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Optics Express

Optics Express

  • Editor: J. H. Eberly
  • Vol. 5, Iss. 5 — Aug. 30, 1999
  • pp: 120–124
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Asymptotic light field in the presence of a bubble-layer

Piotr J. Flatau, Jacek Piskozub, J. Ronald, and V. Zaneveld  »View Author Affiliations


Optics Express, Vol. 5, Issue 5, pp. 120-124 (1999)
http://dx.doi.org/10.1364/OE.5.000120


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Abstract

We report that the submerged microbubbles are an efficient source of diffuse radiance and may contribute to a rapid transition to the diffuse asymptotic regime. In this asymptotic regime an average cosine is easily predictable and measurable.

© Optical Society of America

1 Introduction

2 Results

There is limited knowledge [5

5. D. Stramski. Gas microbubbles: An assessment of their significance to light scattering in quiescent seas. In Ocean optics XII : 13–15 June 1994, Bergen, Norway, Jules S. Jaffe, editor, Proc. SPIEv. 2258, 704–710 (Bellingham, Wash., USA, 1994).

7

7. Curtis D. Mobley. Light and water : radiative transfer in natural waters (Academic Press, San Diego, 1994).

] about the radiative transfer properties of bubble clouds, their inherent optical properties, and their global climatology. Recently, we reported [8

8. P. J. Flatau, M. K. Flatau, J. R. V. Zaneveld, and C. Mobley. “Remote sensing of clouds of bubbles in seawater,” Q. J. Roy. Met. Soc. (1999)(to be published).

] on the influence of submerged bubble clouds within the water on the remote sensing reflectance. Individual bubble clouds persist for several minutes and are generated by breaking waves. There is evidence that at high wind speeds, separate bubble clouds near the surface coalesce, producing a stratus layer [9

9. D. M. Farmer and D. D. Lemon. “The influence of bubbles on ambient noise in the ocean at high wind speeds,” J. Phys. Oceanogr. 14, 1762–1778 (1984). [CrossRef]

,10

10. S. A. Thorpe. “Dynamical processes of transfer at the sea surface,” Prog. Oceanogr. 35, 315–352 (1995).

]. The majority of bubbles injected into the surface layers of natural waters are unstable, either dissolving due to enhanced surface tension and hydrostatic pressures or rising to the air-water interface where they break [11

11. B. D. Johnson and P. J. Wangersky. “Microbubbles: stabilization by monolayers of adsorbed particles,” J. Geophys. Res. 92, 14641–14647 (1987). [CrossRef]

]. However, bubbles with long residence times, i.e. stable microbubbles have been observed [12

12. H. Medwin. “In situ acoustic measurements of microbubbles at sea,” J. Geophys. Res. 82, 971–976, (1977). [CrossRef]

14

14. S. A. Thorpe, P. Bowyer, and D. K. Woolf. “Some factors affecting the size distributions of oceanic bubbles,” J. Phys. Oceanogr. 22, 382–389 (1992). [CrossRef]

]. One of the stabilization mechanisms [15

15. P. J. Mulhearn. “Distribution of microbubbles in coastal waters,” J. Geophys. Res. 86, 6429–6434 (1981). [CrossRef]

,11

11. B. D. Johnson and P. J. Wangersky. “Microbubbles: stabilization by monolayers of adsorbed particles,” J. Geophys. Res. 92, 14641–14647 (1987). [CrossRef]

] assumes that the surfactant material is a natural degradation product of chlorophyll, present in photosynthesizing algae.

Fig. 1. Bubble-stratus layer generated by breaking waves. Bubble population is continually replenished by wave activity (breaking waves at the surface) leading eventually to semi-homogeneous layer.

We consider three simple situations: (1) “infinitely” deep homogeneous ocean composed of CDOM, water, and particulates; (2) “infinitely” deep homogeneous ocean composed of the same CDOM, water, and particulates but also with bubbles; (3) two meter layer of bubbles and “background” CDOM, water, and particulates. In Fig. 1 the two-layer case is presented. (based on [10

10. S. A. Thorpe. “Dynamical processes of transfer at the sea surface,” Prog. Oceanogr. 35, 315–352 (1995).

]).

The background water, CDOM, and particulates are characterized by absorption and scattering coefficients a=0.1801m-1 and b=1.2525m-1 (thus we include water a and b). It corresponds to a chlorophyll concentration of 10mgm-3 at a wavelength λ=550nm. The particulate phase function is that of Petzold for turbid water [7

7. Curtis D. Mobley. Light and water : radiative transfer in natural waters (Academic Press, San Diego, 1994).

]. The phase function for bubbles was calculated by averaging from size parameter x=10-350, where x=2πr/λ, r is radius. The size distribution follows a r -4 law. A phase function was derived using the exact method for spheres and we assume a refractive index n=3/4. The scattering coefficient for bubbles is assumed to be b bubble=0.6181m-1. In our recent paper [8

8. P. J. Flatau, M. K. Flatau, J. R. V. Zaneveld, and C. Mobley. “Remote sensing of clouds of bubbles in seawater,” Q. J. Roy. Met. Soc. (1999)(to be published).

] we discuss in detail the climatology of bubble layer depth, vertical distribution, and dependence of depth on the wind speed. Assumptions made here are typical for 10m/s winds in bubble-stratus regime. The radiative transfer calculations were performed using the Monte-Carlo technique [16

16. J. Piskozub. Effects of surface waves and sea bottom on self-shading of in-water optical instruments. In Ocean optics XII : 13–15 June 1994, Bergen, Norway, Jules S. Jaffe, editor, Proc. SPIEv. 2258, 300–308 (Bellingham, Wash., USA, 1994).

]. The main results of this note are presented in Figs. 23. Fig. 2 shows the average cosine for the downwelling radiation for the three cases discussed above. In this figure “circles” are for the two-layer system. At first there a is rapid decrease in the value of the average cosine as initially collimated photons are efficiently scattered. After exiting the “bubble” layer the light is already diffuse and only a small adjustment is needed to attain an asymptotic regime for the “no bubbles” situation. This double-exponential transition mechanism seems to be particularly efficient in establishing the near-surface diffuse light field. Clearly, the depth of the bubble layer and the inherent optical properties will further determine this efficiency. Fig 3 shows µ¯(z), which contains contribution from the upwelling radiation as well. The upwelling radiance field adjusts gradually when photons interact with the “bubble” layer. There is preferential loss of photons traveling in the horizontal direction. This leads to more collimated light and increased average cosine close to the surface. In reference [8

8. P. J. Flatau, M. K. Flatau, J. R. V. Zaneveld, and C. Mobley. “Remote sensing of clouds of bubbles in seawater,” Q. J. Roy. Met. Soc. (1999)(to be published).

] we discuss in more detail the climatology of bubble clouds, which strongly depends on wind speed. The importance of bubbles on an asymptotic light field depends on wind speed, wind gustiness, and microphysical properties of bubbles. Incoming field projects and laboratory studies should give a clearer answer on the influence of bubbles on marine light fields. In summary we show that the submerged microbubbles are an efficient source of diffuse radiance and, if present, contribute to rapid transition to the diffuse asymptotic regime.

Fig. 2. Average cosine for downwelling radiation µ¯d(z) for (1) “infinitely” deep homogeneous ocean composed of CDOM, pure water, and particulates corresponding to chl=10mgm-3 (triangles); (2) “infinitely” deep homogeneous ocean with bubbles (cubes); (3) two-layer system composed of background CDOM, water, and particulates and 2m layer of submerged bubbles close to the surface (circles).
Fig. 3. Same as 2 but for the average cosine µ¯(z).

Acknowledgements

References and links

1.

J. R. V. Zaneveld. “An asymptotic closure theory for irradiance in the sea and its inversion to obtain the inherent optical properties,” Limnol. Oceanogr. 34,1442–1452 (1989). [CrossRef]

2.

N. J. McCormick. “Mathematical models for the mean cosine of irradiance and the diffuse attenuation coefficient,” Limnol. Oceanogr. 40, 1013–1018 (1995). [CrossRef]

3.

T. T. Bannister. “Model of the mean cosine of underwater radiance and estimation of underwater scalar irradiance,” Limnol. Oceanogr. 37.773–780 (1992). [CrossRef]

4.

J. Berwald, D. Stramski, C. D. Mobley, and D. A. Kiefer. “Influences of absorption and scattering on vertical changes in the average cosine of the underwater light field,” Limnology and Oceanography 40, 1347–1357 (1995). [CrossRef]

5.

D. Stramski. Gas microbubbles: An assessment of their significance to light scattering in quiescent seas. In Ocean optics XII : 13–15 June 1994, Bergen, Norway, Jules S. Jaffe, editor, Proc. SPIEv. 2258, 704–710 (Bellingham, Wash., USA, 1994).

6.

R. Frouin, M. Schwindling, and P.-Y. Deschamps. “Spectral reflectance of sea foam in the visible and near-infrared: In situ measurements and remote sensing implications,” J. Geophys. Res. 101, 14361–14371 (1996). [CrossRef]

7.

Curtis D. Mobley. Light and water : radiative transfer in natural waters (Academic Press, San Diego, 1994).

8.

P. J. Flatau, M. K. Flatau, J. R. V. Zaneveld, and C. Mobley. “Remote sensing of clouds of bubbles in seawater,” Q. J. Roy. Met. Soc. (1999)(to be published).

9.

D. M. Farmer and D. D. Lemon. “The influence of bubbles on ambient noise in the ocean at high wind speeds,” J. Phys. Oceanogr. 14, 1762–1778 (1984). [CrossRef]

10.

S. A. Thorpe. “Dynamical processes of transfer at the sea surface,” Prog. Oceanogr. 35, 315–352 (1995).

11.

B. D. Johnson and P. J. Wangersky. “Microbubbles: stabilization by monolayers of adsorbed particles,” J. Geophys. Res. 92, 14641–14647 (1987). [CrossRef]

12.

H. Medwin. “In situ acoustic measurements of microbubbles at sea,” J. Geophys. Res. 82, 971–976, (1977). [CrossRef]

13.

K. Isao, S. Hara, K. Terauchi, and K. Kogure. “Role of sub-micrometre particles in the ocean,” Nature 345, 242–244 (1990). [CrossRef]

14.

S. A. Thorpe, P. Bowyer, and D. K. Woolf. “Some factors affecting the size distributions of oceanic bubbles,” J. Phys. Oceanogr. 22, 382–389 (1992). [CrossRef]

15.

P. J. Mulhearn. “Distribution of microbubbles in coastal waters,” J. Geophys. Res. 86, 6429–6434 (1981). [CrossRef]

16.

J. Piskozub. Effects of surface waves and sea bottom on self-shading of in-water optical instruments. In Ocean optics XII : 13–15 June 1994, Bergen, Norway, Jules S. Jaffe, editor, Proc. SPIEv. 2258, 300–308 (Bellingham, Wash., USA, 1994).

OCIS Codes
(010.4450) Atmospheric and oceanic optics : Oceanic optics
(290.4210) Scattering : Multiple scattering

ToC Category:
Research Papers

History
Original Manuscript: August 10, 1999
Published: August 30, 1999

Citation
Piotr Flatau, Jacek Piskozub, and J. Ronald Zaneveld, "Asymptotic light field in the presence of a bubble-layer," Opt. Express 5, 120-124 (1999)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-5-5-120


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References

  1. J. R. V. Zaneveld. "An asymptotic closure theory for irradiance in the sea and its inversion to obtain the inherent optical properties," Limnol. Oceanogr. 34,1442-1452 (1989). [CrossRef]
  2. N. J. McCormick. "Mathematical models for the mean cosine of irradiance and the diffuse attenuation coefficient," Limnol. Oceanogr. 40, 1013-1018 (1995). [CrossRef]
  3. T. T. Bannister. "Model of the mean cosine of underwater radiance and estimation of underwater scalar irradiance," Limnol. Oceanogr. 37. 773-780 (1992). [CrossRef]
  4. J. Berwald, D. Stramski, C. D. Mobley, and D. A. Kiefer. "Influences of absorption and scattering on vertical changes in the average cosine of the underwater light field," Limnology and Oceanography 40, 1347-1357 (1995). [CrossRef]
  5. D. Stramski. Gas microbubbles: An assessment of their significance to light scattering in quiescent seas. In Ocean optics XII : 13-15 June 1994, Bergen, Norway, Jules S. Jaffe, editor, Proc. SPIE v. 2258, 704-710 (Bellingham, Wash., USA, 1994).
  6. R. Frouin, M. Schwindling, and P.-Y. Deschamps. "Spectral reflectance of sea foam in the visible and near-infrared: In situ measurements and remote sensing implications," J. Geophys. Res. 101, 14361-14371 (1996). [CrossRef]
  7. Curtis D. Mobley. Light and water : radiative transfer in natural waters (Academic Press, San Diego, 1994).
  8. P. J. Flatau, M. K. Flatau, J. R. V. Zaneveld, and C. Mobley. "Remote sensing of clouds of bubbles in seawater," Q. J. Roy. Met. Soc. (1999)(to be published).
  9. D. M. Farmer and D. D. Lemon. "The influence of bubbles on ambient noise in the ocean at high wind speeds," J. Phys. Oceanogr. 14, 1762-1778 (1984). [CrossRef]
  10. S. A. Thorpe. "Dynamical processes of transfer at the sea surface," Prog. Oceanogr. 35, 315-352 (1995).
  11. B. D. Johnson and P. J. Wangersky. "Microbubbles: stabilization by monolayers of adsorbed particles," J. Geophys. Res. 92, 14641-14647 (1987). [CrossRef]
  12. H. Medwin. "In situ acoustic measurements of microbubbles at sea," J. Geophys. Res. 82, 971-976, (1977). [CrossRef]
  13. K. Isao, S. Hara, K. Terauchi, and K. Kogure. "Role of sub-micrometre particles in the ocean," Nature 345, 242-244 (1990). [CrossRef]
  14. S. A. Thorpe, P. Bowyer, and D. K. Woolf. "Some factors affecting the size distributions of oceanic bubbles," J. Phys. Oceanogr. 22, 382-389 (1992). [CrossRef]
  15. P. J. Mulhearn. "Distribution of microbubbles in coastal waters," J. Geophys. Res. 86, 6429-6434 (1981). [CrossRef]
  16. J. Piskozub. Effects of surface waves and sea bottom on self-shading of in-water optical instruments. In Ocean optics XII : 13-15 June 1994, Bergen, Norway, Jules S. Jaffe, editor, Proc. SPIE v. 2258, 300-308 (Bellingham, Wash., USA, 1994).

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