Abstract

Temperature inhomogeneities in free, isotropic turbulence have the effect of scattering light in near-forward angles. We investigate numerically modifications of free turbulence by a rigid wall and its effect on the propagation of light through turbulence. The wall is a 5 cm optical window placed at the leading edge of an instrument towed with speeds of 0.1 and 1 m/s in free turbulence. The turbulent flow field presents inhomogeneities of an embedded passive scalar (Pr = 7, temperature in water), which are modified by the boundary layer developing on the window. We find that the developing laminar boundary layer has a negligible effect on light scattering for the investigated geometry when considered in terms of the volume-scattering function (differential cross section). This indicates that the boundary layer is not an obstacle for optical measurements of turbulence.

© 2005 Optical Society of America

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References

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  1. D. J. Bogucki, J. A. Domaradzki, R. E. Ecke, R. C. Truman, “Light scattering on oceanic turbulence,” Appl. Opt. 43, 5662–5668 (2004).
    [CrossRef] [PubMed]
  2. C. D. Johnson, C. M. Mayer, “Underwater optical holographic interferometry,” Appl. Phys. Lett. 21, 369–374 (1972).
    [CrossRef]
  3. T. Ammirati, “Holographic observation of a surface under a turbulent boundary layer,” Appl. Opt. 26, 968–969 (1987).
    [CrossRef] [PubMed]
  4. V. I. Tatarski, Wave Propagation in Turbulent Media (McGraw-Hill, 1961).
  5. D. Bogucki, J. A. Domaradzki, D. Stramski, R. Zaneveld, “Comparison of near-forward scattering on turbulence and particles,” Appl. Opt. 37, 4669–4677 (1998).
    [CrossRef]
  6. 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]
  7. J. A. Domaradzki, “Nonlocal triad interactions and the dissipation range of isotropic turbulence,” Phys. Fluids A 9, 2037–2045 (1992).
    [CrossRef]
  8. R. Kerr, “Velocity, scalar, and transfer spectra in numerical turbulence,” J. Fluid Mech. 211, 309–332 (1990).
    [CrossRef]
  9. H. Schlichting, Boundary-Layer Theory, 7th ed. (McGraw-Hill, 1979).
  10. J. A. Domaradzki, R. Metcalfe, “Stabilization of laminar boundary layers by compliant membranes,” Phys. Fluids 30, 695–705 (1987).
    [CrossRef]
  11. W. Liu, J. A. Domaradzki, “Direct numerical simulation of transition to turbulence in Görtler flow,” J. Fluid Mech. 246, 267–299 (1993).
    [CrossRef]
  12. R. C. Millard, G. Seaver, “An index of refraction algorithm for seawater over temperature, pressure, salinity, density, and wavelength,” Deep Sea Res. 37, 1909–1926 (1990).
    [CrossRef]
  13. M. Born, E. Wolf, Principles of Optics (Pergamon, 1964).

2004 (1)

1998 (1)

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]

1993 (1)

W. Liu, J. A. Domaradzki, “Direct numerical simulation of transition to turbulence in Görtler flow,” J. Fluid Mech. 246, 267–299 (1993).
[CrossRef]

1992 (1)

J. A. Domaradzki, “Nonlocal triad interactions and the dissipation range of isotropic turbulence,” Phys. Fluids A 9, 2037–2045 (1992).
[CrossRef]

1990 (2)

R. Kerr, “Velocity, scalar, and transfer spectra in numerical turbulence,” J. Fluid Mech. 211, 309–332 (1990).
[CrossRef]

R. C. Millard, G. Seaver, “An index of refraction algorithm for seawater over temperature, pressure, salinity, density, and wavelength,” Deep Sea Res. 37, 1909–1926 (1990).
[CrossRef]

1987 (2)

T. Ammirati, “Holographic observation of a surface under a turbulent boundary layer,” Appl. Opt. 26, 968–969 (1987).
[CrossRef] [PubMed]

J. A. Domaradzki, R. Metcalfe, “Stabilization of laminar boundary layers by compliant membranes,” Phys. Fluids 30, 695–705 (1987).
[CrossRef]

1972 (1)

C. D. Johnson, C. M. Mayer, “Underwater optical holographic interferometry,” Appl. Phys. Lett. 21, 369–374 (1972).
[CrossRef]

Ammirati, T.

Bogucki, D.

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

Bogucki, D. J.

Born, M.

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

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]

Domaradzki, J. A.

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

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

W. Liu, J. A. Domaradzki, “Direct numerical simulation of transition to turbulence in Görtler flow,” J. Fluid Mech. 246, 267–299 (1993).
[CrossRef]

J. A. Domaradzki, “Nonlocal triad interactions and the dissipation range of isotropic turbulence,” Phys. Fluids A 9, 2037–2045 (1992).
[CrossRef]

J. A. Domaradzki, R. Metcalfe, “Stabilization of laminar boundary layers by compliant membranes,” Phys. Fluids 30, 695–705 (1987).
[CrossRef]

Ecke, R. E.

Johnson, C. D.

C. D. Johnson, C. M. Mayer, “Underwater optical holographic interferometry,” Appl. Phys. Lett. 21, 369–374 (1972).
[CrossRef]

Kerr, R.

R. Kerr, “Velocity, scalar, and transfer spectra in numerical turbulence,” J. Fluid Mech. 211, 309–332 (1990).
[CrossRef]

Liu, W.

W. Liu, J. A. Domaradzki, “Direct numerical simulation of transition to turbulence in Görtler flow,” J. Fluid Mech. 246, 267–299 (1993).
[CrossRef]

Mayer, C. M.

C. D. Johnson, C. M. Mayer, “Underwater optical holographic interferometry,” Appl. Phys. Lett. 21, 369–374 (1972).
[CrossRef]

Metcalfe, R.

J. A. Domaradzki, R. Metcalfe, “Stabilization of laminar boundary layers by compliant membranes,” Phys. Fluids 30, 695–705 (1987).
[CrossRef]

Millard, R. C.

R. C. Millard, G. Seaver, “An index of refraction algorithm for seawater over temperature, pressure, salinity, density, and wavelength,” Deep Sea Res. 37, 1909–1926 (1990).
[CrossRef]

Schlichting, H.

H. Schlichting, Boundary-Layer Theory, 7th ed. (McGraw-Hill, 1979).

Seaver, G.

R. C. Millard, G. Seaver, “An index of refraction algorithm for seawater over temperature, pressure, salinity, density, and wavelength,” Deep Sea Res. 37, 1909–1926 (1990).
[CrossRef]

Stramski, D.

Tatarski, V. I.

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

Truman, R. C.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, 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]

Zaneveld, R.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

C. D. Johnson, C. M. Mayer, “Underwater optical holographic interferometry,” Appl. Phys. Lett. 21, 369–374 (1972).
[CrossRef]

Deep Sea Res. (1)

R. C. Millard, G. Seaver, “An index of refraction algorithm for seawater over temperature, pressure, salinity, density, and wavelength,” Deep Sea Res. 37, 1909–1926 (1990).
[CrossRef]

J. Fluid Mech. (3)

W. Liu, J. A. Domaradzki, “Direct numerical simulation of transition to turbulence in Görtler flow,” J. Fluid Mech. 246, 267–299 (1993).
[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]

R. Kerr, “Velocity, scalar, and transfer spectra in numerical turbulence,” J. Fluid Mech. 211, 309–332 (1990).
[CrossRef]

Phys. Fluids (1)

J. A. Domaradzki, R. Metcalfe, “Stabilization of laminar boundary layers by compliant membranes,” Phys. Fluids 30, 695–705 (1987).
[CrossRef]

Phys. Fluids A (1)

J. A. Domaradzki, “Nonlocal triad interactions and the dissipation range of isotropic turbulence,” Phys. Fluids A 9, 2037–2045 (1992).
[CrossRef]

Other (3)

H. Schlichting, Boundary-Layer Theory, 7th ed. (McGraw-Hill, 1979).

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

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

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Figures (3)

Fig. 1
Fig. 1

(Color online) Map of the scattering angle for all runs. Panel A: initial, isotropic homogeneous flow (T = 0 s); Panel B: isotropic, homogeneous, decaying flow after time T = 0.5 s; Panel C: flow advected once over the optical window with low speed (0.1 m/s), T = 0.5 s; Panel D: flow advected twice over the optical window with high speed (1 m/s), T = 0.1 s.

Fig. 2
Fig. 2

(Color online) VSF for the isotropic homogeneous turbulence forced run (T = 0 s) and the decaying run (T = 0.5 s).

Fig. 3
Fig. 3

(Color online) Comparison of VSF for all BL flows.

Tables (3)

Tables Icon

Table 1 Relevant Parameters, in SI Units, for DNS Simulations of Turbulent Flow Field

Tables Icon

Table 2 Characteristics of the Boundary-Layer Flow

Tables Icon

Table 3 Simulated Databases for the Boundary-Layer Runs (b1 and b2) and the Decaying Turbulence Run (i2)

Equations (10)

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ψ ( x ,     y ,     z = L ) = A 0 ( x ,     y ) exp [ i κ 0 L n ( x ,     y ,     z ) d z ] ,
VSF ( θ ) = d I ( θ ) E O d V .
Γ ( x ,     y ) = 0 L n ( x ,     y ,     z ) d z .
N = [ Γ x ,     Γ y ,     - 1 ] ,
η = ( ν 3 ɛ ) 1 4 ,             η B = P r - 1 / 2 η .
Θ = L int / u ,             τ = η / v K = ( ν / ɛ ) 1 2 .
E ( k ) = 125 4 ν 2 η exp ( - 5 η k ) ,
δ 4.9 ( ν x u 0 ) 1 / 2 ,
R e = u 0 δ / ν .
T r = ( χ r / χ c ) 1 / 2 ( c / r ) 1 / 4 ( ν r / ν c ) 1 / 4 T c ,

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