Abstract

Deviations of experimental data on the effect of atmospheric turbulence on electromagnetic wave propagation from a standard Kolmogorov (or Obukhov-Kolmogorov) model are examined from the standpoint of the behavior of atmospheric passive scalar spectrum. It is pointed out that these deviations are not random and can be explained on the basis of today’s ideas of passive scalar behavior in the atmosphere. This approach allows us to view electromagnetic radiation transfer in random media in a new way and to make the necessary steps for developing a generalized model of this phenomenon.

© 2004 Optical Society of America

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  1. A. M. Obukhov, “Temperature field structure in a turbulent flow,” Izv. Acad. Nauk SSSR Ser. Geog. Geofiz. 13, 58–69 (1949).
  2. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  3. V. I. Tatarski, Wave Propagation in a Turbulent Medium (Nauka, Moscow, 1967).
  4. D. Boreman, C. Dainty, “Zernike expansions for non-Kolmogorov turbulence,” J. Opt. Soc. Am. A 13, 517–522 (1996).
    [CrossRef]
  5. B. E. Stribling, B. M. Welsh, M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” in Atmospheric Propagation and Remote Sensing IV, C. Dainty, ed., Proc. SPIE2471, 181–196 (1995).
    [CrossRef]
  6. T. W. Nicholls, G. D. Boreman, C. Dainty, “Use of a Shack-Hartmann wavefront sensor to measure deviations from a Kolmogorov phase spectrum,” Opt. Lett. 20, 2460–2462 (1995).
    [CrossRef]
  7. A. S. Gurvich, M. S. Belen’kii, “Influence of stratospheric turbulence on infrared imaging,” J. Opt. Soc. Am. A 12, 2517–2522 (1995).
    [CrossRef]
  8. M. S. Belen’kii, S. J. Karis, J. M. Brown, R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 113–123 (1997).
    [CrossRef]
  9. M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” in Adaptive Optics Systems and Technology, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3762, 396–406 (1999).
    [CrossRef]
  10. C. Rao, W. Jiang, N. Ling, “Atmospheric parameters measurements for non-Kolmogorov turbulence with Shack-Hartmann wavefront sensor,” in Propagation and Imaging through the Atmosphere III, M. C. Roggerma, L. R. Bissonnette, eds., Proc. SPIE3763, 84–91 (1999).
    [CrossRef]
  11. C. Rao, W. Jiang, N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
    [CrossRef]
  12. E. Golbraikh, N. Kopeika, “Changes in modulation transfer function and optical resolution in helical turbulent media,” J. Opt. Soc. Am. A 19, 1774–1778 (2002).
    [CrossRef]
  13. C. Rao, W. Jiang, N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
    [CrossRef]
  14. G. K. Batchelor, “Small-scale variation of convected quantities like temperature in turbulent fluid. Part I. General discussion and the case of small conductivity,” J. Fluid Mech. 5, 113–133 (1959).
    [CrossRef]
  15. G. K. Batchelor, I. D. Howells, A. A. Townsend, “Small-scale variation of convected quantities like temperature in turbulent fluid. Part II. The case of large conductivity,” J. Fluid Mech. 5, 134–139 (1959).
    [CrossRef]
  16. C. H. Gibson, W. H. Schwarz, “The universal equilibrium spectra of turbulent velocity and scalar fields,” J. Fluid Mech. 16, 365–384 (1963).
    [CrossRef]
  17. C. H. Gibson, W. T. Ashurst, A. R. Kerstein, “Mixing of strongly diffusive passive scalars like temperature by turbulence,” J. Fluid Mech. 194, 261–293 (1988).
    [CrossRef]
  18. S. S. Moiseev, O. G. Chkhetiani, “Helical scaling in turbulence,” JETP 83, 192–198 (1996).
  19. T. Elperin, N. Kleeorin, I. Rogachevskii, “Isotropic and anisotropic spectra of passive scalar fluctuations in turbulent fluid flow,” Phys. Rev. E 53, 3431–3441 (1996).
    [CrossRef]
  20. J. J. Moreau, “Constants d’un ilot tourbillonnaire en fluide parfait barotrope,” C. R. Acad. Sci. 252, 2810–2812 (1961).
  21. A. Brissaud, U. Frisch, J. Leorat, M. Lesieur, A. Mazure, “Helicity cascades in fully developed isotropic turbulence,” Phys. Fluids 16, 1366–1367 (1973).
    [CrossRef]
  22. E. Golbraikh, S. S. Moiseev, “Different spectra formation in the presence of helical transfer,” Phys. Lett. A 305, 173–175 (2002).
    [CrossRef]
  23. H. Branover, A. Eidelman, E. Golbraikh, S. Gordienko, S. Moiseev, “On the universality of large-scale turbulence,” Phys. Fluids 16, 845–847 (2004).
    [CrossRef]
  24. A. Eidelman, N. Goldbaum, “Large-scale turbulence universality and its application to extreme weather events,” Phys. Chem. Earth 25, 785–788 (2000).
    [CrossRef]
  25. D. Dayton, B. Pierson, B. Spielbusch, J. Gonglewski, “Atmospheric structure function measurements with a Shack-Hartmann wave-front sensor,” Opt. Lett. 17, 1737–1739 (1992).
    [CrossRef] [PubMed]
  26. M. S. Belen’kii, “Effect of the stratosphere on star image motion,” Opt. Lett. 20, 1359–1361 (1995).
    [CrossRef] [PubMed]

2004 (1)

H. Branover, A. Eidelman, E. Golbraikh, S. Gordienko, S. Moiseev, “On the universality of large-scale turbulence,” Phys. Fluids 16, 845–847 (2004).
[CrossRef]

2002 (2)

E. Golbraikh, S. S. Moiseev, “Different spectra formation in the presence of helical transfer,” Phys. Lett. A 305, 173–175 (2002).
[CrossRef]

E. Golbraikh, N. Kopeika, “Changes in modulation transfer function and optical resolution in helical turbulent media,” J. Opt. Soc. Am. A 19, 1774–1778 (2002).
[CrossRef]

2000 (3)

C. Rao, W. Jiang, N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

A. Eidelman, N. Goldbaum, “Large-scale turbulence universality and its application to extreme weather events,” Phys. Chem. Earth 25, 785–788 (2000).
[CrossRef]

C. Rao, W. Jiang, N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

1996 (3)

D. Boreman, C. Dainty, “Zernike expansions for non-Kolmogorov turbulence,” J. Opt. Soc. Am. A 13, 517–522 (1996).
[CrossRef]

S. S. Moiseev, O. G. Chkhetiani, “Helical scaling in turbulence,” JETP 83, 192–198 (1996).

T. Elperin, N. Kleeorin, I. Rogachevskii, “Isotropic and anisotropic spectra of passive scalar fluctuations in turbulent fluid flow,” Phys. Rev. E 53, 3431–3441 (1996).
[CrossRef]

1995 (3)

1992 (1)

1988 (1)

C. H. Gibson, W. T. Ashurst, A. R. Kerstein, “Mixing of strongly diffusive passive scalars like temperature by turbulence,” J. Fluid Mech. 194, 261–293 (1988).
[CrossRef]

1973 (1)

A. Brissaud, U. Frisch, J. Leorat, M. Lesieur, A. Mazure, “Helicity cascades in fully developed isotropic turbulence,” Phys. Fluids 16, 1366–1367 (1973).
[CrossRef]

1963 (1)

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

1961 (1)

J. J. Moreau, “Constants d’un ilot tourbillonnaire en fluide parfait barotrope,” C. R. Acad. Sci. 252, 2810–2812 (1961).

1959 (2)

G. K. Batchelor, “Small-scale variation of convected quantities like temperature in turbulent fluid. Part I. General discussion and the case of small conductivity,” J. Fluid Mech. 5, 113–133 (1959).
[CrossRef]

G. K. Batchelor, I. D. Howells, A. A. Townsend, “Small-scale variation of convected quantities like temperature in turbulent fluid. Part II. The case of large conductivity,” J. Fluid Mech. 5, 134–139 (1959).
[CrossRef]

1949 (1)

A. M. Obukhov, “Temperature field structure in a turbulent flow,” Izv. Acad. Nauk SSSR Ser. Geog. Geofiz. 13, 58–69 (1949).

Ashurst, W. T.

C. H. Gibson, W. T. Ashurst, A. R. Kerstein, “Mixing of strongly diffusive passive scalars like temperature by turbulence,” J. Fluid Mech. 194, 261–293 (1988).
[CrossRef]

Barchers, J. D.

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” in Adaptive Optics Systems and Technology, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3762, 396–406 (1999).
[CrossRef]

Batchelor, G. K.

G. K. Batchelor, “Small-scale variation of convected quantities like temperature in turbulent fluid. Part I. General discussion and the case of small conductivity,” J. Fluid Mech. 5, 113–133 (1959).
[CrossRef]

G. K. Batchelor, I. D. Howells, A. A. Townsend, “Small-scale variation of convected quantities like temperature in turbulent fluid. Part II. The case of large conductivity,” J. Fluid Mech. 5, 134–139 (1959).
[CrossRef]

Belen’kii, M. S.

A. S. Gurvich, M. S. Belen’kii, “Influence of stratospheric turbulence on infrared imaging,” J. Opt. Soc. Am. A 12, 2517–2522 (1995).
[CrossRef]

M. S. Belen’kii, “Effect of the stratosphere on star image motion,” Opt. Lett. 20, 1359–1361 (1995).
[CrossRef] [PubMed]

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” in Adaptive Optics Systems and Technology, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3762, 396–406 (1999).
[CrossRef]

M. S. Belen’kii, S. J. Karis, J. M. Brown, R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 113–123 (1997).
[CrossRef]

Boreman, D.

Boreman, G. D.

Branover, H.

H. Branover, A. Eidelman, E. Golbraikh, S. Gordienko, S. Moiseev, “On the universality of large-scale turbulence,” Phys. Fluids 16, 845–847 (2004).
[CrossRef]

Brissaud, A.

A. Brissaud, U. Frisch, J. Leorat, M. Lesieur, A. Mazure, “Helicity cascades in fully developed isotropic turbulence,” Phys. Fluids 16, 1366–1367 (1973).
[CrossRef]

Brown, J. M.

M. S. Belen’kii, S. J. Karis, J. M. Brown, R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 113–123 (1997).
[CrossRef]

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” in Adaptive Optics Systems and Technology, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3762, 396–406 (1999).
[CrossRef]

Chkhetiani, O. G.

S. S. Moiseev, O. G. Chkhetiani, “Helical scaling in turbulence,” JETP 83, 192–198 (1996).

Dainty, C.

Dayton, D.

Eidelman, A.

H. Branover, A. Eidelman, E. Golbraikh, S. Gordienko, S. Moiseev, “On the universality of large-scale turbulence,” Phys. Fluids 16, 845–847 (2004).
[CrossRef]

A. Eidelman, N. Goldbaum, “Large-scale turbulence universality and its application to extreme weather events,” Phys. Chem. Earth 25, 785–788 (2000).
[CrossRef]

Elperin, T.

T. Elperin, N. Kleeorin, I. Rogachevskii, “Isotropic and anisotropic spectra of passive scalar fluctuations in turbulent fluid flow,” Phys. Rev. E 53, 3431–3441 (1996).
[CrossRef]

Frisch, U.

A. Brissaud, U. Frisch, J. Leorat, M. Lesieur, A. Mazure, “Helicity cascades in fully developed isotropic turbulence,” Phys. Fluids 16, 1366–1367 (1973).
[CrossRef]

Fugate, R. Q.

M. S. Belen’kii, S. J. Karis, J. M. Brown, R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 113–123 (1997).
[CrossRef]

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” in Adaptive Optics Systems and Technology, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3762, 396–406 (1999).
[CrossRef]

Gibson, C. H.

C. H. Gibson, W. T. Ashurst, A. R. Kerstein, “Mixing of strongly diffusive passive scalars like temperature by turbulence,” J. Fluid Mech. 194, 261–293 (1988).
[CrossRef]

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

Golbraikh, E.

H. Branover, A. Eidelman, E. Golbraikh, S. Gordienko, S. Moiseev, “On the universality of large-scale turbulence,” Phys. Fluids 16, 845–847 (2004).
[CrossRef]

E. Golbraikh, S. S. Moiseev, “Different spectra formation in the presence of helical transfer,” Phys. Lett. A 305, 173–175 (2002).
[CrossRef]

E. Golbraikh, N. Kopeika, “Changes in modulation transfer function and optical resolution in helical turbulent media,” J. Opt. Soc. Am. A 19, 1774–1778 (2002).
[CrossRef]

Goldbaum, N.

A. Eidelman, N. Goldbaum, “Large-scale turbulence universality and its application to extreme weather events,” Phys. Chem. Earth 25, 785–788 (2000).
[CrossRef]

Gonglewski, J.

Gordienko, S.

H. Branover, A. Eidelman, E. Golbraikh, S. Gordienko, S. Moiseev, “On the universality of large-scale turbulence,” Phys. Fluids 16, 845–847 (2004).
[CrossRef]

Gurvich, A. S.

Howells, I. D.

G. K. Batchelor, I. D. Howells, A. A. Townsend, “Small-scale variation of convected quantities like temperature in turbulent fluid. Part II. The case of large conductivity,” J. Fluid Mech. 5, 134–139 (1959).
[CrossRef]

Jiang, W.

C. Rao, W. Jiang, N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

C. Rao, W. Jiang, N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

C. Rao, W. Jiang, N. Ling, “Atmospheric parameters measurements for non-Kolmogorov turbulence with Shack-Hartmann wavefront sensor,” in Propagation and Imaging through the Atmosphere III, M. C. Roggerma, L. R. Bissonnette, eds., Proc. SPIE3763, 84–91 (1999).
[CrossRef]

Karis, S. J.

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” in Adaptive Optics Systems and Technology, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3762, 396–406 (1999).
[CrossRef]

M. S. Belen’kii, S. J. Karis, J. M. Brown, R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 113–123 (1997).
[CrossRef]

Kerstein, A. R.

C. H. Gibson, W. T. Ashurst, A. R. Kerstein, “Mixing of strongly diffusive passive scalars like temperature by turbulence,” J. Fluid Mech. 194, 261–293 (1988).
[CrossRef]

Kleeorin, N.

T. Elperin, N. Kleeorin, I. Rogachevskii, “Isotropic and anisotropic spectra of passive scalar fluctuations in turbulent fluid flow,” Phys. Rev. E 53, 3431–3441 (1996).
[CrossRef]

Kopeika, N.

Leorat, J.

A. Brissaud, U. Frisch, J. Leorat, M. Lesieur, A. Mazure, “Helicity cascades in fully developed isotropic turbulence,” Phys. Fluids 16, 1366–1367 (1973).
[CrossRef]

Lesieur, M.

A. Brissaud, U. Frisch, J. Leorat, M. Lesieur, A. Mazure, “Helicity cascades in fully developed isotropic turbulence,” Phys. Fluids 16, 1366–1367 (1973).
[CrossRef]

Ling, N.

C. Rao, W. Jiang, N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

C. Rao, W. Jiang, N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

C. Rao, W. Jiang, N. Ling, “Atmospheric parameters measurements for non-Kolmogorov turbulence with Shack-Hartmann wavefront sensor,” in Propagation and Imaging through the Atmosphere III, M. C. Roggerma, L. R. Bissonnette, eds., Proc. SPIE3763, 84–91 (1999).
[CrossRef]

Mazure, A.

A. Brissaud, U. Frisch, J. Leorat, M. Lesieur, A. Mazure, “Helicity cascades in fully developed isotropic turbulence,” Phys. Fluids 16, 1366–1367 (1973).
[CrossRef]

Moiseev, S.

H. Branover, A. Eidelman, E. Golbraikh, S. Gordienko, S. Moiseev, “On the universality of large-scale turbulence,” Phys. Fluids 16, 845–847 (2004).
[CrossRef]

Moiseev, S. S.

E. Golbraikh, S. S. Moiseev, “Different spectra formation in the presence of helical transfer,” Phys. Lett. A 305, 173–175 (2002).
[CrossRef]

S. S. Moiseev, O. G. Chkhetiani, “Helical scaling in turbulence,” JETP 83, 192–198 (1996).

Moreau, J. J.

J. J. Moreau, “Constants d’un ilot tourbillonnaire en fluide parfait barotrope,” C. R. Acad. Sci. 252, 2810–2812 (1961).

Nicholls, T. W.

Obukhov, A. M.

A. M. Obukhov, “Temperature field structure in a turbulent flow,” Izv. Acad. Nauk SSSR Ser. Geog. Geofiz. 13, 58–69 (1949).

Osmon, C. L.

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” in Adaptive Optics Systems and Technology, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3762, 396–406 (1999).
[CrossRef]

Pierson, B.

Rao, C.

C. Rao, W. Jiang, N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

C. Rao, W. Jiang, N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

C. Rao, W. Jiang, N. Ling, “Atmospheric parameters measurements for non-Kolmogorov turbulence with Shack-Hartmann wavefront sensor,” in Propagation and Imaging through the Atmosphere III, M. C. Roggerma, L. R. Bissonnette, eds., Proc. SPIE3763, 84–91 (1999).
[CrossRef]

Rogachevskii, I.

T. Elperin, N. Kleeorin, I. Rogachevskii, “Isotropic and anisotropic spectra of passive scalar fluctuations in turbulent fluid flow,” Phys. Rev. E 53, 3431–3441 (1996).
[CrossRef]

Roggemann, M. C.

B. E. Stribling, B. M. Welsh, M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” in Atmospheric Propagation and Remote Sensing IV, C. Dainty, ed., Proc. SPIE2471, 181–196 (1995).
[CrossRef]

Schwarz, W. H.

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

Spielbusch, B.

Stribling, B. E.

B. E. Stribling, B. M. Welsh, M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” in Atmospheric Propagation and Remote Sensing IV, C. Dainty, ed., Proc. SPIE2471, 181–196 (1995).
[CrossRef]

Tatarski, V. I.

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

V. I. Tatarski, Wave Propagation in a Turbulent Medium (Nauka, Moscow, 1967).

Townsend, A. A.

G. K. Batchelor, I. D. Howells, A. A. Townsend, “Small-scale variation of convected quantities like temperature in turbulent fluid. Part II. The case of large conductivity,” J. Fluid Mech. 5, 134–139 (1959).
[CrossRef]

Welsh, B. M.

B. E. Stribling, B. M. Welsh, M. C. Roggemann, “Optical propagation in non-Kolmogorov atmospheric turbulence,” in Atmospheric Propagation and Remote Sensing IV, C. Dainty, ed., Proc. SPIE2471, 181–196 (1995).
[CrossRef]

C. R. Acad. Sci. (1)

J. J. Moreau, “Constants d’un ilot tourbillonnaire en fluide parfait barotrope,” C. R. Acad. Sci. 252, 2810–2812 (1961).

Izv. Acad. Nauk SSSR Ser. Geog. Geofiz. (1)

A. M. Obukhov, “Temperature field structure in a turbulent flow,” Izv. Acad. Nauk SSSR Ser. Geog. Geofiz. 13, 58–69 (1949).

J. Fluid Mech. (4)

G. K. Batchelor, “Small-scale variation of convected quantities like temperature in turbulent fluid. Part I. General discussion and the case of small conductivity,” J. Fluid Mech. 5, 113–133 (1959).
[CrossRef]

G. K. Batchelor, I. D. Howells, A. A. Townsend, “Small-scale variation of convected quantities like temperature in turbulent fluid. Part II. The case of large conductivity,” J. Fluid Mech. 5, 134–139 (1959).
[CrossRef]

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

C. H. Gibson, W. T. Ashurst, A. R. Kerstein, “Mixing of strongly diffusive passive scalars like temperature by turbulence,” J. Fluid Mech. 194, 261–293 (1988).
[CrossRef]

J. Mod. Opt. (2)

C. Rao, W. Jiang, N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

C. Rao, W. Jiang, N. Ling, “Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence,” J. Mod. Opt. 47, 1111–1126 (2000).
[CrossRef]

J. Opt. Soc. Am. A (3)

JETP (1)

S. S. Moiseev, O. G. Chkhetiani, “Helical scaling in turbulence,” JETP 83, 192–198 (1996).

Opt. Lett. (3)

Phys. Chem. Earth (1)

A. Eidelman, N. Goldbaum, “Large-scale turbulence universality and its application to extreme weather events,” Phys. Chem. Earth 25, 785–788 (2000).
[CrossRef]

Phys. Fluids (2)

H. Branover, A. Eidelman, E. Golbraikh, S. Gordienko, S. Moiseev, “On the universality of large-scale turbulence,” Phys. Fluids 16, 845–847 (2004).
[CrossRef]

A. Brissaud, U. Frisch, J. Leorat, M. Lesieur, A. Mazure, “Helicity cascades in fully developed isotropic turbulence,” Phys. Fluids 16, 1366–1367 (1973).
[CrossRef]

Phys. Lett. A (1)

E. Golbraikh, S. S. Moiseev, “Different spectra formation in the presence of helical transfer,” Phys. Lett. A 305, 173–175 (2002).
[CrossRef]

Phys. Rev. E (1)

T. Elperin, N. Kleeorin, I. Rogachevskii, “Isotropic and anisotropic spectra of passive scalar fluctuations in turbulent fluid flow,” Phys. Rev. E 53, 3431–3441 (1996).
[CrossRef]

Other (6)

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

V. I. Tatarski, Wave Propagation in a Turbulent Medium (Nauka, Moscow, 1967).

M. S. Belen’kii, S. J. Karis, J. M. Brown, R. Q. Fugate, “Experimental study of the effect of non-Kolmogorov stratospheric turbulence on star image motion,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 113–123 (1997).
[CrossRef]

M. S. Belen’kii, J. D. Barchers, S. J. Karis, C. L. Osmon, J. M. Brown, R. Q. Fugate, “Preliminary experimental evidence of anisotropy of turbulence and the effect of non-Kolmogorov turbulence on wavefront tilt statistics,” in Adaptive Optics Systems and Technology, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3762, 396–406 (1999).
[CrossRef]

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[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

D c (k) dependences (in relative units) for k 0 = 2 and 6 (dashed lines) in logarithmic scale and their approximation by exponentials (solid curves).

Tables (1)

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Table 1 Spectral Index Values in the Outer Scale Region

Equations (10)

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Dnk=Cn2k-γ,
Dnk=Cn2k2+k0211/6.
Dnk=Cn2k-5/311+kηk1/3,
Dnk=const Tk-4/3η1/3.
DCkC1θk-k0k-3+C2θk0-kk-β-4,
θx=1,x00,x<0.
σ0k4Φ¯k,
Φ¯k=Ak0k-γeff-2=C1θk-k0k-5+C2θk0-kk-β-6.
σDDβD2  xβ-1dx,
k-βeff-1θk0-kk-γ1-1+Aθk-k0θkD-kk-γ2-1,

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