Abstract

Laboratory measurements of light beam depolarization by a turbulent flow, corresponding to oceanic turbulence within the oceanic mixed layer, show that the depolarization rate (1×105m1 to 3×103m1) correlates with turbulence strength and is consistent with polarized lidar observations [Opt. Express , 16, 1196 (2008)]. These results imply that one should be able to characterize oceanic turbulence with polarimetric oceanic lidar measurements.

© 2010 Optical Society of America

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References

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    [CrossRef]
  2. D. J. Bogucki, J. A. Domaradzki, R. E. Ecke, and C. R. Truman, “Light scattering on oceanic turbulence,” Appl. Opt. 43, 5662–5668 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. A. Anis and J. Moum, “Surface wave-turbulence interactions. Scaling ε(z) near the sea surface,” J. Phys. Oceanogr. 25, 2025–2045 (1995).
    [CrossRef]
  13. J. W. Strohbehn, “Line-of-sight wave propagation through the turbulent atmosphere,” Proc. IEEE 56, 1301–1318 (1968).
    [CrossRef]
  14. A. D. Kim and M. Moscoso, “Influence of the refractive index on the depolarization of multiply scattered waves,” Phys. Rev. E 64, 026612 (2001).
    [CrossRef]
  15. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  16. L. F. Rojas-Ochoa, D. Lacoste, R. Lenke, P. Schurtenberger, and F. Scheffold, “Depolarization of backscattered linearly polarized light,” J. Opt. Soc. Am. A 21, 1799–1804 (2004).
    [CrossRef]
  17. J. A. Domaradzki and R. W. Metcalfe, “Direct numerical simulations of the effects of shear on turbulent Rayleigh–Bénard convection,” J. Fluid Mech. 193, 499–531 (1988).
    [CrossRef]
  18. D. J. Bogucki (Texas A&M University—Corpus Christi, 6300 Ocean Drive, HRI 102, Corpus Christi, Texas 78412), S. Woods, and J. A. Domaradzki are preparing a manuscript to be called “Laboratory measurements of energy and temperature dissipation rate for convective flows with Ra=4×106 to 109.”
  19. A. M. Fincham and G. R. Spedding, “Low cost, high resolution DPIV for measurement of turbulent fluid flow,” Exp. Fluids 23, 449–462 (1997).
    [CrossRef]
  20. D. J. Bogucki, J. A. Domaradzki, C. Anderson, H. W. Wijesekera, R. V. Zaneveld, and C. Moore, “Optical measurement of rates of dissipation of temperature variance due to oceanic turbulence,” Opt. Express 15, 7224–7230 (2007).
    [CrossRef] [PubMed]
  21. H. Hodara “Laser wave propagation through the atmosphere,” Proc. IEEE 54, 368–375 (1966).

2008 (1)

2007 (2)

2004 (2)

2003 (1)

2001 (1)

A. D. Kim and M. Moscoso, “Influence of the refractive index on the depolarization of multiply scattered waves,” Phys. Rev. E 64, 026612 (2001).
[CrossRef]

1998 (1)

1997 (2)

A. Hielscher, A. Eick, J. Mourant, D. Shen, J. Freyer, and I. Bigio, “Diffuse backscattering Mueller matrices of highly scattering media,” Opt. Express 1, 441–453 (1997).
[CrossRef] [PubMed]

A. M. Fincham and G. R. Spedding, “Low cost, high resolution DPIV for measurement of turbulent fluid flow,” Exp. Fluids 23, 449–462 (1997).
[CrossRef]

1995 (2)

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

J. S. Jaffe, “Monte Carlo modeling of underwater-image formation: validity of the linear and small-angle approximations,” Appl. Opt. 34, 5413–5421 (1995).
[CrossRef] [PubMed]

1993 (1)

1988 (1)

J. A. Domaradzki and R. W. Metcalfe, “Direct numerical simulations of the effects of shear on turbulent Rayleigh–Bénard convection,” J. Fluid Mech. 193, 499–531 (1988).
[CrossRef]

1987 (1)

1980 (1)

1968 (1)

J. W. Strohbehn, “Line-of-sight wave propagation through the turbulent atmosphere,” Proc. IEEE 56, 1301–1318 (1968).
[CrossRef]

1967 (1)

J. W. Strohbehn and S. F. Clifford, “Polarization and angle-of-arrival fluctuations for a plane wave propagated through a turbulent medium,” IEEE Trans. Antennas Propag. 15, 416–421 (1967).
[CrossRef]

Anderson, C.

Anis, A.

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

Asano, S.

Baum, B. A.

Bigio, I.

Bogucki, D. J.

Bohren, C. F.

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

Brown, J.

Carr, M.-E.

Churnside, J. H.

Clifford, S. F.

J. W. Strohbehn and S. F. Clifford, “Polarization and angle-of-arrival fluctuations for a plane wave propagated through a turbulent medium,” IEEE Trans. Antennas Propag. 15, 416–421 (1967).
[CrossRef]

Domaradzki, J. A.

D. J. Bogucki, J. A. Domaradzki, C. Anderson, H. W. Wijesekera, R. V. Zaneveld, and C. Moore, “Optical measurement of rates of dissipation of temperature variance due to oceanic turbulence,” Opt. Express 15, 7224–7230 (2007).
[CrossRef] [PubMed]

D. J. Bogucki, J. A. Domaradzki, R. E. Ecke, and C. R. Truman, “Light scattering on oceanic turbulence,” Appl. Opt. 43, 5662–5668 (2004).
[CrossRef] [PubMed]

D. J. Bogucki, J. A. Domaradzki, D. Stramski, and J. R. Zaneveld, “Comparison of near-forward light scattering on oceanic turbulence and particles,” Appl. Opt. 37, 4669–4677 (1998).
[CrossRef]

J. A. Domaradzki and R. W. Metcalfe, “Direct numerical simulations of the effects of shear on turbulent Rayleigh–Bénard convection,” J. Fluid Mech. 193, 499–531 (1988).
[CrossRef]

D. J. Bogucki (Texas A&M University—Corpus Christi, 6300 Ocean Drive, HRI 102, Corpus Christi, Texas 78412), S. Woods, and J. A. Domaradzki are preparing a manuscript to be called “Laboratory measurements of energy and temperature dissipation rate for convective flows with Ra=4×106 to 109.”

Ecke, R. E.

Eick, A.

Fincham, A. M.

A. M. Fincham and G. R. Spedding, “Low cost, high resolution DPIV for measurement of turbulent fluid flow,” Exp. Fluids 23, 449–462 (1997).
[CrossRef]

Freyer, J.

Herb, P.

Hielscher, A.

Hodara, H.

H. Hodara “Laser wave propagation through the atmosphere,” Proc. IEEE 54, 368–375 (1966).

Hostetler, C. A.

Hu, C.

Hu, Y. X.

Huffman, D. R.

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

Jaffe, J. S.

Kattawar, G. W.

Kim, A. D.

A. D. Kim and M. Moscoso, “Influence of the refractive index on the depolarization of multiply scattered waves,” Phys. Rev. E 64, 026612 (2001).
[CrossRef]

Lacoste, D.

Lenke, R.

Metcalfe, R. W.

J. A. Domaradzki and R. W. Metcalfe, “Direct numerical simulations of the effects of shear on turbulent Rayleigh–Bénard convection,” J. Fluid Mech. 193, 499–531 (1988).
[CrossRef]

Moore, C.

Moscoso, M.

A. D. Kim and M. Moscoso, “Influence of the refractive index on the depolarization of multiply scattered waves,” Phys. Rev. E 64, 026612 (2001).
[CrossRef]

Moum, J.

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

Mourant, J.

Parkin, M. E.

Piskozub, J.

Rojas-Ochoa, L. F.

Sato, M.

Scheffold, F.

Schurtenberger, P.

Shen, D.

Spedding, G. R.

A. M. Fincham and G. R. Spedding, “Low cost, high resolution DPIV for measurement of turbulent fluid flow,” Exp. Fluids 23, 449–462 (1997).
[CrossRef]

Spiers, G. D.

Spinrad, R. W.

Stramski, D.

Strohbehn, J. W.

J. W. Strohbehn, “Line-of-sight wave propagation through the turbulent atmosphere,” Proc. IEEE 56, 1301–1318 (1968).
[CrossRef]

J. W. Strohbehn and S. F. Clifford, “Polarization and angle-of-arrival fluctuations for a plane wave propagated through a turbulent medium,” IEEE Trans. Antennas Propag. 15, 416–421 (1967).
[CrossRef]

Truman, C. R.

Wei, H.

Wijesekera, H. W.

Winker, D. M.

Woods, S.

D. J. Bogucki (Texas A&M University—Corpus Christi, 6300 Ocean Drive, HRI 102, Corpus Christi, Texas 78412), S. Woods, and J. A. Domaradzki are preparing a manuscript to be called “Laboratory measurements of energy and temperature dissipation rate for convective flows with Ra=4×106 to 109.”

Yang, P.

Zaneveld, J. R.

Zaneveld, R. V.

Appl. Opt. (7)

Exp. Fluids (1)

A. M. Fincham and G. R. Spedding, “Low cost, high resolution DPIV for measurement of turbulent fluid flow,” Exp. Fluids 23, 449–462 (1997).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

J. W. Strohbehn and S. F. Clifford, “Polarization and angle-of-arrival fluctuations for a plane wave propagated through a turbulent medium,” IEEE Trans. Antennas Propag. 15, 416–421 (1967).
[CrossRef]

J. Fluid Mech. (1)

J. A. Domaradzki and R. W. Metcalfe, “Direct numerical simulations of the effects of shear on turbulent Rayleigh–Bénard convection,” J. Fluid Mech. 193, 499–531 (1988).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. Oceanogr. (1)

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

Opt. Express (4)

Phys. Rev. E (1)

A. D. Kim and M. Moscoso, “Influence of the refractive index on the depolarization of multiply scattered waves,” Phys. Rev. E 64, 026612 (2001).
[CrossRef]

Proc. IEEE (1)

J. W. Strohbehn, “Line-of-sight wave propagation through the turbulent atmosphere,” Proc. IEEE 56, 1301–1318 (1968).
[CrossRef]

Other (3)

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

D. J. Bogucki (Texas A&M University—Corpus Christi, 6300 Ocean Drive, HRI 102, Corpus Christi, Texas 78412), S. Woods, and J. A. Domaradzki are preparing a manuscript to be called “Laboratory measurements of energy and temperature dissipation rate for convective flows with Ra=4×106 to 109.”

H. Hodara “Laser wave propagation through the atmosphere,” Proc. IEEE 54, 368–375 (1966).

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Figures (6)

Fig. 1
Fig. 1

Depth dependence of the normalized copolarized, P C (solid curve), and cross-polarized, P X , power of an initially polarized beam, with beam attenuation α = 0.1 m 1 and depolarization rates: γ = 6 × 10 3 and 5 × 10 4 m 1 (dashed and dashed–dotted curves, respectively), representative of the oceanic mixed layer. Note that P C is nearly indistinguishable between the two cases.

Fig. 2
Fig. 2

Experimental setup: a linearly polarized He–Ne laser passes through a spatial filter to clean and expand the beam, a linear polarizer to clean the polarization of the beam, a turbulent Rayleigh–Bénard convective tank, a polarized beam splitter, and impinges upon a CCD camera. Each of the beams, P C and P X , illuminates one-half of the CCD array to allow for simultaneous measurement of both orthogonal polarizations.

Fig. 3
Fig. 3

Measured one-dimensional Batchelor dissipation spectrum for R a = 3.3 × 10 9 used to determine the temperature dissipation rate of the flow.

Fig. 4
Fig. 4

Velocity fields averaged over 20 min : (a) horizontal, u and (b) vertical, w , velocity flow fields for R a = 3.3 × 10 9 .

Fig. 5
Fig. 5

Transects of u rms (circles) and w rms (crosses) ( mm / s ) through the convective cell center for R a = 3.3 × 10 9 : (a) vertical and (b) horizontal.

Fig. 6
Fig. 6

Experimentally measured mean depolarization rate, γ , with error bars representing 1 standard deviation of the ensemble mean, as a function of (a) the Rayleigh number and (b) ( χ / ν ) 1 / 2 η B 1 / 2 , a combination of turbulent parameters of the flow, where χ is the temperature dissipation rate, ν is the kinematic viscosity, and η B is the Batchelor length scale. The line corresponds to a linear fit to the experimental data. The data were collected from a turbulent convective flow of purified drinking water over a range of turbulent strengths, corresponding to values observed within the oceanic mixed layer.

Equations (9)

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d P C d z = α P C + γ P X , d P X d z = α P X + γ P C .
P C = P CO e α z cosh ( γ z ) , P X = P CO e α z sinh ( γ z ) .
γ = 1 2 z ln ( P C + P X P C P X ) .
R a = g α T Δ T d 3 D ν ,
N u = H d κ Δ T ,
P C = P CO e α z cosh ( γ z ) + P XO e α z sinh ( γ z ) , P X = P CO e α z sinh ( γ z ) + P XO e α z cosh ( γ z ) ,
γ = 1 2 z [ ln ( P CO P XO P CO + P XO ) + ln ( P C + P X P C P X ) ] .
γ = 1 2 z [ ln ( R O 1 R O + 1 ) + ln ( R + 1 R 1 ) ] .
d γ γ = 2 R O ( R O 2 1 ) [ ln ( R O 1 R O + 1 ) + ln ( R + 1 R 1 ) ] d R O R O 2 R ( R 2 1 ) [ ln ( R O 1 R O + 1 ) + ln ( R + 1 R 1 ) ] d R R .

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