Abstract

Lidar is one of few remote sensing methods available to researchers to sense below the oceanic air-surface. We present polarimetric lidar measurements of turbulence in a laboratory generated turbulent flow. We found that the nearforward light depolarization characterized by the depolarization rate γ(z), varies with the turbulent flow parameter: χ(z)(z)1/4, where χ(z) and (z) are the respective depth dependent, temperature variance, and turbulent kinetic energy dissipation rates. The presence of particles in the flow modifies the values of γ in such a way that the ratio γ(z)/α(z) becomes independent of the particle concentration and depends only on χ(z)(z)1/4. We posit that the mechanism of light depolarization in turbulent flow with particles is forward scattered light interaction between turbulent refractive index inhomogeneities and flow particles. Such interactions result so that the observed depolarization rate, γ(z), is much larger than expected from ‘pure’ turbulent flow. Our observations open up the fascinating possibility of using lidar for turbulence measurements of aquatic flows.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. D. Bogucki and G. Spiers, “What percentage of the oceanic mixed layer is accessible to marine lidar? Global and the Gulf of Mexico prospective,” Opt. Express 21, 23997–24014 (2013).
    [Crossref] [PubMed]
  2. M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
    [Crossref]
  3. J. H. Churnside, R. D. Marchbanks, J. H. Lee, J. A. Shaw, A. Weidemann, and P. L. Donaghay, “Airborne lidar detection and characterization of internal waves in a shallow fjord,” J. Appl. Remote Sens. 6, 063611 (2012).
    [Crossref]
  4. J. H. Churnside, “Airborne lidar estimates of photosynthesis profiles,” in “Geoscience and Remote Sensing Symposium (IGARSS), 2016 IEEE International,” (IEEE, 2016), pp. 3777–3780.
  5. J. H. Churnside and R. D. Marchbanks, “Inversion of oceanographic profiling lidars by a perturbation to a linear regression,” Appl. Opt. 56, 5228–5233 (2017).
    [Crossref] [PubMed]
  6. J. H. Churnside, “Polarization effects on oceanographic lidar,” Opt. Express 16, 1196–1207 (2008).
    [Crossref] [PubMed]
  7. J. H. Churnside, “Ecosystem studies using profiling polarization lidar,” in “Geoscience and Remote Sensing Symposium (IGARSS), 2014 IEEE International,” (IEEE, 2014), pp. 2699–2702.
  8. D. Bogucki, J. A. Domaradzki, D. Stramski, and R. Zaneveld, “Comparison of nearforward scattering on turbulence and particles,” Appl. Opt. 37, 4669–4677 (1998).
    [Crossref]
  9. D. Bogucki, J. Domaradzki, C. Anderson, H. Wijesekera, R. 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]
  10. C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic Press, 1994).
  11. V. I. Tatarski, Wave Propagation in Turbulent Media (McGraw-Hill, 1961).
  12. J. Strohbehn and S. 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]
  13. B. Crosignani, P. Di Porto, and S. F. Clifford, “Coupled-mode theory approach to depolarization associated with propagation in turbulent media,” Appl. Opt. 27, 2183–2186 (1988).
    [Crossref] [PubMed]
  14. M. Charnotskii, “Propagation of polarized waves in inhomogeneous media,” J. Opt. Soc. Am. A 33, 1385–1394 (2016).
    [Crossref]
  15. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press, 1978).
  16. S. Woods, J. Piskozub, W. Freda, M. Jonasz, and D. Bogucki, “Laboratory measurements of light beam depolarization on turbulent convective flow,” Appl. Opt. 49, 3545–3551 (2010).
    [Crossref] [PubMed]
  17. R.-L. Heng, K. C. Sy, and L. Pilon, “Absorption and scattering by bispheres, quadspheres, and circular rings of spheres and their equivalent coated spheres,” J. Opt. Soc. Am. A 32, 46–60 (2015).
    [Crossref]
  18. E. Calzavarini, M. Kerscher, D. Lohse, and F. Toschi, “Dimensionality and morphology of particle and bubble clusters in turbulent flow,” J. Fluid Mech. 607, 13–24 (2008).
    [Crossref]
  19. J. P. Salazar, J. De Jong, L. Cao, S. H. Woodward, H. Meng, and L. R. Collins, “Experimental and numerical investigation of inertial particle clustering in isotropic turbulence,” J. Fluid Mech. 600, 245–256 (2008).
    [Crossref]
  20. T. Zhou, R. Antonia, L. Danaila, and F. Anselmet, “Transport equations for the mean energy and temperature dissipation rates in grid turbulence,” Exp. Fluids 28, 143–151 (2000).
    [Crossref]
  21. D. J. Bogucki, K. Huguenard, B. Haus, T. Özgökmen, A. Reniers, and N. Laxague, “Scaling laws for the upper ocean temperature dissipation rate,” Geophys. Res. Lett. 42, 839–846 (2015).
    [Crossref]
  22. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 2008).
  23. M. Stephens, C. Weimer, E. Saiki, and M. Lieber, “On-orbit models of the CALIOP lidar for enabling future mission design,” in “Proc. SPIE” 7807, 7807–7820 (2010).

2017 (1)

2016 (1)

2015 (2)

R.-L. Heng, K. C. Sy, and L. Pilon, “Absorption and scattering by bispheres, quadspheres, and circular rings of spheres and their equivalent coated spheres,” J. Opt. Soc. Am. A 32, 46–60 (2015).
[Crossref]

D. J. Bogucki, K. Huguenard, B. Haus, T. Özgökmen, A. Reniers, and N. Laxague, “Scaling laws for the upper ocean temperature dissipation rate,” Geophys. Res. Lett. 42, 839–846 (2015).
[Crossref]

2013 (2)

D. Bogucki and G. Spiers, “What percentage of the oceanic mixed layer is accessible to marine lidar? Global and the Gulf of Mexico prospective,” Opt. Express 21, 23997–24014 (2013).
[Crossref] [PubMed]

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
[Crossref]

2012 (1)

J. H. Churnside, R. D. Marchbanks, J. H. Lee, J. A. Shaw, A. Weidemann, and P. L. Donaghay, “Airborne lidar detection and characterization of internal waves in a shallow fjord,” J. Appl. Remote Sens. 6, 063611 (2012).
[Crossref]

2010 (1)

2008 (3)

J. H. Churnside, “Polarization effects on oceanographic lidar,” Opt. Express 16, 1196–1207 (2008).
[Crossref] [PubMed]

E. Calzavarini, M. Kerscher, D. Lohse, and F. Toschi, “Dimensionality and morphology of particle and bubble clusters in turbulent flow,” J. Fluid Mech. 607, 13–24 (2008).
[Crossref]

J. P. Salazar, J. De Jong, L. Cao, S. H. Woodward, H. Meng, and L. R. Collins, “Experimental and numerical investigation of inertial particle clustering in isotropic turbulence,” J. Fluid Mech. 600, 245–256 (2008).
[Crossref]

2007 (1)

2000 (1)

T. Zhou, R. Antonia, L. Danaila, and F. Anselmet, “Transport equations for the mean energy and temperature dissipation rates in grid turbulence,” Exp. Fluids 28, 143–151 (2000).
[Crossref]

1998 (1)

1988 (1)

1967 (1)

J. Strohbehn and S. 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.

Anselmet, F.

T. Zhou, R. Antonia, L. Danaila, and F. Anselmet, “Transport equations for the mean energy and temperature dissipation rates in grid turbulence,” Exp. Fluids 28, 143–151 (2000).
[Crossref]

Antonia, R.

T. Zhou, R. Antonia, L. Danaila, and F. Anselmet, “Transport equations for the mean energy and temperature dissipation rates in grid turbulence,” Exp. Fluids 28, 143–151 (2000).
[Crossref]

Behrenfeld, M. J.

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
[Crossref]

Bogucki, D.

Bogucki, D. J.

D. J. Bogucki, K. Huguenard, B. Haus, T. Özgökmen, A. Reniers, and N. Laxague, “Scaling laws for the upper ocean temperature dissipation rate,” Geophys. Res. Lett. 42, 839–846 (2015).
[Crossref]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 2008).

Calzavarini, E.

E. Calzavarini, M. Kerscher, D. Lohse, and F. Toschi, “Dimensionality and morphology of particle and bubble clusters in turbulent flow,” J. Fluid Mech. 607, 13–24 (2008).
[Crossref]

Cao, L.

J. P. Salazar, J. De Jong, L. Cao, S. H. Woodward, H. Meng, and L. R. Collins, “Experimental and numerical investigation of inertial particle clustering in isotropic turbulence,” J. Fluid Mech. 600, 245–256 (2008).
[Crossref]

Charnotskii, M.

Churnside, J. H.

J. H. Churnside and R. D. Marchbanks, “Inversion of oceanographic profiling lidars by a perturbation to a linear regression,” Appl. Opt. 56, 5228–5233 (2017).
[Crossref] [PubMed]

J. H. Churnside, R. D. Marchbanks, J. H. Lee, J. A. Shaw, A. Weidemann, and P. L. Donaghay, “Airborne lidar detection and characterization of internal waves in a shallow fjord,” J. Appl. Remote Sens. 6, 063611 (2012).
[Crossref]

J. H. Churnside, “Polarization effects on oceanographic lidar,” Opt. Express 16, 1196–1207 (2008).
[Crossref] [PubMed]

J. H. Churnside, “Ecosystem studies using profiling polarization lidar,” in “Geoscience and Remote Sensing Symposium (IGARSS), 2014 IEEE International,” (IEEE, 2014), pp. 2699–2702.

J. H. Churnside, “Airborne lidar estimates of photosynthesis profiles,” in “Geoscience and Remote Sensing Symposium (IGARSS), 2016 IEEE International,” (IEEE, 2016), pp. 3777–3780.

Clifford, S.

J. Strohbehn and S. 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]

Clifford, S. F.

Collins, L. R.

J. P. Salazar, J. De Jong, L. Cao, S. H. Woodward, H. Meng, and L. R. Collins, “Experimental and numerical investigation of inertial particle clustering in isotropic turbulence,” J. Fluid Mech. 600, 245–256 (2008).
[Crossref]

Crosignani, B.

Dall’Olmo, G.

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
[Crossref]

Danaila, L.

T. Zhou, R. Antonia, L. Danaila, and F. Anselmet, “Transport equations for the mean energy and temperature dissipation rates in grid turbulence,” Exp. Fluids 28, 143–151 (2000).
[Crossref]

De Jong, J.

J. P. Salazar, J. De Jong, L. Cao, S. H. Woodward, H. Meng, and L. R. Collins, “Experimental and numerical investigation of inertial particle clustering in isotropic turbulence,” J. Fluid Mech. 600, 245–256 (2008).
[Crossref]

Di Porto, P.

Domaradzki, J.

Domaradzki, J. A.

Donaghay, P. L.

J. H. Churnside, R. D. Marchbanks, J. H. Lee, J. A. Shaw, A. Weidemann, and P. L. Donaghay, “Airborne lidar detection and characterization of internal waves in a shallow fjord,” J. Appl. Remote Sens. 6, 063611 (2012).
[Crossref]

Freda, W.

Hair, J. W.

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
[Crossref]

Haus, B.

D. J. Bogucki, K. Huguenard, B. Haus, T. Özgökmen, A. Reniers, and N. Laxague, “Scaling laws for the upper ocean temperature dissipation rate,” Geophys. Res. Lett. 42, 839–846 (2015).
[Crossref]

Heng, R.-L.

Hostetler, C. A.

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
[Crossref]

Hu, Y.

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
[Crossref]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 2008).

Huguenard, K.

D. J. Bogucki, K. Huguenard, B. Haus, T. Özgökmen, A. Reniers, and N. Laxague, “Scaling laws for the upper ocean temperature dissipation rate,” Geophys. Res. Lett. 42, 839–846 (2015).
[Crossref]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press, 1978).

Jonasz, M.

Kerscher, M.

E. Calzavarini, M. Kerscher, D. Lohse, and F. Toschi, “Dimensionality and morphology of particle and bubble clusters in turbulent flow,” J. Fluid Mech. 607, 13–24 (2008).
[Crossref]

Laxague, N.

D. J. Bogucki, K. Huguenard, B. Haus, T. Özgökmen, A. Reniers, and N. Laxague, “Scaling laws for the upper ocean temperature dissipation rate,” Geophys. Res. Lett. 42, 839–846 (2015).
[Crossref]

Lee, J. H.

J. H. Churnside, R. D. Marchbanks, J. H. Lee, J. A. Shaw, A. Weidemann, and P. L. Donaghay, “Airborne lidar detection and characterization of internal waves in a shallow fjord,” J. Appl. Remote Sens. 6, 063611 (2012).
[Crossref]

Lieber, M.

M. Stephens, C. Weimer, E. Saiki, and M. Lieber, “On-orbit models of the CALIOP lidar for enabling future mission design,” in “Proc. SPIE” 7807, 7807–7820 (2010).

Lohse, D.

E. Calzavarini, M. Kerscher, D. Lohse, and F. Toschi, “Dimensionality and morphology of particle and bubble clusters in turbulent flow,” J. Fluid Mech. 607, 13–24 (2008).
[Crossref]

Marchbanks, R. D.

J. H. Churnside and R. D. Marchbanks, “Inversion of oceanographic profiling lidars by a perturbation to a linear regression,” Appl. Opt. 56, 5228–5233 (2017).
[Crossref] [PubMed]

J. H. Churnside, R. D. Marchbanks, J. H. Lee, J. A. Shaw, A. Weidemann, and P. L. Donaghay, “Airborne lidar detection and characterization of internal waves in a shallow fjord,” J. Appl. Remote Sens. 6, 063611 (2012).
[Crossref]

Meng, H.

J. P. Salazar, J. De Jong, L. Cao, S. H. Woodward, H. Meng, and L. R. Collins, “Experimental and numerical investigation of inertial particle clustering in isotropic turbulence,” J. Fluid Mech. 600, 245–256 (2008).
[Crossref]

Mobley, C. D.

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic Press, 1994).

Moore, C.

Özgökmen, T.

D. J. Bogucki, K. Huguenard, B. Haus, T. Özgökmen, A. Reniers, and N. Laxague, “Scaling laws for the upper ocean temperature dissipation rate,” Geophys. Res. Lett. 42, 839–846 (2015).
[Crossref]

Pilon, L.

Piskozub, J.

Reniers, A.

D. J. Bogucki, K. Huguenard, B. Haus, T. Özgökmen, A. Reniers, and N. Laxague, “Scaling laws for the upper ocean temperature dissipation rate,” Geophys. Res. Lett. 42, 839–846 (2015).
[Crossref]

Rodier, S. D.

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
[Crossref]

Saiki, E.

M. Stephens, C. Weimer, E. Saiki, and M. Lieber, “On-orbit models of the CALIOP lidar for enabling future mission design,” in “Proc. SPIE” 7807, 7807–7820 (2010).

Salazar, J. P.

J. P. Salazar, J. De Jong, L. Cao, S. H. Woodward, H. Meng, and L. R. Collins, “Experimental and numerical investigation of inertial particle clustering in isotropic turbulence,” J. Fluid Mech. 600, 245–256 (2008).
[Crossref]

Shaw, J. A.

J. H. Churnside, R. D. Marchbanks, J. H. Lee, J. A. Shaw, A. Weidemann, and P. L. Donaghay, “Airborne lidar detection and characterization of internal waves in a shallow fjord,” J. Appl. Remote Sens. 6, 063611 (2012).
[Crossref]

Spiers, G.

Stephens, M.

M. Stephens, C. Weimer, E. Saiki, and M. Lieber, “On-orbit models of the CALIOP lidar for enabling future mission design,” in “Proc. SPIE” 7807, 7807–7820 (2010).

Stramski, D.

Strohbehn, J.

J. Strohbehn and S. 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]

Sy, K. C.

Tatarski, V. I.

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

Toschi, F.

E. Calzavarini, M. Kerscher, D. Lohse, and F. Toschi, “Dimensionality and morphology of particle and bubble clusters in turbulent flow,” J. Fluid Mech. 607, 13–24 (2008).
[Crossref]

Trepte, C. R.

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
[Crossref]

Weidemann, A.

J. H. Churnside, R. D. Marchbanks, J. H. Lee, J. A. Shaw, A. Weidemann, and P. L. Donaghay, “Airborne lidar detection and characterization of internal waves in a shallow fjord,” J. Appl. Remote Sens. 6, 063611 (2012).
[Crossref]

Weimer, C.

M. Stephens, C. Weimer, E. Saiki, and M. Lieber, “On-orbit models of the CALIOP lidar for enabling future mission design,” in “Proc. SPIE” 7807, 7807–7820 (2010).

Wijesekera, H.

Woods, S.

Woodward, S. H.

J. P. Salazar, J. De Jong, L. Cao, S. H. Woodward, H. Meng, and L. R. Collins, “Experimental and numerical investigation of inertial particle clustering in isotropic turbulence,” J. Fluid Mech. 600, 245–256 (2008).
[Crossref]

Zaneveld, R.

Zhou, T.

T. Zhou, R. Antonia, L. Danaila, and F. Anselmet, “Transport equations for the mean energy and temperature dissipation rates in grid turbulence,” Exp. Fluids 28, 143–151 (2000).
[Crossref]

Appl. Opt. (4)

Exp. Fluids (1)

T. Zhou, R. Antonia, L. Danaila, and F. Anselmet, “Transport equations for the mean energy and temperature dissipation rates in grid turbulence,” Exp. Fluids 28, 143–151 (2000).
[Crossref]

Geophys. Res. Lett. (2)

D. J. Bogucki, K. Huguenard, B. Haus, T. Özgökmen, A. Reniers, and N. Laxague, “Scaling laws for the upper ocean temperature dissipation rate,” Geophys. Res. Lett. 42, 839–846 (2015).
[Crossref]

M. J. Behrenfeld, Y. Hu, C. A. Hostetler, G. Dall’Olmo, S. D. Rodier, J. W. Hair, and C. R. Trepte, “Space-based lidar measurements of global ocean carbon stocks,” Geophys. Res. Lett. 40, 4355–4360 (2013).
[Crossref]

IEEE Trans. Antennas Propag. (1)

J. Strohbehn and S. 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. Appl. Remote Sens. (1)

J. H. Churnside, R. D. Marchbanks, J. H. Lee, J. A. Shaw, A. Weidemann, and P. L. Donaghay, “Airborne lidar detection and characterization of internal waves in a shallow fjord,” J. Appl. Remote Sens. 6, 063611 (2012).
[Crossref]

J. Fluid Mech. (2)

E. Calzavarini, M. Kerscher, D. Lohse, and F. Toschi, “Dimensionality and morphology of particle and bubble clusters in turbulent flow,” J. Fluid Mech. 607, 13–24 (2008).
[Crossref]

J. P. Salazar, J. De Jong, L. Cao, S. H. Woodward, H. Meng, and L. R. Collins, “Experimental and numerical investigation of inertial particle clustering in isotropic turbulence,” J. Fluid Mech. 600, 245–256 (2008).
[Crossref]

J. Opt. Soc. Am. A (2)

Opt. Express (3)

Other (7)

C. D. Mobley, Light and Water: Radiative Transfer in Natural Waters (Academic Press, 1994).

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

J. H. Churnside, “Ecosystem studies using profiling polarization lidar,” in “Geoscience and Remote Sensing Symposium (IGARSS), 2014 IEEE International,” (IEEE, 2014), pp. 2699–2702.

J. H. Churnside, “Airborne lidar estimates of photosynthesis profiles,” in “Geoscience and Remote Sensing Symposium (IGARSS), 2016 IEEE International,” (IEEE, 2016), pp. 3777–3780.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press, 1978).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 2008).

M. Stephens, C. Weimer, E. Saiki, and M. Lieber, “On-orbit models of the CALIOP lidar for enabling future mission design,” in “Proc. SPIE” 7807, 7807–7820 (2010).

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Figures (4)

Fig. 1
Fig. 1 A single backscattering event on a small spherical particle located at the distance z0 from the lidar. beam represents the incoming and sc the scattered lidar pulse. The solid angle Ω corresponds to the lidar receiver field of view.
Fig. 2
Fig. 2 Left: The USC water tank with the lidar beam (green) location. 1. Lidar beam entrance, 2. Laser Beam, 3. Test Section 4. Draining Reservoir 5. Filling Reservoir 6. Turbulence Generating Grid 7. Heater Grid. Right: Photo of a lidar pulse propagating along the tank center.
Fig. 3
Fig. 3 Lidar measured irradiance P c * ( z ) (left panel) and D ( z ) P x * ( z ) / P c * ( z ) (right panel) over the nominal interval. The parameters P c * ( z ) and D(z) were normalized to their respective values at a distance of 6.2m from the lidar. The least-square derived α and γ (Eq. (15) and Eq. (13)) are presented in Table 1.
Fig. 4
Fig. 4 Left: Lidar measured: γ/α derived from Eq. (15) and Eq. (13) (averaged over nominal interval). Black circles denote runs seeded with 10μm particles and red dots - water laden with tank debris particles. Right: Comparison of lidar measured γ (black symbols with run names) in our grid turbulence flow with the data of [16] from the convective turbulent flow (blue dots). All errors are reported as two standard deviations.

Tables (1)

Tables Icon

Table 1 Summary of all the experiment runs. The runs labeled with (*) - i.e.: (DEC31 runs) were carried out with the water containing polydisperse debris particles. Rest of the runs: the tank was filled with clean tap water and seeded with varying concentrations of monodisperse 10μm neutrally buoyant beads. Both dissipation parameters χ and were estimated at a distance of z1 = 6.3 m downstream from the grid. The mean polarized beam attenuation coefficient α and the mean depolarization rate γ correspond to their values over the nominal interval. The relative errors on and χ were 2σ/∊̄ = 0.6 and 2σχ/χ̄ = 1.2 respectively. All uncertainties are equal to two standard deviations - corresponding to a 95.5% confidence interval for the reported quantities.

Equations (18)

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

d P c d z = α ( z ) P c ( z ) + γ ( z ) P x ( z )
d P x d z = γ ( z ) P c ( z ) α ( z ) P x ( z ) ,
X ^ beam ( z 0 ) = e A ( z 0 ) T beam [ P c 0 P x 0 ] ; Where : T beam = [ cosh Γ ( z 0 ) sinh Γ ( z 0 ) sinh Γ ( z 0 ) cosh Γ ( z 0 ) ]
X ^ sc ( z 0 ) = T part ( z 0 ) X ^ beam ( z 0 ) ; where T part = [ β c ( π , z 0 ) β x ( π , z 0 ) β x ( π , z 0 ) β c ( π , z 0 ) ]
d X ^ sc d z = [ [ α ( z ) + 2 z z 0 ] γ ( z ) γ ( z ) [ α ( z ) + 2 z z 0 ] ] X ^ sc ( z ) .
X ^ ( z ) = e A 1 ( z ) 4 π ( z z 0 ) 2 T sc [ P c sc ( z 0 ) P x sc ( z 0 ) ] . Here : T sc [ cosh Γ 1 ( z ) sinh Γ 1 ( z ) sinh Γ 1 ( z ) cosh Γ 1 ( z ) ]
X ^ ( z 0 ) = π R t 2 4 π z 0 2 e 2 A ( z 0 ) T sc T part T beam X ^ 0 ,
D ( Z 0 ) = tanh { 2 Γ ( z 0 ) } + [ 1 tanh 2 { 2 Γ ( z 0 ) } ] δ + sinh { 2 Γ ( z 0 ) } cosh 3 { 2 Γ ( z 0 ) } δ 2 + O ( δ ) 3
1 2 d D ( z 0 ) d z 0 1 [ 1 tanh 2 { 2 Γ ( z 0 ) } ] 1 γ ( z 0 ) = 1 2 tanh { 2 Γ ( z 0 ) } δ + O ( δ ) 2 .
d D ( z 0 ) d z 0 = 2 δ 2 ( z 0 ) γ + d δ ( z 0 ) d z 0 + 2 γ + O ( γ 2 z 0 δ ( z 0 ) ) .
d D ( z 0 ) ¯ d z 0 = 2 δ 2 ( z 0 ) γ ¯ + d δ ¯ d z 0 + 2 γ
X ^ ( z 0 ) = R t 2 β c ( π , z 0 ) 4 z 0 2 e 2 A ( z 0 ) [ cosh { 2 Γ ( z 0 ) } sinh { 2 Γ ( z 0 ) } sinh { 2 Γ ( z 0 ) } cosh { 2 Γ ( z 0 ) } ] [ P c 0 P x 0 ] .
γ ( z 0 ) = 1 2 d D d z | z = z 0 1 [ 1 D 2 ( z 0 ) ] 1 2 d D d z | z = z 0 .
α ( z 0 ) = 1 2 P c ( z 0 ) d P c ( z ) d z | z = z 0 1 z 0 + γ ( z 0 ) D ( z 0 ) .
α ( z 0 ) = d d z { 1 2 log [ z 2 P c ( z ) ] } | z = z 0
[ P c * ( z 0 ) P x * ( z 0 ) ] = R t 2 β c ( π , z 0 ) 4 z 0 2 G ( z 0 ) e 2 A ( z 0 ) [ cosh { 2 Γ ( z 0 ) } sinh { 2 Γ ( z 0 ) } sinh { 2 Γ ( z 0 ) } cosh { 2 Γ ( z 0 ) } ] [ P c 0 * P x 0 * ] ;
α ( z 0 ) = d d z { 1 2 log [ z 2 P c * ( z ) G ( z ) ] } | z = z 0 .
= 0.90 U 3 ( z 1 / M ) n 1 , and : χ = 0.99 10 6 1 / U P 0 2 ( z 1 / M ) m 1 ,

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