Abstract

We study the change in the behavior of the modulation transfer function and resolution with changing properties of a turbulent medium. It is shown that the form and the behavior of the functions under study undergo significant changes at the transition from Kolmogorov’s to a helical type of turbulent medium. These changes should be taken into account in developing models of electromagnetic radiation propagation through a medium as well as in interpreting experimental data.

© 2002 Optical Society of America

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References

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  1. V. I. Tatarsky, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  2. A. Brissaud, U. Frisch, J. Leorat, M. Lesieur, A. Mazure, “Helicity cascades in fully developed isotropic turbulence,” Phys. Fluids 16, 1366–1367 (1973).
    [CrossRef]
  3. S. S. Moiseev, O. G. Chkhetiani, “Helical scaling in turbulence,” JETP 83, 192–198 (1996).
  4. J. J. Moreau, “Constants d’un ilot tourbillonnaire en fluide parfait barotrope,” C. R. Acad. Sci. Paris 252, 2810–2812 (1961).
  5. F. Krause, K.-H. Raedler, Mean-Field Magnetohydrodynamics and Dynamo Theory (Pergamon, Oxford, UK, 1980).
  6. H. Branover, O. Chkhetiani, A. Eidelman, E. Golbraikh, S. Moiseev, “Chiral phenomena in MHD and MHD-like media,” Magnetohydrodynamics 37, 31–37 (2001).
  7. H. Branover, A. Eidelman, E. Golbraikh, S. Moiseev, Turbulence and Structures (Academic, New York, 1999).
  8. S. Moiseev, H. Branover, A. Eidelman, “Helical turbulence and study of atmospheric and MHD laboratory flows,” in Progress in Turbulence Research, H. Branover, Y. Unger, eds. (American Institute of Aeronautics and Astronautics, Washington, D.C., 1998), pp. 225–242.
  9. H. Branover, A. Eidelman, E. Golbraikh, “Recent results in MHD turbulence studies and similarities between MHD and atmospheric turbulence,” in Proceedings of the 4th International PAMIR Conference on Magnetohydrodynamics at Dawn of Third Millennium, A. Alemany, H. Branover, O. Lielausis, eds. (Institut National Polytechnique de Grenoble, Grenoble, France, 2000), pp. 9–14.
  10. A. Alemany, R. Moreau, P. L. Sulem, U. Frisch, “Influence of an external magnetic field on homogeneous MHD turbulence,” J. Mecanique 18, 277–313 (1979).
  11. S. I. Vainshtein, Ya. B. Zeldovich, A. A. Ruzmaikin, Turbulent Dynamo in Astrophysics (Nauka, Moscow, 1980).
  12. D. K. Lilly, “The structure, energetics and propagation of rotating convective storms. Part II: helicity and storm stabilization,” J. Atmos. Sci. 43, 126–140 (1986).
    [CrossRef]
  13. O. Chkhetiani, S. Moiseev, E. Golbraikh, “Helicity generation in turbulent MHD flows,” Zh. Eksp. Teor. Fiz. 114, 946–955 (1998).
  14. D. L. Fried, “Limiting resolution looking down through the atmosphere,” J. Opt. Soc. Am. 56, 1380–1384 (1966).
    [CrossRef]
  15. D. L. Fried, “Optical resolution through a randomly inhomogeneous medium for very long and short exposition,” J. Opt. Soc. Am. 56, 1372–1379 (1966).
    [CrossRef]
  16. D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am. 55, 1427–1435 (1965).
    [CrossRef]
  17. D. L. Fried, Corrections to “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am. 56, 410 (1966).

2001

H. Branover, O. Chkhetiani, A. Eidelman, E. Golbraikh, S. Moiseev, “Chiral phenomena in MHD and MHD-like media,” Magnetohydrodynamics 37, 31–37 (2001).

1998

O. Chkhetiani, S. Moiseev, E. Golbraikh, “Helicity generation in turbulent MHD flows,” Zh. Eksp. Teor. Fiz. 114, 946–955 (1998).

1996

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

1986

D. K. Lilly, “The structure, energetics and propagation of rotating convective storms. Part II: helicity and storm stabilization,” J. Atmos. Sci. 43, 126–140 (1986).
[CrossRef]

1979

A. Alemany, R. Moreau, P. L. Sulem, U. Frisch, “Influence of an external magnetic field on homogeneous MHD turbulence,” J. Mecanique 18, 277–313 (1979).

1973

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

1966

1965

1961

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

Alemany, A.

A. Alemany, R. Moreau, P. L. Sulem, U. Frisch, “Influence of an external magnetic field on homogeneous MHD turbulence,” J. Mecanique 18, 277–313 (1979).

Branover, H.

H. Branover, O. Chkhetiani, A. Eidelman, E. Golbraikh, S. Moiseev, “Chiral phenomena in MHD and MHD-like media,” Magnetohydrodynamics 37, 31–37 (2001).

H. Branover, A. Eidelman, E. Golbraikh, “Recent results in MHD turbulence studies and similarities between MHD and atmospheric turbulence,” in Proceedings of the 4th International PAMIR Conference on Magnetohydrodynamics at Dawn of Third Millennium, A. Alemany, H. Branover, O. Lielausis, eds. (Institut National Polytechnique de Grenoble, Grenoble, France, 2000), pp. 9–14.

S. Moiseev, H. Branover, A. Eidelman, “Helical turbulence and study of atmospheric and MHD laboratory flows,” in Progress in Turbulence Research, H. Branover, Y. Unger, eds. (American Institute of Aeronautics and Astronautics, Washington, D.C., 1998), pp. 225–242.

H. Branover, A. Eidelman, E. Golbraikh, S. Moiseev, Turbulence and Structures (Academic, New York, 1999).

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]

Chkhetiani, O.

H. Branover, O. Chkhetiani, A. Eidelman, E. Golbraikh, S. Moiseev, “Chiral phenomena in MHD and MHD-like media,” Magnetohydrodynamics 37, 31–37 (2001).

O. Chkhetiani, S. Moiseev, E. Golbraikh, “Helicity generation in turbulent MHD flows,” Zh. Eksp. Teor. Fiz. 114, 946–955 (1998).

Chkhetiani, O. G.

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

Eidelman, A.

H. Branover, O. Chkhetiani, A. Eidelman, E. Golbraikh, S. Moiseev, “Chiral phenomena in MHD and MHD-like media,” Magnetohydrodynamics 37, 31–37 (2001).

H. Branover, A. Eidelman, E. Golbraikh, “Recent results in MHD turbulence studies and similarities between MHD and atmospheric turbulence,” in Proceedings of the 4th International PAMIR Conference on Magnetohydrodynamics at Dawn of Third Millennium, A. Alemany, H. Branover, O. Lielausis, eds. (Institut National Polytechnique de Grenoble, Grenoble, France, 2000), pp. 9–14.

H. Branover, A. Eidelman, E. Golbraikh, S. Moiseev, Turbulence and Structures (Academic, New York, 1999).

S. Moiseev, H. Branover, A. Eidelman, “Helical turbulence and study of atmospheric and MHD laboratory flows,” in Progress in Turbulence Research, H. Branover, Y. Unger, eds. (American Institute of Aeronautics and Astronautics, Washington, D.C., 1998), pp. 225–242.

Fried, D. L.

Frisch, U.

A. Alemany, R. Moreau, P. L. Sulem, U. Frisch, “Influence of an external magnetic field on homogeneous MHD turbulence,” J. Mecanique 18, 277–313 (1979).

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

Golbraikh, E.

H. Branover, O. Chkhetiani, A. Eidelman, E. Golbraikh, S. Moiseev, “Chiral phenomena in MHD and MHD-like media,” Magnetohydrodynamics 37, 31–37 (2001).

O. Chkhetiani, S. Moiseev, E. Golbraikh, “Helicity generation in turbulent MHD flows,” Zh. Eksp. Teor. Fiz. 114, 946–955 (1998).

H. Branover, A. Eidelman, E. Golbraikh, “Recent results in MHD turbulence studies and similarities between MHD and atmospheric turbulence,” in Proceedings of the 4th International PAMIR Conference on Magnetohydrodynamics at Dawn of Third Millennium, A. Alemany, H. Branover, O. Lielausis, eds. (Institut National Polytechnique de Grenoble, Grenoble, France, 2000), pp. 9–14.

H. Branover, A. Eidelman, E. Golbraikh, S. Moiseev, Turbulence and Structures (Academic, New York, 1999).

Krause, F.

F. Krause, K.-H. Raedler, Mean-Field Magnetohydrodynamics and Dynamo Theory (Pergamon, Oxford, UK, 1980).

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]

Lilly, D. K.

D. K. Lilly, “The structure, energetics and propagation of rotating convective storms. Part II: helicity and storm stabilization,” J. Atmos. Sci. 43, 126–140 (1986).
[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, O. Chkhetiani, A. Eidelman, E. Golbraikh, S. Moiseev, “Chiral phenomena in MHD and MHD-like media,” Magnetohydrodynamics 37, 31–37 (2001).

O. Chkhetiani, S. Moiseev, E. Golbraikh, “Helicity generation in turbulent MHD flows,” Zh. Eksp. Teor. Fiz. 114, 946–955 (1998).

S. Moiseev, H. Branover, A. Eidelman, “Helical turbulence and study of atmospheric and MHD laboratory flows,” in Progress in Turbulence Research, H. Branover, Y. Unger, eds. (American Institute of Aeronautics and Astronautics, Washington, D.C., 1998), pp. 225–242.

H. Branover, A. Eidelman, E. Golbraikh, S. Moiseev, Turbulence and Structures (Academic, New York, 1999).

Moiseev, S. S.

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. Paris 252, 2810–2812 (1961).

Moreau, R.

A. Alemany, R. Moreau, P. L. Sulem, U. Frisch, “Influence of an external magnetic field on homogeneous MHD turbulence,” J. Mecanique 18, 277–313 (1979).

Raedler, K.-H.

F. Krause, K.-H. Raedler, Mean-Field Magnetohydrodynamics and Dynamo Theory (Pergamon, Oxford, UK, 1980).

Ruzmaikin, A. A.

S. I. Vainshtein, Ya. B. Zeldovich, A. A. Ruzmaikin, Turbulent Dynamo in Astrophysics (Nauka, Moscow, 1980).

Sulem, P. L.

A. Alemany, R. Moreau, P. L. Sulem, U. Frisch, “Influence of an external magnetic field on homogeneous MHD turbulence,” J. Mecanique 18, 277–313 (1979).

Tatarsky, V. I.

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

Vainshtein, S. I.

S. I. Vainshtein, Ya. B. Zeldovich, A. A. Ruzmaikin, Turbulent Dynamo in Astrophysics (Nauka, Moscow, 1980).

Zeldovich, Ya. B.

S. I. Vainshtein, Ya. B. Zeldovich, A. A. Ruzmaikin, Turbulent Dynamo in Astrophysics (Nauka, Moscow, 1980).

C. R. Acad. Sci. Paris

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

J. Atmos. Sci.

D. K. Lilly, “The structure, energetics and propagation of rotating convective storms. Part II: helicity and storm stabilization,” J. Atmos. Sci. 43, 126–140 (1986).
[CrossRef]

J. Mecanique

A. Alemany, R. Moreau, P. L. Sulem, U. Frisch, “Influence of an external magnetic field on homogeneous MHD turbulence,” J. Mecanique 18, 277–313 (1979).

J. Opt. Soc. Am.

JETP

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

Magnetohydrodynamics

H. Branover, O. Chkhetiani, A. Eidelman, E. Golbraikh, S. Moiseev, “Chiral phenomena in MHD and MHD-like media,” Magnetohydrodynamics 37, 31–37 (2001).

Phys. Fluids

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

Zh. Eksp. Teor. Fiz.

O. Chkhetiani, S. Moiseev, E. Golbraikh, “Helicity generation in turbulent MHD flows,” Zh. Eksp. Teor. Fiz. 114, 946–955 (1998).

Other

S. I. Vainshtein, Ya. B. Zeldovich, A. A. Ruzmaikin, Turbulent Dynamo in Astrophysics (Nauka, Moscow, 1980).

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

F. Krause, K.-H. Raedler, Mean-Field Magnetohydrodynamics and Dynamo Theory (Pergamon, Oxford, UK, 1980).

H. Branover, A. Eidelman, E. Golbraikh, S. Moiseev, Turbulence and Structures (Academic, New York, 1999).

S. Moiseev, H. Branover, A. Eidelman, “Helical turbulence and study of atmospheric and MHD laboratory flows,” in Progress in Turbulence Research, H. Branover, Y. Unger, eds. (American Institute of Aeronautics and Astronautics, Washington, D.C., 1998), pp. 225–242.

H. Branover, A. Eidelman, E. Golbraikh, “Recent results in MHD turbulence studies and similarities between MHD and atmospheric turbulence,” in Proceedings of the 4th International PAMIR Conference on Magnetohydrodynamics at Dawn of Third Millennium, A. Alemany, H. Branover, O. Lielausis, eds. (Institut National Polytechnique de Grenoble, Grenoble, France, 2000), pp. 9–14.

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Figures (2)

Fig. 1
Fig. 1

MTF dependencies on x=λRk/d for the values d/r0=0.5 and 2.

Fig. 2
Fig. 2

Dependence of normalized R values on d/r0. Curve A, long-exposure results; curve B, short-exposure near-field results; curve C, short-exposure far-field results. For the sake of comparison, the respective values for Kolmogorov’s case15 are given (points A0, B0, C0).

Equations (29)

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

D(r)r2/3.
D(r)r4/3,
DPS(r)r1/3.
H=V(v·w)dV,
Cn(r, s)=n(r1)n(r2),
Dn(r, s)=2[Cn(0, s)-Cn(r, s)],
Dn(r, s)=1π 0k21-sin(kr)krCˆn(k, s)dk
Dn(r, s)=CN2(s)r2/3,
Dn(r, s)=CN2(s)r1/3,
Cˆn(k, s)=4.47CN2(s)r10/3.
D(r)=k122π 0zds0Cˆn(κ1/2, s)[1-J0(κ1/2rs/s)]dκ,
D(r)=1.46k12r4/30zCN2(s)(s/z)4/3ds.
MTFLE(k)=MTF0(k)exp[-12Dˆn(λRk)],
MTFSE(k)=MTF0(k)exp[-12Dˆn(λRk)-λRka2],
MTF0(x)=2π[arccos x-x(1-x2)1/2],x10,x>1,
a2=64d4 0dr[FC(r, d)-FL(r, d)]Dϕ(r)dr
FC(r, d)=1π r arccos(r/d)-2 rd 1-rd21/2,
FL(r, d)=1π r arccos(r/d)-14 rd-8rd2×1-rd21/2,
(farfield)Dϕ12Dˆn(r),d(Lλ)1/2,
(nearfield)DϕDˆn(r),d(Lλ)1/2,
(aλkR)2=1.062·A(λRk/r0)4/3(λRk/d)2/3(nearfield)
=1.0622·A(λRk/r0)4/3(λRk/d)2/3,(farfield)
Dˆn(r)=Ar4/3.
Dˆn(r)=αrr04/36.1rr04/3,
MTFSEnfMTF0(k)exp{-3.05(λRk/r0)3/2×[1-(λRk/d)2/3]},
MTFSEffMTF0(k)exp{-3.05(λRk/r0)4/3×[1-12(λRk/d)2/3},
RL=dr0201xdx[arccos(x)-x(1-x2)1/2]×exp-3.05dr04/3x4/3,
Rnf=dr0201xdx[arccos(x)-x(1-x2)1/2]×exp-3.05dr04/3x4/3(1-x2/3),
Rff=dr0201xdx[arccos(x)-x(1-x2)1/2]×exp-3.05dr04/3x4/31-12x2/3,

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