intensity and phase spectra in the cross-section perpendicular to the light path under weak-fluctuation conditions [1]. Under strong fluctuation conditions, theoretical expressions for high-frequency and low-frequency parts of light intensity fluctuation are also written in 2D form [4]. Recently, theoretical studies tend to describe light propagation in non-Kolmgorov turbulence in the form of 2D or 3D spectra [5]. However, experimental measurements are usually carried out at one fixed position to obtain the time series of temperature fluctuation (which can be converted to refractive index fluctuation) or light scintillation [6]. The one-dimensional (1D) spatial series can be derived from the time series based on the Taylor Frozen Hypothesis [7]. And the 2D and 3D spectra are usually generated under the isotropy assumption [8].

#206000 - $15.00 USD (C) 2014 OSA

Received 6 Feb 2014; revised 2 Mar 2014; accepted 10 Mar 2014; published 19 Mar 2014 24 March 2014 | Vol. 22, No. 6 | DOI:10.1364/OE.22.007194 | OPTICS EXPRESS 7195

Several key parameters, such as the structure constant, inner-scale, and outer-scale of turbulence, which are closely related to characteristics of 3D spectra, are needed to describe the behavior of light propagation. These parameters are usually obtained under the assumption of isotropy and via a series of time-space conversion [9, 10]. Based on this assumption, Large Aperture Scintillometers (LAS) have been widely used to measure the heat flux and the wind speed [9, 11]. For the 2D distributions of light intensity, if the real 2D fluctuations are measured by experiments, we can directly compare them with the theoretical 2D distributions of light intensity and then obtain the required parameters by spectra analysis. Light propagation experiments are usually conducted in the atmosphere boundary layer (ABL) where atmospheric turbulent flows mainly happen. The ABL is located in the lowest part of the troposphere, overlying the earth’s surface. One of the most important features of the ABL is that it is always turbulent. Turbulence is usually generated by convection in the daytime, so the ABL with convection is often called the convective boundary layer (CBL) and the turbulent convection results in a nearly homogeneous mixed layer (ML) [7]. Optical waves propagating in the ABL must be influenced by turbulence and there are therefore turbulent effects, such as beam drift, flickering and jittering. Limited by measurement methods and observation conditions, so far such research is mostly carried out in the near-surface layer and it is very difficult to expand to the whole ABL. That is why water tank experiments are often used to study the fundamental characteristics of turbulent flows in the ABL. According to similarity theory, water tank experiments can be used to study the dynamics of origination and development of the ABL and the behavior of turbulence in the real ABL [12–14]. The water-tank experiments are also suitable for studying the effects of turbulence on light propagation. For example, they are used to investigate the characteristics of light intensity distributions under strong-fluctuation conditions [15], and to estimate the inner scale [16–18] and the coherent length [19] of turbulence by measuring the arrival-angle fluctuation of light. However, in the previous studies, the measurements usually merely provide time series of light signals, and the turbulence field is usually set to be steady. That is to say, the results in the previous works are usually obtained under ideal conditions. The advantage of the water-tank experiment in this study is that the 2D distribution of light intensity fluctuation can be obtained, which can help us determine whether the turbulence is isotropic or not. Further, the results are more convincing for evaluating the suitability of theoretical descriptions of light propagation in the real atmosphere. In this paper, we attempt to analyze the characteristics of 2D light intensity distributions by water tank experiments. The laser beam transmitted from a collimated light system was set to pass through the simulated ML and created the image with fluctuating intensity on the receiving screen. The CCDs serve to record the 2D gray-scale images which are proportional to the light intensity. Meanwhile, numerical methods were used to study the characteristics of light propagation in turbulent mediums. Images of 2D light intensity fluctuations were obtained to compare and verify with water tank observations. In fact, water tank experiments can effectively simulate the different characteristics of the ML and the entrainment zone (EZ). We pay great attention to the turbulence features and features of spatial light scintillation spectra in the mixed layer in this paper, and leave it to another paper to discuss those in the EZ [20]. The paper is organized as follows. In Section 2, we will introduce the theoretical models of turbulence spectra and light intensity fluctuation spectra. Section 3 presents the set-up of the water tank simulations and the relevant experimental measurements. Numerical simulation methods are presented in Section 4. Section 5 gives the results of the experiments; Section 6 presents conclusions. 2. Theory In this section, we will introduce the formula for turbulence spectra in the water, and light intensity fluctuation spectra of a plane wave after it propagates in a turbulent medium for some distance.

#206000 - $15.00 USD (C) 2014 OSA

Received 6 Feb 2014; revised 2 Mar 2014; accepted 10 Mar 2014; published 19 Mar 2014 24 March 2014 | Vol. 22, No. 6 | DOI:10.1364/OE.22.007194 | OPTICS EXPRESS 7196

2.1 Turbulence spectra in water The temperature spectrum in water has been given by Batchelor [15, 21],

Φ T (κ ) = K (α )CT2κ −α −2ϕT (κ ) where T denotes temperature, κ is the wavenumber, α is named Γ(α + 1) π K (α ) = sin[(α − 1) ] . When turbulent flows satisfy the 2 4π 2 homogeneous isotropy and the power-law α of turbulence spectrum equals 5/3, K (α ) = 0.033 . CT2 is the temperature structure constant.

(1) spectral power-law, hypothesis of local in the inertial range In order to describe

temperature fluctuations in dissipation range, a component Cn2 ≠ 0 is introduced into Eq. (1). The values of ϕT (κ ) vary from the convective inertial range ( κ

Simulation study on light propagation in an isotropic turbulence field of the mixed layer.

Water tank experiments and numerical simulations are employed to investigate the characteristics of light propagation in the convective boundary layer...
2MB Sizes 0 Downloads 3 Views