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

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2012 (2)

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, A. F. Moene, “Towards a validation of scintillometer measurements: the LITFASS-2009 Experiment,” Boundary Layer Meteorol. 144, 83–112 (2012).

V. A. Kulikov, M. S. Andreeva, A. V. e. Koryabin, V. I. Shmalhausen, “Method of estimation of turbulence characteristic scales,” Appl. Opt. 51(36), 8505–8515 (2012).
[CrossRef] [PubMed]

2011 (2)

D. Peng, Y. Xiuhua, Z. Yanan, Z. Ming, 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).

R. Yuan, X. Wu, T. Luo, H. Liu, J. Sun, “A review of water tank modeling of the convective atmospheric boundary layer,” J. Wind Eng. Ind. Aerodyn. 99(10), 1099–1114 (2011).
[CrossRef]

2010 (1)

2008 (1)

T. Luo, R. Yuan, X. Wu, S. Deng, “A new parameterization of temperature structure parameter in entraining convective boundary layer,” Opt. Commun. 281(23), 5683–5686 (2008).
[CrossRef]

2006 (1)

M. Kelly, J. C. Wyngaard, “Two-dimensional spectra in the atmospheric boundary layer,” J. Atmos. Sci. 63(11), 3066–3070 (2006).
[CrossRef]

2002 (1)

R. Yuan, J. Sun, K. Yao, Z. Zeng, 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).

2001 (1)

J. Zhang, Z. Y. Zeng, “Statistical properties of optical turbulence in a convective tank: experimental results,” J. Opt. 3(4), 236–241 (2001).
[CrossRef]

1999 (1)

1998 (2)

Z. B. Gong, Y. J. Wang, Y. Wu, “Finite temporal measurements of the statistical characteristics of the atmospheric coherence length,” Appl. Opt. 37(21), 4541–4543 (1998).
[CrossRef] [PubMed]

F. Beyrich, 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).
[CrossRef]

1997 (1)

A. Maccioni, J. C. Dainty, “Measurement of thermally induced optical turbulence in a water cell,” J. Mod. Opt. 44(6), 1111–1126 (1997).
[CrossRef]

1994 (2)

M. F. Hibberd, B. L. Sawford, “Design criteria for water tank models of dispersion in the planetary convective boundary-layer,” Boundary Layer Meteorol. 67, 97–118 (1994).

R. Frehlich, “Effects of global intermittency on laser propagation in the atmosphere,” Appl. Opt. 33(24), 5764–5769 (1994).
[CrossRef] [PubMed]

1992 (1)

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).
[CrossRef]

1988 (2)

1986 (1)

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21(6), 929–948 (1986).
[CrossRef]

1980 (1)

J. W. Deardorff, G. E. Willis, B. H. Stockton, “Laboratory studies of the entrainment zone of a convectively mixed layer,” J. Fluid Mech. 100(01), 41–64 (1980).
[CrossRef]

1979 (1)

S. J. Caughey, 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).
[CrossRef]

1978 (2)

R. J. Hill, 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).
[CrossRef]

R. J. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88(03), 541–562 (1978).
[CrossRef]

1977 (1)

A. S. Gurvich, M. A. Kallistratova, 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).
[CrossRef]

1976 (1)

J. C. Kaimal, J. C. Wyngaard, D. A. Haugen, O. R. Cote, Y. Izumi, S. J. Caughey, C. J. Readings, “Turbulence structure in convective boundary-layer,” J. Atmos. Sci. 33(11), 2152–2169 (1976).
[CrossRef]

1973 (1)

H. M. Dobbins, E. R. Peck, “Change of refractive index of water as a function of temperature,” J. Opt. Soc. Am. A 63(3), 318–320 (1973).
[CrossRef]

1968 (1)

H. L. Grant, B. A. Hughes, W. M. Vogel, A. Moilliet, “The spectrum of temperature fluctuations in turbulent flow,” J. Fluid Mech. 34(03), 423–442 (1968).
[CrossRef]

1963 (1)

C. H. Gibson, W. H. Schwarz, “The universal equilibrium spectra of turbulent velocity and scalar fields,” J. Fluid Mech. 16(03), 365–384 (1963).
[CrossRef]

1959 (1)

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).
[CrossRef]

Andreeva, M. S.

Bange, J.

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, A. F. Moene, “Towards a validation of scintillometer measurements: the LITFASS-2009 Experiment,” Boundary Layer Meteorol. 144, 83–112 (2012).

Batchelor, G. K.

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).
[CrossRef]

Beyrich, F.

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, A. F. Moene, “Towards a validation of scintillometer measurements: the LITFASS-2009 Experiment,” Boundary Layer Meteorol. 144, 83–112 (2012).

F. Beyrich, 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).
[CrossRef]

Braam, M.

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, A. F. Moene, “Towards a validation of scintillometer measurements: the LITFASS-2009 Experiment,” Boundary Layer Meteorol. 144, 83–112 (2012).

Cao, X. G.

Caughey, S. J.

S. J. Caughey, 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).
[CrossRef]

J. C. Kaimal, J. C. Wyngaard, D. A. Haugen, O. R. Cote, Y. Izumi, S. J. Caughey, C. J. Readings, “Turbulence structure in convective boundary-layer,” J. Atmos. Sci. 33(11), 2152–2169 (1976).
[CrossRef]

Churnside, J. H.

Clifford, S. F.

R. J. Hill, 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).
[CrossRef]

Codona, J. L.

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21(6), 929–948 (1986).
[CrossRef]

Cote, O. R.

J. C. Kaimal, J. C. Wyngaard, D. A. Haugen, O. R. Cote, Y. Izumi, S. J. Caughey, C. J. Readings, “Turbulence structure in convective boundary-layer,” J. Atmos. Sci. 33(11), 2152–2169 (1976).
[CrossRef]

Creamer, D. B.

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21(6), 929–948 (1986).
[CrossRef]

Cui, L. Y.

Dainty, J. C.

A. Maccioni, J. C. Dainty, “Measurement of thermally induced optical turbulence in a water cell,” J. Mod. Opt. 44(6), 1111–1126 (1997).
[CrossRef]

Deardorff, J. W.

J. W. Deardorff, G. E. Willis, B. H. Stockton, “Laboratory studies of the entrainment zone of a convectively mixed layer,” J. Fluid Mech. 100(01), 41–64 (1980).
[CrossRef]

Deng, S.

T. Luo, R. Yuan, X. Wu, S. Deng, “A new parameterization of temperature structure parameter in entraining convective boundary layer,” Opt. Commun. 281(23), 5683–5686 (2008).
[CrossRef]

Dobbins, H. M.

H. M. Dobbins, E. R. Peck, “Change of refractive index of water as a function of temperature,” J. Opt. Soc. Am. A 63(3), 318–320 (1973).
[CrossRef]

Dong, J. K.

Flatte, S. M.

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21(6), 929–948 (1986).
[CrossRef]

Flatté, S. M.

Frehlich, R.

Frehlich, R. G.

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21(6), 929–948 (1986).
[CrossRef]

Gibson, C. H.

C. H. Gibson, W. H. Schwarz, “The universal equilibrium spectra of turbulent velocity and scalar fields,” J. Fluid Mech. 16(03), 365–384 (1963).
[CrossRef]

Gong, Z. B.

Graef, D.

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, A. F. Moene, “Towards a validation of scintillometer measurements: the LITFASS-2009 Experiment,” Boundary Layer Meteorol. 144, 83–112 (2012).

Grant, H. L.

H. L. Grant, B. A. Hughes, W. M. Vogel, A. Moilliet, “The spectrum of temperature fluctuations in turbulent flow,” J. Fluid Mech. 34(03), 423–442 (1968).
[CrossRef]

Gryning, S. E.

F. Beyrich, 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).
[CrossRef]

Gurvich, A. S.

A. S. Gurvich, M. A. Kallistratova, 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).
[CrossRef]

Hanjun, L.

D. Peng, Y. Xiuhua, Z. Yanan, Z. Ming, 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).

Hartogensis, O. K.

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, A. F. Moene, “Towards a validation of scintillometer measurements: the LITFASS-2009 Experiment,” Boundary Layer Meteorol. 144, 83–112 (2012).

Haugen, D. A.

J. C. Kaimal, J. C. Wyngaard, D. A. Haugen, O. R. Cote, Y. Izumi, S. J. Caughey, C. J. Readings, “Turbulence structure in convective boundary-layer,” J. Atmos. Sci. 33(11), 2152–2169 (1976).
[CrossRef]

Henyey, F. S.

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21(6), 929–948 (1986).
[CrossRef]

Hibberd, M. F.

M. F. Hibberd, B. L. Sawford, “Design criteria for water tank models of dispersion in the planetary convective boundary-layer,” Boundary Layer Meteorol. 67, 97–118 (1994).

Hill, R. J.

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).
[CrossRef]

R. J. Hill, J. H. Churnside, “Observational challenges of strong scintillations of irradiance,” J. Opt. Soc. Am. A 5(3), 445–447 (1988).
[CrossRef]

R. J. Hill, 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).
[CrossRef]

R. J. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88(03), 541–562 (1978).
[CrossRef]

Hughes, B. A.

H. L. Grant, B. A. Hughes, W. M. Vogel, A. Moilliet, “The spectrum of temperature fluctuations in turbulent flow,” J. Fluid Mech. 34(03), 423–442 (1968).
[CrossRef]

Izumi, Y.

J. C. Kaimal, J. C. Wyngaard, D. A. Haugen, O. R. Cote, Y. Izumi, S. J. Caughey, C. J. Readings, “Turbulence structure in convective boundary-layer,” J. Atmos. Sci. 33(11), 2152–2169 (1976).
[CrossRef]

Jiang, W.

R. Yuan, J. Sun, K. Yao, Z. Zeng, 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).

Kaimal, J. C.

J. C. Kaimal, J. C. Wyngaard, D. A. Haugen, O. R. Cote, Y. Izumi, S. J. Caughey, C. J. Readings, “Turbulence structure in convective boundary-layer,” J. Atmos. Sci. 33(11), 2152–2169 (1976).
[CrossRef]

Kallistratova, M. A.

A. S. Gurvich, M. A. Kallistratova, 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).
[CrossRef]

Kelly, M.

M. Kelly, J. C. Wyngaard, “Two-dimensional spectra in the atmospheric boundary layer,” J. Atmos. Sci. 63(11), 3066–3070 (2006).
[CrossRef]

Koryabin, A. V. e.

Kulikov, V. A.

Liu, H.

R. Yuan, X. Wu, T. Luo, H. Liu, J. Sun, “A review of water tank modeling of the convective atmospheric boundary layer,” J. Wind Eng. Ind. Aerodyn. 99(10), 1099–1114 (2011).
[CrossRef]

Liu, X. C.

Luo, T.

R. Yuan, X. Wu, T. Luo, H. Liu, J. Sun, “A review of water tank modeling of the convective atmospheric boundary layer,” J. Wind Eng. Ind. Aerodyn. 99(10), 1099–1114 (2011).
[CrossRef]

T. Luo, R. Yuan, X. Wu, S. Deng, “A new parameterization of temperature structure parameter in entraining convective boundary layer,” Opt. Commun. 281(23), 5683–5686 (2008).
[CrossRef]

Maccioni, A.

A. Maccioni, J. C. Dainty, “Measurement of thermally induced optical turbulence in a water cell,” J. Mod. Opt. 44(6), 1111–1126 (1997).
[CrossRef]

Maronga, B.

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, A. F. Moene, “Towards a validation of scintillometer measurements: the LITFASS-2009 Experiment,” Boundary Layer Meteorol. 144, 83–112 (2012).

Martin, J. M.

Martin, S.

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, A. F. Moene, “Towards a validation of scintillometer measurements: the LITFASS-2009 Experiment,” Boundary Layer Meteorol. 144, 83–112 (2012).

Martvel, F. E.

A. S. Gurvich, M. A. Kallistratova, 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).
[CrossRef]

Ming, Z.

D. Peng, Y. Xiuhua, Z. Yanan, Z. Ming, 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).

Moene, A. F.

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, A. F. Moene, “Towards a validation of scintillometer measurements: the LITFASS-2009 Experiment,” Boundary Layer Meteorol. 144, 83–112 (2012).

Moilliet, A.

H. L. Grant, B. A. Hughes, W. M. Vogel, A. Moilliet, “The spectrum of temperature fluctuations in turbulent flow,” J. Fluid Mech. 34(03), 423–442 (1968).
[CrossRef]

Palmer, S. G.

S. J. Caughey, 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).
[CrossRef]

Peck, E. R.

H. M. Dobbins, E. R. Peck, “Change of refractive index of water as a function of temperature,” J. Opt. Soc. Am. A 63(3), 318–320 (1973).
[CrossRef]

Peng, D.

D. Peng, Y. Xiuhua, Z. Yanan, Z. Ming, 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).

Raasch, S.

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, A. F. Moene, “Towards a validation of scintillometer measurements: the LITFASS-2009 Experiment,” Boundary Layer Meteorol. 144, 83–112 (2012).

Rao, R. Z.

Readings, C. J.

J. C. Kaimal, J. C. Wyngaard, D. A. Haugen, O. R. Cote, Y. Izumi, S. J. Caughey, C. J. Readings, “Turbulence structure in convective boundary-layer,” J. Atmos. Sci. 33(11), 2152–2169 (1976).
[CrossRef]

Sawford, B. L.

M. F. Hibberd, B. L. Sawford, “Design criteria for water tank models of dispersion in the planetary convective boundary-layer,” Boundary Layer Meteorol. 67, 97–118 (1994).

Schwarz, W. H.

C. H. Gibson, W. H. Schwarz, “The universal equilibrium spectra of turbulent velocity and scalar fields,” J. Fluid Mech. 16(03), 365–384 (1963).
[CrossRef]

Shmalhausen, V. I.

Stockton, B. H.

J. W. Deardorff, G. E. Willis, B. H. Stockton, “Laboratory studies of the entrainment zone of a convectively mixed layer,” J. Fluid Mech. 100(01), 41–64 (1980).
[CrossRef]

Sun, J.

R. Yuan, X. Wu, T. Luo, H. Liu, J. Sun, “A review of water tank modeling of the convective atmospheric boundary layer,” J. Wind Eng. Ind. Aerodyn. 99(10), 1099–1114 (2011).
[CrossRef]

R. Yuan, J. Sun, K. Yao, Z. Zeng, 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).

van den Kroonenberg, A. C.

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, A. F. Moene, “Towards a validation of scintillometer measurements: the LITFASS-2009 Experiment,” Boundary Layer Meteorol. 144, 83–112 (2012).

van Dinther, D.

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, A. F. Moene, “Towards a validation of scintillometer measurements: the LITFASS-2009 Experiment,” Boundary Layer Meteorol. 144, 83–112 (2012).

van Kesteren, B.

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, A. F. Moene, “Towards a validation of scintillometer measurements: the LITFASS-2009 Experiment,” Boundary Layer Meteorol. 144, 83–112 (2012).

Vogel, W. M.

H. L. Grant, B. A. Hughes, W. M. Vogel, A. Moilliet, “The spectrum of temperature fluctuations in turbulent flow,” J. Fluid Mech. 34(03), 423–442 (1968).
[CrossRef]

Wang, J. N.

Wang, S. P.

Wang, Y. J.

Willis, G. E.

J. W. Deardorff, G. E. Willis, B. H. Stockton, “Laboratory studies of the entrainment zone of a convectively mixed layer,” J. Fluid Mech. 100(01), 41–64 (1980).
[CrossRef]

Wu, X.

R. Yuan, X. Wu, T. Luo, H. Liu, J. Sun, “A review of water tank modeling of the convective atmospheric boundary layer,” J. Wind Eng. Ind. Aerodyn. 99(10), 1099–1114 (2011).
[CrossRef]

T. Luo, R. Yuan, X. Wu, S. Deng, “A new parameterization of temperature structure parameter in entraining convective boundary layer,” Opt. Commun. 281(23), 5683–5686 (2008).
[CrossRef]

Wu, Y.

Wyngaard, J. C.

M. Kelly, J. C. Wyngaard, “Two-dimensional spectra in the atmospheric boundary layer,” J. Atmos. Sci. 63(11), 3066–3070 (2006).
[CrossRef]

J. C. Kaimal, J. C. Wyngaard, D. A. Haugen, O. R. Cote, Y. Izumi, S. J. Caughey, C. J. Readings, “Turbulence structure in convective boundary-layer,” J. Atmos. Sci. 33(11), 2152–2169 (1976).
[CrossRef]

Xiuhua, Y.

D. Peng, Y. Xiuhua, Z. Yanan, Z. Ming, 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).

Xue, B. D.

Yanan, Z.

D. Peng, Y. Xiuhua, Z. Yanan, Z. Ming, 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).

Yao, K.

R. Yuan, J. Sun, K. Yao, Z. Zeng, 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).

Yuan, R.

R. Yuan, X. Wu, T. Luo, H. Liu, J. Sun, “A review of water tank modeling of the convective atmospheric boundary layer,” J. Wind Eng. Ind. Aerodyn. 99(10), 1099–1114 (2011).
[CrossRef]

T. Luo, R. Yuan, X. Wu, S. Deng, “A new parameterization of temperature structure parameter in entraining convective boundary layer,” Opt. Commun. 281(23), 5683–5686 (2008).
[CrossRef]

R. Yuan, J. Sun, K. Yao, Z. Zeng, 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).

Zeng, Z.

R. Yuan, J. Sun, K. Yao, Z. Zeng, 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).

Zeng, Z. Y.

J. Zhang, Z. Y. Zeng, “Statistical properties of optical turbulence in a convective tank: experimental results,” J. Opt. 3(4), 236–241 (2001).
[CrossRef]

Zhang, J.

J. Zhang, Z. Y. Zeng, “Statistical properties of optical turbulence in a convective tank: experimental results,” J. Opt. 3(4), 236–241 (2001).
[CrossRef]

Appl. Opt. (4)

Boundary Layer Meteorol. (2)

M. F. Hibberd, B. L. Sawford, “Design criteria for water tank models of dispersion in the planetary convective boundary-layer,” Boundary Layer Meteorol. 67, 97–118 (1994).

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, A. F. Moene, “Towards a validation of scintillometer measurements: the LITFASS-2009 Experiment,” Boundary Layer Meteorol. 144, 83–112 (2012).

Chin. J. Atmos. Sci. (1)

R. Yuan, J. Sun, K. Yao, Z. Zeng, 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).

J. Appl. Meteorol. Climatol. (1)

F. Beyrich, 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).
[CrossRef]

J. Atmos. Sci. (2)

J. C. Kaimal, J. C. Wyngaard, D. A. Haugen, O. R. Cote, Y. Izumi, S. J. Caughey, C. J. Readings, “Turbulence structure in convective boundary-layer,” J. Atmos. Sci. 33(11), 2152–2169 (1976).
[CrossRef]

M. Kelly, J. C. Wyngaard, “Two-dimensional spectra in the atmospheric boundary layer,” J. Atmos. Sci. 63(11), 3066–3070 (2006).
[CrossRef]

J. Fluid Mech. (5)

R. J. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88(03), 541–562 (1978).
[CrossRef]

J. W. Deardorff, G. E. Willis, B. H. Stockton, “Laboratory studies of the entrainment zone of a convectively mixed layer,” J. Fluid Mech. 100(01), 41–64 (1980).
[CrossRef]

C. H. Gibson, W. H. Schwarz, “The universal equilibrium spectra of turbulent velocity and scalar fields,” J. Fluid Mech. 16(03), 365–384 (1963).
[CrossRef]

H. L. Grant, B. A. Hughes, W. M. Vogel, A. Moilliet, “The spectrum of temperature fluctuations in turbulent flow,” J. Fluid Mech. 34(03), 423–442 (1968).
[CrossRef]

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).
[CrossRef]

J. Mod. Opt. (1)

A. Maccioni, J. C. Dainty, “Measurement of thermally induced optical turbulence in a water cell,” J. Mod. Opt. 44(6), 1111–1126 (1997).
[CrossRef]

J. Opt. (1)

J. Zhang, Z. Y. Zeng, “Statistical properties of optical turbulence in a convective tank: experimental results,” J. Opt. 3(4), 236–241 (2001).
[CrossRef]

J. Opt. Soc. Am. A (4)

R. Z. Rao, S. P. Wang, X. C. Liu, 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).
[CrossRef]

R. J. Hill, 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).
[CrossRef]

H. M. Dobbins, E. R. Peck, “Change of refractive index of water as a function of temperature,” J. Opt. Soc. Am. A 63(3), 318–320 (1973).
[CrossRef]

R. J. Hill, J. H. Churnside, “Observational challenges of strong scintillations of irradiance,” J. Opt. Soc. Am. A 5(3), 445–447 (1988).
[CrossRef]

J. Phys. Conf. Ser. (1)

D. Peng, Y. Xiuhua, Z. Yanan, Z. Ming, 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).

J. Wind Eng. Ind. Aerodyn. (1)

R. Yuan, X. Wu, T. Luo, H. Liu, J. Sun, “A review of water tank modeling of the convective atmospheric boundary layer,” J. Wind Eng. Ind. Aerodyn. 99(10), 1099–1114 (2011).
[CrossRef]

Opt. Commun. (1)

T. Luo, R. Yuan, X. Wu, S. Deng, “A new parameterization of temperature structure parameter in entraining convective boundary layer,” Opt. Commun. 281(23), 5683–5686 (2008).
[CrossRef]

Opt. Express (1)

Q. J. R. Meteorol. Soc. (1)

S. J. Caughey, 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).
[CrossRef]

Radio Sci. (1)

J. L. Codona, D. B. Creamer, S. M. Flatte, R. G. Frehlich, F. S. Henyey, “Solution for the fourth moment of waves propagating in random media,” Radio Sci. 21(6), 929–948 (1986).
[CrossRef]

Radiophys. Quantum Electron. (1)

A. S. Gurvich, M. A. Kallistratova, 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).
[CrossRef]

Waves Random Media (1)

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).
[CrossRef]

Other (5)

R. B. Stull, An Introduction to Boundary Layer Meteorology (Kluwer Academic, 1988).

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE, 2005).

P. Stoica and R. L. Moses, Introduction to Spectral Analysis (Prentice-Hall, 1997).

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.”

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Figures (9)

Fig. 1
Fig. 1

Schematic form of the component φ T ( κ ) of spectrum of the temperature in water η k is Kolmogorov micro scale, κ m is the scale which meet the conditions when Function φ T ( κ ) in Eq. (2′) in κ m 1 / η k equals φ T ( κ ) = 1 in Eq. (2). In range 1, φ T ( κ ) follows Eq. (2), φ T ( κ ) in range 2 and 3 follows Eq. (2′).

Fig. 2
Fig. 2

Sketch of water tank with measurement instruments. (A) Steel frame of water tank, (B) Oil tank, (C) Extra oil box, (D) Sensor for mean temperature, (E) A pole with sensors for measuring the horizontal distribution of temperature at different heights, (F) A small vehicle on a track at the tank top, (G) Computer for measurement, (H) Initial light beam and (I) Image on the receiving screen.

Fig. 3
Fig. 3

Temperature profiles with time. From the left, nine profiles were recorded at the moment of 0s, 458s, 755s, 984s, 1370s, 1665s, 1991s, 2210s and 2591s respectively.

Fig. 4
Fig. 4

Temperature distribution at 7 different heights corresponding to Fig. 2 at the moment of 1991s. The numbers 10mm, 30mm, etc. indicate the heights of sensors respectively.

Fig. 5
Fig. 5

Measured (dot) and fitted (line) temperature fluctuation spectrum at the height of 30mm in Fig. 4.

Fig. 6
Fig. 6

A photograph of cross-section of the collimated laser beam from measurement (a), and normalized variance varies with height (b).

Fig. 7
Fig. 7

1D horizontal and vertical spectra of light intensity fluctuation at different heights (a) 31.2mm (b)58.3mm (c)85.4mm (d)121.6mm.

Fig. 8
Fig. 8

Peak wavenumber varies with height.

Fig. 9
Fig. 9

Image of the light intensity fluctuation from numerical simulation (a) using the turbulence parameters at the height of 30 mm, and the comparison of 1D spectral of light intensity fluctuation between water tank and numerical simulation (b).

Tables (1)

Tables Icon

Table 1 Parameters of the Refractive Index Fluctuations Spectra Computed from the Fitted Temperature Spectra and the SI Computed from both Numerical and Water Tank Simulation

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

Φ T (κ)=K(α) C T 2 κ α2 φ T (κ)
φ T (κ)=1, κ<<1/ η k ,
φ T (κ)= a 2πK(α) C θ (κ η k ) 2/3 exp( a P r (κ η k ) 2 ), κ1/ η k ,
Φ T (κ)=K(α) C T 2 κ α2 φ T (κ)[1exp( κ 2 L 0 2 /16 π 2 )]
E 1 ( κ 1 )= Φ T ( κ )d κ 2 d κ 3
E 1 ( κ 1 )= κ 1 Φ T (κ)2πκdκ
n=1.332156+[8.889(T20)0.161 (T20) 2 ] 10 5
F I ( κ ,L)=4π k 2 L[1 k κ 2 L sin( κ 2 L k )] Φ n ( κ )
F I hf (κ,L)= 1 2π 0 exp[LD(s)] J 0 (sκ)sds
D(s)=4π k 2 Φ n ( κ )[1cos( κ s )]d κ
F I lf (κ,L)=8π k 2 Φ n ( κ ) 0 L d z 1 sin 2 [ κ 2 2k (L z 1 )]exp{ 0 L D[ κ k g(z, z 1 )]dz }
β= I 2 I 2 I 2
χ 2 =7.37 l 0 -7/3 0 L C n 2 (η) (Lη) 2 dη
χ 2m 2 =7.37 l 0 -7/3 0 1.5 C n 2 (η) (2η) 2 dη =7.37 l 0 -7/3 C n 2 0 1.5 (2η) 2 dη =19.3 l 0 -7/3 C n 2
β 2m =4 χ 2m 2 =77.2 l 0 -7/3 C n 2
χ 1.5m 2 =7.37 l 0 -7/3 0 1.5 C n 2 (η) (1.5η) 2 dη =7.37 l 0 -7/3 C n 2 0 1.5 (1.5η) 2 dη =8.295 l 0 -7/3 C n 2
β 1.5m =4 χ 1.5m 2 =33.18 l 0 -7/3 C n 2

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