Abstract

We examine and compare near-forward light scattering that is caused by turbulence and typical particulate assemblages in the ocean. The near-forward scattering by particles was calculated using Mie theory for homogeneous spheres and particle size distributions representative of natural assemblages in the ocean. Direct numerical simulations of a passive scalar with Prandtl number 7 mixed by homogeneous turbulence were used to represent temperature fluctuations and resulting inhomogeneities in the refractive index of water. Light scattering on the simulated turbulent flow was calculated using the geometrical-optics approximation. We found that the smallest temperature scales contribute the most to scattering, and that scattering on turbulence typically dominates over scattering on particles for small angles as large as 0.1°. The scattering angle deviation that is due to turbulence for a light beam propagating over a 0.25-m path length in the oceanic water can be as large as 0.1°. In addition, we carried out a preliminary laboratory experiment that illustrates the differences in the near-forward scattering on refractive-index inhomogeneities and particles.

© 1998 Optical Society of America

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  7. R. C. Honey, G. P. Sorensen, “Optical absorbtion and turbulence induced narrow-angle forward scatter in the sea,” in Electromagnetics of the Sea (Advisory Group for Aerospace Research and Development, NATO, 92 Neuilly-Sur-Seine, France, 1970), pp. 39.1–39.7.
  8. J. Zaneveld, R. Hodgson, G. F. Beardsley, “Image degradation over sea water paths—a review,” in Electromagnetics of the Sea (Advisory Group for Aerospace Research and Development, NATO, 92 Neuilly-Sur-Seine, France, 1973).
  9. R. J. Hill, “Optical propagation in turbulent water,” J. Opt. Soc. Am. 68, 1067–1071 (1978).
    [CrossRef]
  10. R. A. Elliot, J. R. Kerr, P. A. Pincus, “Optical propagation in laboratory-generated turbulence,” Appl. Opt. 18, 3315–3323 (1979).
    [CrossRef]
  11. D. Bogucki, A. Domaradzki, P. K. Yeung, “Direct numerical simulations of passive scalars with Pr > 1 advected by turbulent flow,” J. Fluid Mech. 343, 111–130 (1997).
    [CrossRef]
  12. A. Morel, Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates: a tentative assessment of their scattering role in oceanic waters compared to those of bacterial and algal cell,” J. Mar. Res. 49, 1–26 (1991).
    [CrossRef]
  13. D. Stramski, D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
    [CrossRef]
  14. N. G. Jerlov, Marine Optics (Elsevier, New York, 1976).
  15. R. W. Preisendorfer, Hydrologic Optics, Vol. 1, (National Oceanic and Atmosphere Administration, Washington, D.C., 1976).
  16. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 530.
  17. A. Morel, A. Bricaud, “Inherent properties of algal cells including picoplankton: theoretical and experimental results,” in Photosynthetic Picoplankton, T. Platt, W. Li, eds., Can. J. Fisheries Aquatic Sci.214, 521–559 (1986).
  18. J. B. Riley, “Laser diffraction particle sizing: sampling and inversion,” Ph.D. dissertation (MIT–Woods Hole Joint Program in Ocean Engineering, Cambridge, Mass., 1987).
  19. H. R. Gordon, O. B. Brown, “A theoretical model of light scattering by Sargasso Sea particulates,” Limnol. Oceanogr. 17, 826–832 (1972).
    [CrossRef]
  20. I. N. McCave, “Vertical flux of particles in the ocean,” Deep-Sea Res. 22, 491–502 (1975).
  21. M. Jonasz, “Particle-size distributions in the Baltic,” Tellus 35B, 346–358 (1983).
    [CrossRef]
  22. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, England, 1964).
  23. J. Moum, College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oreg. 37331 (personal communication, 1994).
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    [CrossRef]
  26. D. J. Bogucki, A. Domaradzki, R. Zaneveld, T. Dickey, “Light scattering induced by turbulent flow,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 247–255 (1994).
    [CrossRef]
  27. M. J. Kennish, Practical Handbook of Marine Sciences (CRC Press, New York, 1989).
  28. T. M. Dillon, D. R. Caldwell, “The Batchelor spectrum and dissipation in the upper ocean,” J. Geophys. Res. 85, 1910–1916 (1980).
    [CrossRef]
  29. D. M. Farmer, J. R. Gemmrich, “Measurements of temperature fluctuations in breaking surface waves,” J. Phys. Oceanogr. 26, 816–825 (1996).
    [CrossRef]
  30. T. M. Dillon, “The energetics of overturning structures: implications for the theory of fossil turbulence,” J. Phys. Oceanogr. 14, 541–549 (1984).
    [CrossRef]
  31. A. Anis, J. N. Moum, “Surface wave-turbulence interactions: scaling ∊(z) near the sea surface,” J. Phys. Oceanogr. 25, 2025–2045 (1995).
    [CrossRef]
  32. S. M. Rytov, Y. A. Kravtsov, V. I. Tatarski, Principles of Statistical Radiophysics (Springer-Verlag, Berlin, 1989).
  33. A. M. Obukhov, “Structure of the temperature field in turbulent flows,” Izv. Akad. Nauk SSSR Ser. Geogr. Geofiz. 13, 58–69 (1949).
  34. S. Corrsin, “On the spectrum of isotropic temperature fluctuations in isotropic turbulence,” J. Appl. Phys. 22, 452–469 (1951).
  35. R. Kraichnan, “Small-scale structure of a scalar field convected by turbulence,” Phys. Fluids 11, 941–945 (1968).
    [CrossRef]
  36. R. C. Mjølsness, “Diffusion of a passive scalar at large Prandtl number according to the abridged Lagrangian interaction theory,” Phys. Fluids 18, 1393–1394 (1975).
    [CrossRef]
  37. R. J. Hill, “Models of the scalar spectrum for turbulent advection,” J. Fluid Mech. 88, 541–562 (1978).
    [CrossRef]
  38. A. S. Gurvich, M. A. Kallistrova, F. E. Martvel, “An investigation of strong fluctuations of light intensity in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20, 705–715 (1976).
    [CrossRef]
  39. J. A. Domaradzki, W. Liu, C. Hartel, L. Kleiser, “Energy-transfer in numerically simulated wall-bounded turbulent flows,” Phys. Fluids 6, 1583–1599 (1994).
    [CrossRef]

1997 (1)

D. Bogucki, A. Domaradzki, P. K. Yeung, “Direct numerical simulations of passive scalars with Pr > 1 advected by turbulent flow,” J. Fluid Mech. 343, 111–130 (1997).
[CrossRef]

1996 (1)

D. M. Farmer, J. R. Gemmrich, “Measurements of temperature fluctuations in breaking surface waves,” J. Phys. Oceanogr. 26, 816–825 (1996).
[CrossRef]

1995 (1)

A. Anis, J. N. Moum, “Surface wave-turbulence interactions: scaling ∊(z) near the sea surface,” J. Phys. Oceanogr. 25, 2025–2045 (1995).
[CrossRef]

1994 (1)

J. A. Domaradzki, W. Liu, C. Hartel, L. Kleiser, “Energy-transfer in numerically simulated wall-bounded turbulent flows,” Phys. Fluids 6, 1583–1599 (1994).
[CrossRef]

1991 (2)

A. Morel, Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates: a tentative assessment of their scattering role in oceanic waters compared to those of bacterial and algal cell,” J. Mar. Res. 49, 1–26 (1991).
[CrossRef]

D. Stramski, D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
[CrossRef]

1984 (1)

T. M. Dillon, “The energetics of overturning structures: implications for the theory of fossil turbulence,” J. Phys. Oceanogr. 14, 541–549 (1984).
[CrossRef]

1983 (1)

M. Jonasz, “Particle-size distributions in the Baltic,” Tellus 35B, 346–358 (1983).
[CrossRef]

1980 (1)

T. M. Dillon, D. R. Caldwell, “The Batchelor spectrum and dissipation in the upper ocean,” J. Geophys. Res. 85, 1910–1916 (1980).
[CrossRef]

1979 (1)

1978 (3)

1976 (1)

A. S. Gurvich, M. A. Kallistrova, F. E. Martvel, “An investigation of strong fluctuations of light intensity in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20, 705–715 (1976).
[CrossRef]

1975 (2)

R. C. Mjølsness, “Diffusion of a passive scalar at large Prandtl number according to the abridged Lagrangian interaction theory,” Phys. Fluids 18, 1393–1394 (1975).
[CrossRef]

I. N. McCave, “Vertical flux of particles in the ocean,” Deep-Sea Res. 22, 491–502 (1975).

1972 (1)

H. R. Gordon, O. B. Brown, “A theoretical model of light scattering by Sargasso Sea particulates,” Limnol. Oceanogr. 17, 826–832 (1972).
[CrossRef]

1971 (1)

1968 (1)

R. Kraichnan, “Small-scale structure of a scalar field convected by turbulence,” Phys. Fluids 11, 941–945 (1968).
[CrossRef]

1964 (1)

1951 (1)

S. Corrsin, “On the spectrum of isotropic temperature fluctuations in isotropic turbulence,” J. Appl. Phys. 22, 452–469 (1951).

1949 (1)

A. M. Obukhov, “Structure of the temperature field in turbulent flows,” Izv. Akad. Nauk SSSR Ser. Geogr. Geofiz. 13, 58–69 (1949).

Ahn, Y.-H.

A. Morel, Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates: a tentative assessment of their scattering role in oceanic waters compared to those of bacterial and algal cell,” J. Mar. Res. 49, 1–26 (1991).
[CrossRef]

Anis, A.

A. Anis, J. N. Moum, “Surface wave-turbulence interactions: scaling ∊(z) near the sea surface,” J. Phys. Oceanogr. 25, 2025–2045 (1995).
[CrossRef]

Beardsley, G. F.

J. Zaneveld, R. Hodgson, G. F. Beardsley, “Image degradation over sea water paths—a review,” in Electromagnetics of the Sea (Advisory Group for Aerospace Research and Development, NATO, 92 Neuilly-Sur-Seine, France, 1973).

Bogucki, D.

D. Bogucki, A. Domaradzki, P. K. Yeung, “Direct numerical simulations of passive scalars with Pr > 1 advected by turbulent flow,” J. Fluid Mech. 343, 111–130 (1997).
[CrossRef]

Bogucki, D. J.

D. J. Bogucki, A. Domaradzki, R. Zaneveld, T. Dickey, “Light scattering induced by turbulent flow,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 247–255 (1994).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 530.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, England, 1964).

Bricaud, A.

A. Morel, A. Bricaud, “Inherent properties of algal cells including picoplankton: theoretical and experimental results,” in Photosynthetic Picoplankton, T. Platt, W. Li, eds., Can. J. Fisheries Aquatic Sci.214, 521–559 (1986).

Brown, O. B.

H. R. Gordon, O. B. Brown, “A theoretical model of light scattering by Sargasso Sea particulates,” Limnol. Oceanogr. 17, 826–832 (1972).
[CrossRef]

Caldwell, D. R.

T. M. Dillon, D. R. Caldwell, “The Batchelor spectrum and dissipation in the upper ocean,” J. Geophys. Res. 85, 1910–1916 (1980).
[CrossRef]

Corrsin, S.

S. Corrsin, “On the spectrum of isotropic temperature fluctuations in isotropic turbulence,” J. Appl. Phys. 22, 452–469 (1951).

Dickey, T.

D. J. Bogucki, A. Domaradzki, R. Zaneveld, T. Dickey, “Light scattering induced by turbulent flow,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 247–255 (1994).
[CrossRef]

Dillon, T. M.

T. M. Dillon, “The energetics of overturning structures: implications for the theory of fossil turbulence,” J. Phys. Oceanogr. 14, 541–549 (1984).
[CrossRef]

T. M. Dillon, D. R. Caldwell, “The Batchelor spectrum and dissipation in the upper ocean,” J. Geophys. Res. 85, 1910–1916 (1980).
[CrossRef]

Domaradzki, A.

D. Bogucki, A. Domaradzki, P. K. Yeung, “Direct numerical simulations of passive scalars with Pr > 1 advected by turbulent flow,” J. Fluid Mech. 343, 111–130 (1997).
[CrossRef]

D. J. Bogucki, A. Domaradzki, R. Zaneveld, T. Dickey, “Light scattering induced by turbulent flow,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 247–255 (1994).
[CrossRef]

Domaradzki, J. A.

J. A. Domaradzki, W. Liu, C. Hartel, L. Kleiser, “Energy-transfer in numerically simulated wall-bounded turbulent flows,” Phys. Fluids 6, 1583–1599 (1994).
[CrossRef]

Elliot, R. A.

Farmer, D. M.

D. M. Farmer, J. R. Gemmrich, “Measurements of temperature fluctuations in breaking surface waves,” J. Phys. Oceanogr. 26, 816–825 (1996).
[CrossRef]

Gemmrich, J. R.

D. M. Farmer, J. R. Gemmrich, “Measurements of temperature fluctuations in breaking surface waves,” J. Phys. Oceanogr. 26, 816–825 (1996).
[CrossRef]

Gordon, H. R.

H. R. Gordon, O. B. Brown, “A theoretical model of light scattering by Sargasso Sea particulates,” Limnol. Oceanogr. 17, 826–832 (1972).
[CrossRef]

Gurvich, A. S.

A. S. Gurvich, M. A. Kallistrova, F. E. Martvel, “An investigation of strong fluctuations of light intensity in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20, 705–715 (1976).
[CrossRef]

Hartel, C.

J. A. Domaradzki, W. Liu, C. Hartel, L. Kleiser, “Energy-transfer in numerically simulated wall-bounded turbulent flows,” Phys. Fluids 6, 1583–1599 (1994).
[CrossRef]

Hill, R. J.

R. J. Hill, “Optical propagation in turbulent water,” J. Opt. Soc. Am. 68, 1067–1071 (1978).
[CrossRef]

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

Hodara, H.

H. Hodara, “Experimental results of small-angle scattering,” in Electromagnetics of the Sea (Advisory Group for Aerospace Research and Development, NATO, 92 Neuilly-Sur-Seine, France, 1973).

Hodgson, R.

J. Zaneveld, R. Hodgson, G. F. Beardsley, “Image degradation over sea water paths—a review,” in Electromagnetics of the Sea (Advisory Group for Aerospace Research and Development, NATO, 92 Neuilly-Sur-Seine, France, 1973).

Honey, R. C.

R. C. Honey, G. P. Sorensen, “Optical absorbtion and turbulence induced narrow-angle forward scatter in the sea,” in Electromagnetics of the Sea (Advisory Group for Aerospace Research and Development, NATO, 92 Neuilly-Sur-Seine, France, 1970), pp. 39.1–39.7.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 530.

Hufnagel, R. E.

Jerlov, N. G.

N. G. Jerlov, Marine Optics (Elsevier, New York, 1976).

Jonasz, M.

M. Jonasz, “Particle-size distributions in the Baltic,” Tellus 35B, 346–358 (1983).
[CrossRef]

Kallistrova, M. A.

A. S. Gurvich, M. A. Kallistrova, F. E. Martvel, “An investigation of strong fluctuations of light intensity in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20, 705–715 (1976).
[CrossRef]

Kennish, M. J.

M. J. Kennish, Practical Handbook of Marine Sciences (CRC Press, New York, 1989).

Kerr, J. R.

Kiefer, D. A.

D. Stramski, D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
[CrossRef]

Kleiser, L.

J. A. Domaradzki, W. Liu, C. Hartel, L. Kleiser, “Energy-transfer in numerically simulated wall-bounded turbulent flows,” Phys. Fluids 6, 1583–1599 (1994).
[CrossRef]

Kraichnan, R.

R. Kraichnan, “Small-scale structure of a scalar field convected by turbulence,” Phys. Fluids 11, 941–945 (1968).
[CrossRef]

Kravtsov, Y. A.

S. M. Rytov, Y. A. Kravtsov, V. I. Tatarski, Principles of Statistical Radiophysics (Springer-Verlag, Berlin, 1989).

Liu, W.

J. A. Domaradzki, W. Liu, C. Hartel, L. Kleiser, “Energy-transfer in numerically simulated wall-bounded turbulent flows,” Phys. Fluids 6, 1583–1599 (1994).
[CrossRef]

Martvel, F. E.

A. S. Gurvich, M. A. Kallistrova, F. E. Martvel, “An investigation of strong fluctuations of light intensity in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20, 705–715 (1976).
[CrossRef]

McCave, I. N.

I. N. McCave, “Vertical flux of particles in the ocean,” Deep-Sea Res. 22, 491–502 (1975).

Mjølsness, R. C.

R. C. Mjølsness, “Diffusion of a passive scalar at large Prandtl number according to the abridged Lagrangian interaction theory,” Phys. Fluids 18, 1393–1394 (1975).
[CrossRef]

Morel, A.

A. Morel, Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates: a tentative assessment of their scattering role in oceanic waters compared to those of bacterial and algal cell,” J. Mar. Res. 49, 1–26 (1991).
[CrossRef]

A. Morel, A. Bricaud, “Inherent properties of algal cells including picoplankton: theoretical and experimental results,” in Photosynthetic Picoplankton, T. Platt, W. Li, eds., Can. J. Fisheries Aquatic Sci.214, 521–559 (1986).

Moum, J.

J. Moum, College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oreg. 37331 (personal communication, 1994).

Moum, J. N.

A. Anis, J. N. Moum, “Surface wave-turbulence interactions: scaling ∊(z) near the sea surface,” J. Phys. Oceanogr. 25, 2025–2045 (1995).
[CrossRef]

Obukhov, A. M.

A. M. Obukhov, “Structure of the temperature field in turbulent flows,” Izv. Akad. Nauk SSSR Ser. Geogr. Geofiz. 13, 58–69 (1949).

Pak, H.

Petzold, T. H.

T. H. Petzold, “Volume scattering functions for selected ocean waters,” Tech. Rep. SIO Ref. 72, (University of California, San Diego, 1972), pp. 1–79.

Pincus, P. A.

Preisendorfer, R. W.

R. W. Preisendorfer, Hydrologic Optics, Vol. 1, (National Oceanic and Atmosphere Administration, Washington, D.C., 1976).

Riley, J. B.

J. B. Riley, “Laser diffraction particle sizing: sampling and inversion,” Ph.D. dissertation (MIT–Woods Hole Joint Program in Ocean Engineering, Cambridge, Mass., 1987).

Rytov, S. M.

S. M. Rytov, Y. A. Kravtsov, V. I. Tatarski, Principles of Statistical Radiophysics (Springer-Verlag, Berlin, 1989).

Shifrin, K. S.

K. S. Shifrin, Physical Optics of Ocean Water, AIP Translation Series (American Institute of Physics, New York, 1988).

Sorensen, G. P.

R. C. Honey, G. P. Sorensen, “Optical absorbtion and turbulence induced narrow-angle forward scatter in the sea,” in Electromagnetics of the Sea (Advisory Group for Aerospace Research and Development, NATO, 92 Neuilly-Sur-Seine, France, 1970), pp. 39.1–39.7.

Spinrad, R. W.

Stanley, N. R.

Stramski, D.

D. Stramski, D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
[CrossRef]

Tatarski, V. I.

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

S. M. Rytov, Y. A. Kravtsov, V. I. Tatarski, Principles of Statistical Radiophysics (Springer-Verlag, Berlin, 1989).

Wells, W. H.

W. H. Wells, “Theory of small-angle scattering,” in Electromagnetics of the Sea (Advisory Group for Aerospace Research and Development, NATO, 92 Neuilly-Sur-Seine, France, 1973).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, England, 1964).

Yeung, P. K.

D. Bogucki, A. Domaradzki, P. K. Yeung, “Direct numerical simulations of passive scalars with Pr > 1 advected by turbulent flow,” J. Fluid Mech. 343, 111–130 (1997).
[CrossRef]

Yura, H. T.

Zaneveld, J.

J. Zaneveld, R. Hodgson, G. F. Beardsley, “Image degradation over sea water paths—a review,” in Electromagnetics of the Sea (Advisory Group for Aerospace Research and Development, NATO, 92 Neuilly-Sur-Seine, France, 1973).

Zaneveld, J. R.

Zaneveld, R.

D. J. Bogucki, A. Domaradzki, R. Zaneveld, T. Dickey, “Light scattering induced by turbulent flow,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 247–255 (1994).
[CrossRef]

Appl. Opt. (3)

Deep-Sea Res. (1)

I. N. McCave, “Vertical flux of particles in the ocean,” Deep-Sea Res. 22, 491–502 (1975).

Izv. Akad. Nauk SSSR Ser. Geogr. Geofiz. (1)

A. M. Obukhov, “Structure of the temperature field in turbulent flows,” Izv. Akad. Nauk SSSR Ser. Geogr. Geofiz. 13, 58–69 (1949).

J. Appl. Phys. (1)

S. Corrsin, “On the spectrum of isotropic temperature fluctuations in isotropic turbulence,” J. Appl. Phys. 22, 452–469 (1951).

J. Fluid Mech. (2)

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

D. Bogucki, A. Domaradzki, P. K. Yeung, “Direct numerical simulations of passive scalars with Pr > 1 advected by turbulent flow,” J. Fluid Mech. 343, 111–130 (1997).
[CrossRef]

J. Geophys. Res. (1)

T. M. Dillon, D. R. Caldwell, “The Batchelor spectrum and dissipation in the upper ocean,” J. Geophys. Res. 85, 1910–1916 (1980).
[CrossRef]

J. Mar. Res. (1)

A. Morel, Y.-H. Ahn, “Optics of heterotrophic nanoflagellates and ciliates: a tentative assessment of their scattering role in oceanic waters compared to those of bacterial and algal cell,” J. Mar. Res. 49, 1–26 (1991).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Phys. Oceanogr. (3)

D. M. Farmer, J. R. Gemmrich, “Measurements of temperature fluctuations in breaking surface waves,” J. Phys. Oceanogr. 26, 816–825 (1996).
[CrossRef]

T. M. Dillon, “The energetics of overturning structures: implications for the theory of fossil turbulence,” J. Phys. Oceanogr. 14, 541–549 (1984).
[CrossRef]

A. Anis, J. N. Moum, “Surface wave-turbulence interactions: scaling ∊(z) near the sea surface,” J. Phys. Oceanogr. 25, 2025–2045 (1995).
[CrossRef]

Limnol. Oceanogr. (1)

H. R. Gordon, O. B. Brown, “A theoretical model of light scattering by Sargasso Sea particulates,” Limnol. Oceanogr. 17, 826–832 (1972).
[CrossRef]

Phys. Fluids (3)

J. A. Domaradzki, W. Liu, C. Hartel, L. Kleiser, “Energy-transfer in numerically simulated wall-bounded turbulent flows,” Phys. Fluids 6, 1583–1599 (1994).
[CrossRef]

R. Kraichnan, “Small-scale structure of a scalar field convected by turbulence,” Phys. Fluids 11, 941–945 (1968).
[CrossRef]

R. C. Mjølsness, “Diffusion of a passive scalar at large Prandtl number according to the abridged Lagrangian interaction theory,” Phys. Fluids 18, 1393–1394 (1975).
[CrossRef]

Prog. Oceanogr. (1)

D. Stramski, D. A. Kiefer, “Light scattering by microorganisms in the open ocean,” Prog. Oceanogr. 28, 343–383 (1991).
[CrossRef]

Radiophys. Quantum Electron. (1)

A. S. Gurvich, M. A. Kallistrova, F. E. Martvel, “An investigation of strong fluctuations of light intensity in a turbulent medium at a small wave parameter,” Radiophys. Quantum Electron. 20, 705–715 (1976).
[CrossRef]

Tellus (1)

M. Jonasz, “Particle-size distributions in the Baltic,” Tellus 35B, 346–358 (1983).
[CrossRef]

Other (17)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, England, 1964).

J. Moum, College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oreg. 37331 (personal communication, 1994).

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

D. J. Bogucki, A. Domaradzki, R. Zaneveld, T. Dickey, “Light scattering induced by turbulent flow,” in Ocean Optics XII, J. S. Jaffe, ed., Proc. SPIE2258, 247–255 (1994).
[CrossRef]

M. J. Kennish, Practical Handbook of Marine Sciences (CRC Press, New York, 1989).

T. H. Petzold, “Volume scattering functions for selected ocean waters,” Tech. Rep. SIO Ref. 72, (University of California, San Diego, 1972), pp. 1–79.

K. S. Shifrin, Physical Optics of Ocean Water, AIP Translation Series (American Institute of Physics, New York, 1988).

W. H. Wells, “Theory of small-angle scattering,” in Electromagnetics of the Sea (Advisory Group for Aerospace Research and Development, NATO, 92 Neuilly-Sur-Seine, France, 1973).

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Figures (9)

Fig. 1
Fig. 1

Differential size distribution of oceanic particles used in our Mie-scattering calculations.

Fig. 2
Fig. 2

Results of Mie-scattering calculations of near-forward VSF for the particle size distribution shown in Fig. 1. The VSF representing two upper size limits and two refractive indices are included.

Fig. 3
Fig. 3

Optical interpretation of the turbulent parameters χ and ∊.

Fig. 4
Fig. 4

Profiles of ∊, χ, temperature, and salinity from the Oregon coast (courtesy of J. Moum23).

Fig. 5
Fig. 5

Scatterplot of the observed ∊ versus χ in the data set from Fig. 4 (courtesy of J. Moum23).

Fig. 6
Fig. 6

Schematic diagram underlying calculations of turbulence-induced light scattering.

Fig. 7
Fig. 7

Value of kE θ(k) for different scales of the flow. The physical scale is inversely proportional to k. Area I roughly marks the contribution to the scattering from the large-scale structures [less than 8% as calculated from Eq. (15)]. Area II denotes the contribution from the smallest, and most effective in scattering, scales.

Fig. 8
Fig. 8

Simulated VSF for a range of turbulent flows in the ocean, for varying χ and constant ∊ as indicated. The particulate VSF is shown for comparison (solid curve).

Fig. 9
Fig. 9

(a) Light intensity distribution after propagation through water with no IRI and no beads. (b) Intensity distribution of scattered light by water with 10-μm beads. (c) and (d) Intensity distribution of scattered light by water with beads and turbulent IRI: two realizations a few seconds apart.

Tables (1)

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Table 1 Volume-Scattering Function (V0, α0) and the Standard Deviation of the Scattering Angle (〈α2〉)1/2

Equations (17)

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β α = dI α E 0 dV .
b = 2 π   0 π   β α sin α d α .
2 + κ 2 E = - 2 κ 2 n r E ,
E x ,   y ,   z = ψ x ,   y ,   z exp i κ z
2 i κ   ψ z + T 2 ψ + 2 κ 2 n ψ = 0 ,
ψ x ,   y ,   z = A 0 p exp i κ   0 z   n x ,   y ,   z d z ,   z L ,
Γ p = 0 L   n x ,   y ,   z d z
N = Γ x ,   Γ y ,   1
tan α = α x 2 + α y 2 1 / 2 ,
α x = Γ p x ;   α y = Γ p y .
α 2 α x 2 + α y 2 .
α x 2 = lim Δ x 0 Γ p 1 - Γ p 2 2 Δ x 2 .
Γ p 1 - Γ p 2 2     L   0   Φ nn k 1 - J 0 kp d k ,
α 2     L   0   E θ k k d k .
E θ k η B χ ν / 1 / 2 η B = q k η B - 1 × 1 + 6 q 1 / 2 k η B exp - 6 q 1 / 2 k η B ,
VSF ,   χ ,   α = V 0 ,   χ exp - α / α 0 ,   χ 2 ,
α 2 1 / 2 L ,   χ ,   = C 0.25 χ ,   L / L 0 1 / 2 ,

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