Abstract

Inhomogeneities in the refractive index induced by temperature fluctuations in turbulent flows have the effect of scattering light in near-forward angles. We have developed a method that extracts the rate of Temperature Variance Dissipation (TVD) and its spectrum from the properties of light scattering and have built an instrument - Optical Turbulence Sensor (OTS) - that implements the method. OTS uses a linear wavefront sensing Hartmann array and allows for nearly instantaneous measurements of temperature variance in turbulent flows. The instrument has been tested in an situ experiment carried out from a drifting vessel at a site off the coast of Newport, Oregon. Here we compare the temperature variance measured by OTS and its spectra with both theoretical predictions and with spectra obtained from a fast thermistor sensor.

©2007 Optical Society of America

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References

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  1. R. V. Ozmidov, “On the turbulent exchange in a stably stratified ocean.” Izvestiya, Atmospheric and Oceanic Physics 1, 493–497 (1965).
  2. W. H. Wells, “Theory of Small-angle Scattering,” (Advisory Group for Aerospace Research and Development, NATO, 92 Neuilly-Sur-Seine, France, 1973).
  3. D. Bogucki, J. A. Domaradzki, D. Stramski, and J. R. V. Zaneveld, “Comparison of nearforward scattering on turbulence and particles,” Applied Optics 37, 4669–4677 (1998).
    [Crossref]
  4. D. J. Bogucki, J. A. Domaradzki, R. E. Ecke, and R. C. Truman, “Light scattering on oceanic turbulence,” Appl. Opt. 43, 5662–5676 (2004).
    [Crossref] [PubMed]
  5. D. J. Bogucki, J. A. Domaradzki, R. E. Ecke, C. R. Truman, and J. R. V. Zaneveld, “Near-forward light scattering on oceaqnic turbulence and particulates: an experimental comparison,” vol. SPIE, Ocean Optics XIV (1998).
  6. R. G. Lueck, D. Huang, D. Newman, and J. Box, “Turbulence Measurement with a Moored Instrument,” Journal of Atmospheric and Oceanic Technology 14, 143–161 (1997).
    [Crossref]
  7. M. C. Gregg, “Uncertainties and Limitations in Measuring ε and χ.” Journal of Atmospheric and Oceanic Technology 16, 1484–1490 (1998).
  8. V. I. Tatarski, Wave Propagation in Turbulent Media (McGraw-Hill, New York, 1961).
  9. V. I. Tatarski, The effects of the turbulent atmosphere on the wave propagation (Israel program for Scientific Translation, Jerusalem, 1971).
  10. A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence (The MIT press, 1981).
  11. D. Bogucki, A. Domaradzki, and 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. D. Bogucki and J. Domaradzki, “Numerical study of light scattering by a boundary-layer flow,” Appl. Opt. 44, 5286–5291 (2005).
    [Crossref] [PubMed]

2005 (1)

2004 (1)

1998 (2)

M. C. Gregg, “Uncertainties and Limitations in Measuring ε and χ.” Journal of Atmospheric and Oceanic Technology 16, 1484–1490 (1998).

D. Bogucki, J. A. Domaradzki, D. Stramski, and J. R. V. Zaneveld, “Comparison of nearforward scattering on turbulence and particles,” Applied Optics 37, 4669–4677 (1998).
[Crossref]

1997 (2)

R. G. Lueck, D. Huang, D. Newman, and J. Box, “Turbulence Measurement with a Moored Instrument,” Journal of Atmospheric and Oceanic Technology 14, 143–161 (1997).
[Crossref]

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

1965 (1)

R. V. Ozmidov, “On the turbulent exchange in a stably stratified ocean.” Izvestiya, Atmospheric and Oceanic Physics 1, 493–497 (1965).

Bogucki, D.

D. Bogucki and J. Domaradzki, “Numerical study of light scattering by a boundary-layer flow,” Appl. Opt. 44, 5286–5291 (2005).
[Crossref] [PubMed]

D. Bogucki, J. A. Domaradzki, D. Stramski, and J. R. V. Zaneveld, “Comparison of nearforward scattering on turbulence and particles,” Applied Optics 37, 4669–4677 (1998).
[Crossref]

D. Bogucki, A. Domaradzki, and 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, J. A. Domaradzki, R. E. Ecke, and R. C. Truman, “Light scattering on oceanic turbulence,” Appl. Opt. 43, 5662–5676 (2004).
[Crossref] [PubMed]

D. J. Bogucki, J. A. Domaradzki, R. E. Ecke, C. R. Truman, and J. R. V. Zaneveld, “Near-forward light scattering on oceaqnic turbulence and particulates: an experimental comparison,” vol. SPIE, Ocean Optics XIV (1998).

Box, J.

R. G. Lueck, D. Huang, D. Newman, and J. Box, “Turbulence Measurement with a Moored Instrument,” Journal of Atmospheric and Oceanic Technology 14, 143–161 (1997).
[Crossref]

Domaradzki, A.

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

Domaradzki, J.

Domaradzki, J. A.

D. J. Bogucki, J. A. Domaradzki, R. E. Ecke, and R. C. Truman, “Light scattering on oceanic turbulence,” Appl. Opt. 43, 5662–5676 (2004).
[Crossref] [PubMed]

D. Bogucki, J. A. Domaradzki, D. Stramski, and J. R. V. Zaneveld, “Comparison of nearforward scattering on turbulence and particles,” Applied Optics 37, 4669–4677 (1998).
[Crossref]

D. J. Bogucki, J. A. Domaradzki, R. E. Ecke, C. R. Truman, and J. R. V. Zaneveld, “Near-forward light scattering on oceaqnic turbulence and particulates: an experimental comparison,” vol. SPIE, Ocean Optics XIV (1998).

Ecke, R. E.

D. J. Bogucki, J. A. Domaradzki, R. E. Ecke, and R. C. Truman, “Light scattering on oceanic turbulence,” Appl. Opt. 43, 5662–5676 (2004).
[Crossref] [PubMed]

D. J. Bogucki, J. A. Domaradzki, R. E. Ecke, C. R. Truman, and J. R. V. Zaneveld, “Near-forward light scattering on oceaqnic turbulence and particulates: an experimental comparison,” vol. SPIE, Ocean Optics XIV (1998).

Gregg, M. C.

M. C. Gregg, “Uncertainties and Limitations in Measuring ε and χ.” Journal of Atmospheric and Oceanic Technology 16, 1484–1490 (1998).

Huang, D.

R. G. Lueck, D. Huang, D. Newman, and J. Box, “Turbulence Measurement with a Moored Instrument,” Journal of Atmospheric and Oceanic Technology 14, 143–161 (1997).
[Crossref]

Lueck, R. G.

R. G. Lueck, D. Huang, D. Newman, and J. Box, “Turbulence Measurement with a Moored Instrument,” Journal of Atmospheric and Oceanic Technology 14, 143–161 (1997).
[Crossref]

Monin, A. S.

A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence (The MIT press, 1981).

Newman, D.

R. G. Lueck, D. Huang, D. Newman, and J. Box, “Turbulence Measurement with a Moored Instrument,” Journal of Atmospheric and Oceanic Technology 14, 143–161 (1997).
[Crossref]

Ozmidov, R. V.

R. V. Ozmidov, “On the turbulent exchange in a stably stratified ocean.” Izvestiya, Atmospheric and Oceanic Physics 1, 493–497 (1965).

Stramski, D.

D. Bogucki, J. A. Domaradzki, D. Stramski, and J. R. V. Zaneveld, “Comparison of nearforward scattering on turbulence and particles,” Applied Optics 37, 4669–4677 (1998).
[Crossref]

Tatarski, V. I.

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

V. I. Tatarski, The effects of the turbulent atmosphere on the wave propagation (Israel program for Scientific Translation, Jerusalem, 1971).

Truman, C. R.

D. J. Bogucki, J. A. Domaradzki, R. E. Ecke, C. R. Truman, and J. R. V. Zaneveld, “Near-forward light scattering on oceaqnic turbulence and particulates: an experimental comparison,” vol. SPIE, Ocean Optics XIV (1998).

Truman, R. C.

Wells, W. H.

W. H. Wells, “Theory of Small-angle Scattering,” (Advisory Group for Aerospace Research and Development, NATO, 92 Neuilly-Sur-Seine, France, 1973).

Yaglom, A. M.

A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence (The MIT press, 1981).

Yeung, P. K.

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

Zaneveld, J. R. V.

D. Bogucki, J. A. Domaradzki, D. Stramski, and J. R. V. Zaneveld, “Comparison of nearforward scattering on turbulence and particles,” Applied Optics 37, 4669–4677 (1998).
[Crossref]

D. J. Bogucki, J. A. Domaradzki, R. E. Ecke, C. R. Truman, and J. R. V. Zaneveld, “Near-forward light scattering on oceaqnic turbulence and particulates: an experimental comparison,” vol. SPIE, Ocean Optics XIV (1998).

Appl. Opt. (2)

Applied Optics (1)

D. Bogucki, J. A. Domaradzki, D. Stramski, and J. R. V. Zaneveld, “Comparison of nearforward scattering on turbulence and particles,” Applied Optics 37, 4669–4677 (1998).
[Crossref]

Izvestiya, Atmospheric and Oceanic Physics (1)

R. V. Ozmidov, “On the turbulent exchange in a stably stratified ocean.” Izvestiya, Atmospheric and Oceanic Physics 1, 493–497 (1965).

J. Fluid Mech. (1)

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

Journal of Atmospheric and Oceanic Technology (2)

R. G. Lueck, D. Huang, D. Newman, and J. Box, “Turbulence Measurement with a Moored Instrument,” Journal of Atmospheric and Oceanic Technology 14, 143–161 (1997).
[Crossref]

M. C. Gregg, “Uncertainties and Limitations in Measuring ε and χ.” Journal of Atmospheric and Oceanic Technology 16, 1484–1490 (1998).

Other (5)

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

V. I. Tatarski, The effects of the turbulent atmosphere on the wave propagation (Israel program for Scientific Translation, Jerusalem, 1971).

A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence (The MIT press, 1981).

D. J. Bogucki, J. A. Domaradzki, R. E. Ecke, C. R. Truman, and J. R. V. Zaneveld, “Near-forward light scattering on oceaqnic turbulence and particulates: an experimental comparison,” vol. SPIE, Ocean Optics XIV (1998).

W. H. Wells, “Theory of Small-angle Scattering,” (Advisory Group for Aerospace Research and Development, NATO, 92 Neuilly-Sur-Seine, France, 1973).

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Figures (3)

Fig. 1.
Fig. 1. Optical Turbulence Sensor - (A) Photograph of the developed and sea tested sensor. (B) Schematic representation of the various OTS parts. The light source is on the left hand side. The right hand side contains the receiving unit. Examples of displaced spots (only 4 of 110 available in OTS) produced by lenslets are presented on the right hand side of Figure (B). The light source and the acquisition board with CCD are enclosed in a hermetic enclosure.

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Fig. 2.
Fig. 2. Example of temperature spectrum ET (k) - panel (A) and dissipation spectrum k 2 ET (k) - panel (B) measured by OTS (2 sec ensemble), compared to theoretical prediction for turbulent flow [11].

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Fig. 3.
Fig. 3. The 2 hour time series of ? measured by OTS and the thermistor at each measurement depth.

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Equations (7)

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ψ ( x , y ) = A 0 ( x , y ) exp ( 2 πi λ ∫ 0 L n ( x , y , z′ ) dz′ ) ,
N = [ ∂ Γ ∂ x , ∂ Γ ∂ y , 1 ] ,
α ( x , y ) = { ( ∂ Γ ∂ x ) 2 + ( ∂ Γ ∂ x ) 2 } 1 / 2 ,
B ( ρ ) = ∫ D α ( ρ′ ) α ( ρ − ρ′ ) dρ′
M 2 ∫ 0 ∞ k J 0 ( kρ ) E T ( k ) dk = 1 ρ B ( ρ ) ,
E T ( k ) = 1 M 2 ∫ 0 ∞ J 0 ( kρ ) B ( ρ ) dρ .
χ = 2 κ ∫ 0 ∞ E T ( k ) k 2 dk .

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