Abstract

The convective atmospheric boundary layer was modeled in the water tank. In the entrainment zone (EZ), which is at the top of the convective boundary layer (CBL), the turbulence is anisotropic. An anisotropy coefficient was introduced in the presented anisotropic turbulence model. A laser beam was set to horizontally go through the EZ modeled in the water tank. The image of two-dimensional (2D) light intensity fluctuation was formed on the receiving plate perpendicular to the light path and was recorded by the CCD. The spatial spectra of both horizontal and vertical light intensity fluctuations were analyzed. Results indicate that the light intensity fluctuation in the EZ exhibits strong anisotropic characteristics. Numerical simulation shows there is a linear relationship between the anisotropy coefficients and the ratio of horizontal to vertical fluctuation spectra peak wavelength. By using the measured temperature fluctuations along the light path at different heights, together with the relationship between temperature and refractive index, the one-dimensional (1D) refractive index fluctuation spectra were derived. The anisotropy coefficients were estimated from the 2D light intensity fluctuation spectra modeled by the water tank. Then the turbulence parameters can be obtained using the 1D refractive index fluctuation spectra and the corresponding anisotropy coefficients. These parameters were used in numerical simulation of light propagation. The results of numerical simulations show this approach can reproduce the anisotropic features of light intensity fluctuations in the EZ modeled by the water tank experiment.

© 2014 Optical Society of America

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References

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    [CrossRef]
  3. A. S. Gurvich, I. P. Chunchuzov, “Parameters of the fine density structure in the stratosphere obtained from spacecraft observations of stellar scintillations,” J. Geophys. Res. 108, 4166 (2003).
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    [CrossRef]
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    [CrossRef] [PubMed]
  8. 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 (in Chinese),” Chin. J. Atmos. Sci. 26, 773–780 (2002).
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    [CrossRef]
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    [CrossRef]
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  22. 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]
  23. L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media (SPIE, 2005).
  24. 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]
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    [CrossRef]
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    [CrossRef]
  28. V. A. Kulikov and V. I. Shmalhausen, “Thread-shaped intensity field after light propagation through the convective cell,” Cornell University Library, Atmospheric and oceanic physics, arXiv:1310.5273 (2013).

2014

2013

V. F. Sofieva, F. Dalaudier, J. Vernin, “Using stellar scintillation for studies of turbulence in the Earth's atmosphere,” Philos. Trans. R. Soc. A 371, 20120174 (2013).

2012

V. Kan, V. F. Sofieva, F. Dalaudier, “Anisotropy of small-scale stratospheric irregularities retrieved from scintillations of a double star alpha-Cru observed by GOMOS/ENVISAT,” Atmos. Meas. Tech. 5(11), 2713–2722 (2012).
[CrossRef]

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]

2009

J. P. L. C. Salazar, L. R. Collins, “Two-particle dispersion in isotropic turbulent flows,” Annu. Rev. Fluid Mech. 41(1), 405–432 (2009).

2008

A. S. Gurvich, I. P. Chunchuzov, “Three-dimensional spectrum of temperature fluctuations in stably stratified atmosphere,” Ann. Geophys. 26(7), 2037–2042 (2008).
[CrossRef]

2007

M. Antonelli, A. Lanotte, A. Mazzino, “Anisotropies and universality of buoyancy-dominated turbulent fluctuations: A large-eddy simulation study,” J. Atmos. Sci. 64(7), 2642–2656 (2007).
[CrossRef]

V. F. Sofieva, A. S. Gurvich, F. Dalaudier, V. Kan, “Reconstruction of internal gravity wave and turbulence parameters in the stratosphere using GOMOS scintillation measurements,” J. Geophys. Res. 112, D12113 (2007).

2003

A. S. Gurvich, I. P. Chunchuzov, “Parameters of the fine density structure in the stratosphere obtained from spacecraft observations of stellar scintillations,” J. Geophys. Res. 108, 4166 (2003).

2002

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 (in Chinese),” Chin. J. Atmos. Sci. 26, 773–780 (2002).

2001

J. L. Lumley, A. M. Yaglom, “A century of turbulence,” Flow Turbul. Combust. 66, 241–286 (2001).

A. S. Gurvich, V. L. Brekhovskikh, “Study of the turbulence and inner waves in the stratosphere based on the observations of stellar scintillations from space: a model of scintillation spectra,” Waves Random Media 11(3), 163–181 (2001).
[CrossRef]

1997

A. S. Gurvich, “A heuristic model of three-dimensional spectra of temperature inhomogeneities in the stably stratified atmosphere,” Ann. Geophys. 15, 856–869 (1997).

1989

S. Kida, J. C. R. Hunt, “Interaction between different scales of turbulence over short times,” J. Fluid Mech. 201(1), 411–445 (1989).
[CrossRef]

1988

1986

R. M. Manning, “An anisotropic turbulence model for wave propagation near the surface of the Earth,” IEEE Trans. Antennas Propag. 34(2), 258–261 (1986).
[CrossRef]

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]

1978

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]

1973

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]

1970

1959

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(1), 113–133 (1959).
[CrossRef]

1941

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds number,” Dokl. Akad. Nauk SSSR 30, 299–303 (1941).

Antonelli, M.

M. Antonelli, A. Lanotte, A. Mazzino, “Anisotropies and universality of buoyancy-dominated turbulent fluctuations: A large-eddy simulation study,” J. Atmos. Sci. 64(7), 2642–2656 (2007).
[CrossRef]

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(1), 113–133 (1959).
[CrossRef]

Brekhovskikh, V. L.

A. S. Gurvich, V. L. Brekhovskikh, “Study of the turbulence and inner waves in the stratosphere based on the observations of stellar scintillations from space: a model of scintillation spectra,” Waves Random Media 11(3), 163–181 (2001).
[CrossRef]

Chunchuzov, I. P.

A. S. Gurvich, I. P. Chunchuzov, “Three-dimensional spectrum of temperature fluctuations in stably stratified atmosphere,” Ann. Geophys. 26(7), 2037–2042 (2008).
[CrossRef]

A. S. Gurvich, I. P. Chunchuzov, “Parameters of the fine density structure in the stratosphere obtained from spacecraft observations of stellar scintillations,” J. Geophys. Res. 108, 4166 (2003).

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]

Collins, L. R.

J. P. L. C. Salazar, L. R. Collins, “Two-particle dispersion in isotropic turbulent flows,” Annu. Rev. Fluid Mech. 41(1), 405–432 (2009).

Consortini, A.

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]

Dalaudier, F.

V. F. Sofieva, F. Dalaudier, J. Vernin, “Using stellar scintillation for studies of turbulence in the Earth's atmosphere,” Philos. Trans. R. Soc. A 371, 20120174 (2013).

V. Kan, V. F. Sofieva, F. Dalaudier, “Anisotropy of small-scale stratospheric irregularities retrieved from scintillations of a double star alpha-Cru observed by GOMOS/ENVISAT,” Atmos. Meas. Tech. 5(11), 2713–2722 (2012).
[CrossRef]

V. F. Sofieva, A. S. Gurvich, F. Dalaudier, V. Kan, “Reconstruction of internal gravity wave and turbulence parameters in the stratosphere using GOMOS scintillation measurements,” J. Geophys. Res. 112, D12113 (2007).

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]

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. 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]

Gurvich, A. S.

A. S. Gurvich, I. P. Chunchuzov, “Three-dimensional spectrum of temperature fluctuations in stably stratified atmosphere,” Ann. Geophys. 26(7), 2037–2042 (2008).
[CrossRef]

V. F. Sofieva, A. S. Gurvich, F. Dalaudier, V. Kan, “Reconstruction of internal gravity wave and turbulence parameters in the stratosphere using GOMOS scintillation measurements,” J. Geophys. Res. 112, D12113 (2007).

A. S. Gurvich, I. P. Chunchuzov, “Parameters of the fine density structure in the stratosphere obtained from spacecraft observations of stellar scintillations,” J. Geophys. Res. 108, 4166 (2003).

A. S. Gurvich, V. L. Brekhovskikh, “Study of the turbulence and inner waves in the stratosphere based on the observations of stellar scintillations from space: a model of scintillation spectra,” Waves Random Media 11(3), 163–181 (2001).
[CrossRef]

A. S. Gurvich, “A heuristic model of three-dimensional spectra of temperature inhomogeneities in the stably stratified atmosphere,” Ann. Geophys. 15, 856–869 (1997).

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]

Hill, R. J.

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]

Hunt, J. C. R.

S. Kida, J. C. R. Hunt, “Interaction between different scales of turbulence over short times,” J. Fluid Mech. 201(1), 411–445 (1989).
[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 (in Chinese),” Chin. J. Atmos. Sci. 26, 773–780 (2002).

Kan, V.

V. Kan, V. F. Sofieva, F. Dalaudier, “Anisotropy of small-scale stratospheric irregularities retrieved from scintillations of a double star alpha-Cru observed by GOMOS/ENVISAT,” Atmos. Meas. Tech. 5(11), 2713–2722 (2012).
[CrossRef]

V. F. Sofieva, A. S. Gurvich, F. Dalaudier, V. Kan, “Reconstruction of internal gravity wave and turbulence parameters in the stratosphere using GOMOS scintillation measurements,” J. Geophys. Res. 112, D12113 (2007).

Kida, S.

S. Kida, J. C. R. Hunt, “Interaction between different scales of turbulence over short times,” J. Fluid Mech. 201(1), 411–445 (1989).
[CrossRef]

Kolmogorov, A. N.

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds number,” Dokl. Akad. Nauk SSSR 30, 299–303 (1941).

Lanotte, A.

M. Antonelli, A. Lanotte, A. Mazzino, “Anisotropies and universality of buoyancy-dominated turbulent fluctuations: A large-eddy simulation study,” J. Atmos. Sci. 64(7), 2642–2656 (2007).
[CrossRef]

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]

Lu, C.

Lumley, J. L.

J. L. Lumley, A. M. Yaglom, “A century of turbulence,” Flow Turbul. Combust. 66, 241–286 (2001).

Luo, T.

R. Yuan, J. Sun, T. Luo, X. Wu, C. Wang, C. Lu, “Simulation study on light propagation in an isotropic turbulence field of the mixed layer,” Opt. Express 22(6), 7194–7209 (2014).
[CrossRef] [PubMed]

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]

Manning, R. M.

R. M. Manning, “An anisotropic turbulence model for wave propagation near the surface of the Earth,” IEEE Trans. Antennas Propag. 34(2), 258–261 (1986).
[CrossRef]

Martin, J. M.

Mazzino, A.

M. Antonelli, A. Lanotte, A. Mazzino, “Anisotropies and universality of buoyancy-dominated turbulent fluctuations: A large-eddy simulation study,” J. Atmos. Sci. 64(7), 2642–2656 (2007).
[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]

Ronchi, L.

Salazar, J. P. L. C.

J. P. L. C. Salazar, L. R. Collins, “Two-particle dispersion in isotropic turbulent flows,” Annu. Rev. Fluid Mech. 41(1), 405–432 (2009).

Sofieva, V. F.

V. F. Sofieva, F. Dalaudier, J. Vernin, “Using stellar scintillation for studies of turbulence in the Earth's atmosphere,” Philos. Trans. R. Soc. A 371, 20120174 (2013).

V. Kan, V. F. Sofieva, F. Dalaudier, “Anisotropy of small-scale stratospheric irregularities retrieved from scintillations of a double star alpha-Cru observed by GOMOS/ENVISAT,” Atmos. Meas. Tech. 5(11), 2713–2722 (2012).
[CrossRef]

V. F. Sofieva, A. S. Gurvich, F. Dalaudier, V. Kan, “Reconstruction of internal gravity wave and turbulence parameters in the stratosphere using GOMOS scintillation measurements,” J. Geophys. Res. 112, D12113 (2007).

Stefanutti, L.

Sun, J.

R. Yuan, J. Sun, T. Luo, X. Wu, C. Wang, C. Lu, “Simulation study on light propagation in an isotropic turbulence field of the mixed layer,” Opt. Express 22(6), 7194–7209 (2014).
[CrossRef] [PubMed]

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 (in Chinese),” Chin. J. Atmos. Sci. 26, 773–780 (2002).

Vernin, J.

V. F. Sofieva, F. Dalaudier, J. Vernin, “Using stellar scintillation for studies of turbulence in the Earth's atmosphere,” Philos. Trans. R. Soc. A 371, 20120174 (2013).

Wang, C.

Wu, X.

R. Yuan, J. Sun, T. Luo, X. Wu, C. Wang, C. Lu, “Simulation study on light propagation in an isotropic turbulence field of the mixed layer,” Opt. Express 22(6), 7194–7209 (2014).
[CrossRef] [PubMed]

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]

Yaglom, A. M.

J. L. Lumley, A. M. Yaglom, “A century of turbulence,” Flow Turbul. Combust. 66, 241–286 (2001).

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 (in Chinese),” Chin. J. Atmos. Sci. 26, 773–780 (2002).

Yuan, R.

R. Yuan, J. Sun, T. Luo, X. Wu, C. Wang, C. Lu, “Simulation study on light propagation in an isotropic turbulence field of the mixed layer,” Opt. Express 22(6), 7194–7209 (2014).
[CrossRef] [PubMed]

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 (in Chinese),” 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 (in Chinese),” Chin. J. Atmos. Sci. 26, 773–780 (2002).

Ann. Geophys.

A. S. Gurvich, “A heuristic model of three-dimensional spectra of temperature inhomogeneities in the stably stratified atmosphere,” Ann. Geophys. 15, 856–869 (1997).

A. S. Gurvich, I. P. Chunchuzov, “Three-dimensional spectrum of temperature fluctuations in stably stratified atmosphere,” Ann. Geophys. 26(7), 2037–2042 (2008).
[CrossRef]

Annu. Rev. Fluid Mech.

J. P. L. C. Salazar, L. R. Collins, “Two-particle dispersion in isotropic turbulent flows,” Annu. Rev. Fluid Mech. 41(1), 405–432 (2009).

Appl. Opt.

Atmos. Meas. Tech.

V. Kan, V. F. Sofieva, F. Dalaudier, “Anisotropy of small-scale stratospheric irregularities retrieved from scintillations of a double star alpha-Cru observed by GOMOS/ENVISAT,” Atmos. Meas. Tech. 5(11), 2713–2722 (2012).
[CrossRef]

Chin. J. Atmos. Sci.

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 (in Chinese),” Chin. J. Atmos. Sci. 26, 773–780 (2002).

Dokl. Akad. Nauk SSSR

A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds number,” Dokl. Akad. Nauk SSSR 30, 299–303 (1941).

Flow Turbul. Combust.

J. L. Lumley, A. M. Yaglom, “A century of turbulence,” Flow Turbul. Combust. 66, 241–286 (2001).

IEEE Trans. Antennas Propag.

R. M. Manning, “An anisotropic turbulence model for wave propagation near the surface of the Earth,” IEEE Trans. Antennas Propag. 34(2), 258–261 (1986).
[CrossRef]

J. Atmos. Sci.

M. Antonelli, A. Lanotte, A. Mazzino, “Anisotropies and universality of buoyancy-dominated turbulent fluctuations: A large-eddy simulation study,” J. Atmos. Sci. 64(7), 2642–2656 (2007).
[CrossRef]

J. Fluid Mech.

S. Kida, J. C. R. Hunt, “Interaction between different scales of turbulence over short times,” J. Fluid Mech. 201(1), 411–445 (1989).
[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(1), 113–133 (1959).
[CrossRef]

J. Geophys. Res.

A. S. Gurvich, I. P. Chunchuzov, “Parameters of the fine density structure in the stratosphere obtained from spacecraft observations of stellar scintillations,” J. Geophys. Res. 108, 4166 (2003).

V. F. Sofieva, A. S. Gurvich, F. Dalaudier, V. Kan, “Reconstruction of internal gravity wave and turbulence parameters in the stratosphere using GOMOS scintillation measurements,” J. Geophys. Res. 112, D12113 (2007).

J. Opt. Soc. Am. A

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, 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]

J. Wind Eng. Ind. Aerodyn.

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. Express

Philos. Trans. R. Soc. A

V. F. Sofieva, F. Dalaudier, J. Vernin, “Using stellar scintillation for studies of turbulence in the Earth's atmosphere,” Philos. Trans. R. Soc. A 371, 20120174 (2013).

Radio Sci.

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]

Waves Random Media

A. S. Gurvich, V. L. Brekhovskikh, “Study of the turbulence and inner waves in the stratosphere based on the observations of stellar scintillations from space: a model of scintillation spectra,” Waves Random Media 11(3), 163–181 (2001).
[CrossRef]

Other

E. S. Wheelon, I. Geometrical Optics (Cambridge University, 2001).

E. S. Wheelon, II. Weak Scattering (Cambridge University, 2003).

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).

V. A. Kulikov and V. I. Shmalhausen, “Thread-shaped intensity field after light propagation through the convective cell,” Cornell University Library, Atmospheric and oceanic physics, arXiv:1310.5273 (2013).

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Fig. 1
Fig. 1

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

Fig. 2
Fig. 2

1D horizontal and vertical spectra of light intensity fluctuation at the height of 196mm.

Fig. 3
Fig. 3

Peak wavelengths vary with heights (a) and peak wavelength ratios with heights (b).

Fig. 4
Fig. 4

Image of the light intensity fluctuation from numerical simulation (a) and corresponding 1D horizontal and vertical spectra of light intensity fluctuation from numerical simulation (b).

Fig. 5
Fig. 5

The relationship between the peak-wavelength ratios and the anisotropic coefficients.

Fig. 6
Fig. 6

Temperature distribution at 5 different heights recorded at same moment as Fig. 1. The numbers 110mm, 127mm, etc. indicate the heights of sensors respectively.

Fig. 7
Fig. 7

Measured (dot) and fitted (line) temperature fluctuation spectrum at the height of 190mm in Fig. 6.

Tables (1)

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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 (10)

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q =( κ x * C aniso , κ y * C aniso , κ z / C aniso )
Φ T (q)=K(α) C T 2 q α2 ϕ T (q)
ϕ T (q)=1 q<<1/ η k
ϕ T (q)= a 2πK(α) C θ (q η k ) 2/3 exp[ a P r (q η k ) 2 ] q1/ η k
Φ T (q)=K(α) C T 2 q α2 ϕ T (q)[1exp( q 2 L 0 2 /16 π 2 )]
E T ( κ y )=2π k y C aniso Φ T (q)qdq
E T ( κ z )= 2π C aniso k z / C aniso Φ T (q)qdq
n=1.332156+[8.889(T20)0.161 (T20) 2 ] 10 5
β= I 2 I 2 I 2
λ H λ V =1+2.5( C aniso 1)

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