OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 35, Iss. 33 — Nov. 20, 1996
  • pp: 6504–6513

Lévy statistics of light scattering in turbulent mixing layers

J. A. Viecelli  »View Author Affiliations

Applied Optics, Vol. 35, Issue 33, pp. 6504-6513 (1996)

View Full Text Article

Enhanced HTML    Acrobat PDF (375 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Experimental evidence and computational evidence suggest that the distribution of random segment lengths defined by the intersections of ray paths with the contorted and folded interface between two fluids mixed by turbulence follows a probability distribution with a Lévy law tail. Assuming that the two fluids have different optical properties, one finds that the statistics of light scattered by the mixing interface reflect the probability distribution for the random distances between the intersection points of straight ray paths with the interface. Examples of light-scattering calculations for limiting cases, including the planetary albedo problem and imaging through a transparent mixing layer, are discussed.

© 1996 Optical Society of America

Original Manuscript: November 17, 1995
Revised Manuscript: April 30, 1996
Published: November 20, 1996

J. A. Viecelli, "Lévy statistics of light scattering in turbulent mixing layers," Appl. Opt. 35, 6504-6513 (1996)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. R. Sreenivasan, C. Meneveau, “The fractal facets of turbulence,” J. Fluid Mech. 173, 357–386 (1986). [CrossRef]
  2. R. R. Prasad, K. R. Sreenivasan, “Quantitative three-dimensional imaging and the structure of passive scalar fields in fully turbulent flows,” J. Fluid Mech. 216, 1–34 (1990). [CrossRef]
  3. G. F. Lane-Serff, “Investigation of the fractal structure of jets and plumes,” J. Fluid Mech. 249, 521–534 (1993). [CrossRef]
  4. P. Flohr, D. Olivari, “Fractal and multifractal characteristics of a scalar dispersed in a turbulent jet,” Physica D 76, 278–290 (1994). [CrossRef]
  5. P. Constantin, I. Procaccia, K. R. Sreenivasan, “Fractal geometry of isoscalar surfaces in turbulence: theory and experiments,” Phys. Rev. Lett. 67, 1739–1742 (1991). [CrossRef] [PubMed]
  6. S. Lovejoy, “Area-perimeter relation for rain and cloud areas,” Science 216, 185–187 (1982). [CrossRef] [PubMed]
  7. P. L. Miller, P. E. Dimotakis, “Stochastic geometric properties of scalar interfaces in turbulent jets,” Phys. Fluids A 3, 168–177 (1991). [CrossRef]
  8. P. Lévy, Théorie de l’Addition des Variables Aléatoires (Gauthier-Villars, Paris, 1937).
  9. B. V. Gnedenko, A. N. Kolmogorov, Limit Distributions for Sums of Random Variables (Addison-Wesley, Cambridge, 1954), p. 162.
  10. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  11. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  12. G. C. Pomraning, “A model for interface intensities in stochastic particle transport,” J. Quant. Spectrosc. Radiat. Transfer 46, 221–236 (1991). [CrossRef]
  13. G. C. Pomraning, “Radiative transfer in random media with scattering,” J. Quant. Spectrosc. Radiat. Transfer 40, 479–487 (1988). [CrossRef]
  14. G. C. Pomraning, “Classic transport problems in binary homogeneous markov statistical mixtures,” Transp. Theory Stat. 17, 595–613 (1988). [CrossRef]
  15. C. D. Levermore, J. Wong, G. C. Pomraning, “Renewal theory for transport processes in binary statistical mixtures,” J. Math. Phys. 29, 995–1004 (1988). [CrossRef]
  16. D. Vanderhaegen, “Impact of a mixing structure on radiative transfer in random media,” J. Quant. Spectrosc. Radiat. Transfer 39, 333–337 (1988). [CrossRef]
  17. D. Vanderhaegen, “Radiative transfer in statistically heterogeneous mixtures,” J. Quant. Spectrosc. Radiat. Transfer 36, 557–561 (1986). [CrossRef]
  18. C. D. Levermore, G. C. Pomraning, D. L. Sanzo, J. Wong, “Linear transport theory in a random medium,” J. Math. Phys. 27, 2526–2536 (1986). [CrossRef]
  19. J. Klafter, G. Zumofen, M. F. Shlesinger, “Fractal description of anomalous diffusion in dynamical systems,” Fractals 1, 111–126 (1993). [CrossRef]
  20. W. M. Irvine, “Diffuse reelection and transmission by clouds and dust layers,” J. Quant. Spectrosc. Radiat. Transfer 8, 471–485 (1968). [CrossRef]
  21. H. C. van de Hulst, Multiple Light Scattering Tables, Formulas and Application (Academic, New York, 1980).
  22. W. E. Meador, W. R. Weaver, “Two-stream approximations to radiative transfer in planetary atmospheres: a unified description of existing methods and a new improvement,” J. Atmos. Sci. 37, 630–643 (1980). [CrossRef]
  23. A. Ben-David, “Multiple-scattering transmission and an effective average photon path length of a plane-parallel beam in a homogeneous medium,” Appl. Opt. 34, 2802–2810 (1995). [CrossRef] [PubMed]
  24. D. Mihalas, Stellar Atmospheres, 2nd ed. (Freeman, San Francisco, Calif., 1978).
  25. F. H. Shu, The Physics of Astrophysics, Vol. 1. Radiation (University Science, Mill Valley, Calif., 1991).
  26. W. B. Rossow, R. A. Schiffer, “ISCCP cloud data products,” Bull. Am. Meteorol. Soc. 72, 2–20 (1991). [CrossRef]
  27. V. R. Taylor, L. L. Stowe, “Reflectance characteristics of uniform Earth and cloud surfaces derived from NIMBUS-7 ERB,” J. Geophys. Res. 89, 4987–4996 (1984). [CrossRef]
  28. G. L. Stephens, “Radiative transfer through arbitrarily shaped optical media. Part II: group theory and simple closures,” J. Atmos. Sci. 45, 1837–1848 (1988). [CrossRef]
  29. V. Ramanathan, R. D. Cess, E. F. Harrison, P. Minnis, B. R. Barkstrom, E. Ahmad, D. Hartmann, “Cloud-radiative forcing and climate: results from the earth radiation budget experiment,” Science 243, 57–63 (1989). [CrossRef] [PubMed]
  30. B. R. Barkstrom, E. F. Harrison, R. B. Lee, the ERBE Science Team, “Climate and the Earth’s radiation budget,” Eos 71, 297–304 (1990). [CrossRef]
  31. R. M. Cameron, M. Bader, R. E. Mobley, “Design and operation of the NASA 91.5 cm airborne telescope,” Appl. Opt. 10, 2011–2015 (1971). [CrossRef] [PubMed]
  32. J. E. Craig, C. Allen, “Aero-optical turbulent boundary layer/shear layer experiment on the KC-135 aircraft revisited,” Opt. Eng. 24, 446–454 (1985).
  33. E. P. Magee, B. M. Welsh, “Characterization of laboratory-generated turbulence by optical phase measurements,” Opt. Eng. 33, 3810–3817 (1994). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited