Abstract

The spectrum of optical refractive-index fluctuations caused by temperature or salinity fluctuations in turbulent water is much different from the refractive-index spectrum of temperature or humidity fluctuations in air. This occurs because the ratio of kinematic viscosity to diffusivity is much greater for temperature and salinity fluctuations in water than for temperature and humidity fluctuations in air. In turbulent water the temperature and salinity spectra have viscous-convective ranges that extend roughly one and two decades in wave number, respectively. The consequences of these viscousconvective ranges for optical propagation in water are examined. It is found that the variance of log intensity, as a function of Fresnel-zone size, rises far above its large Fresnel-zone-size asymptotic form, and the covariance function of log-amplitude is relatively narrow when the viscous-convective range dominates its shape. If the viscous-convective range dominates the shape of the structure function of phase, then the structure function is proportional to the spacing and is less sensitive to outer scale effects than for propagation in air. Likewise, the lateral coherence length has a new asymptotic form arising from a viscous-convective range and is also less sensitive to outer scale effects than for propagation in air.

© 1978 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. K. Batchelor, "Small-scale variation of convected quantities like temperature in turbulent fluid, Part I, General discussion and the case of small conductivity," J. Fluid Mech. 5, 113–133 (1959).
  2. S. Corrsin, "On the spectrum of isotropic temperature fluctuations in isotropic turbulence," J. Appl. Phys. 22, 469–473 (1951).
  3. R. J. Hill, "Spectra of fluctuations in refractivity, temperature, humidity, and the temperature-humidity cospectrum in the inertial and dissipation ranges," Radio Sci. (to be published).
  4. H. L. Grant, B. A. Hughes, W. M. Vogel, and A. Moilliet, "The spectrum of temperature fluctuations in turbulent flow," J. Fluid Mech. 34, 423–492 (1968).
  5. C. H. Gibson, R. R. Lyon, and I. Hirschsohn, "Reaction product fluctuations in a sphere wake," AIAA J. 8, 1859–1863 (1970).
  6. R. J. Hill, "Models of the scalar spectrum for turbulent advection," J. Fluid Mech. (to be published).
  7. F. H. Champagne, C. A. Friehe, J. C. LaRue, and J. C. Wyngaard, "Flux measurements, flux-estimation techniques, and fine-scale turbulence measurements in the unstable surface layer over land," J. Atmos. Sci. 34, 515–530 (1977).
  8. R. M. Williams, Jr. and C. A. Paulson, "Microscale temperature and velocity spectra in the atmospheric boundary layer," J. Fluid Mech. 83, 547–567 (1977).
  9. R. S. Lawrence and J. W. Strohbehn, "A survey of clear-air propagation effects relevant to optical communications," Proc. IEEE 58, 1523–1545 (1970).
  10. R. J. Hill and S. F. Clifford, "The modified spectrum at atmospheric temperature fluctuations and its application to optical propagation," J. Opt. Soc. Am. 68, 892–899 (1978).
  11. A. Consortini, L. Ronchi, and E. Moroder, "Role of the outer scale of turbulence in atmospheric degradation of optical images," J. Opt. Soc. Am. 63, 1246–1248 (1973).
  12. H. T. Yura, "Optical beam spread in a turbulent medium: effect of the outer scale of turbulence," J. Opt. Soc. Am. 63, 107–109 (1973).

1978

1977

F. H. Champagne, C. A. Friehe, J. C. LaRue, and J. C. Wyngaard, "Flux measurements, flux-estimation techniques, and fine-scale turbulence measurements in the unstable surface layer over land," J. Atmos. Sci. 34, 515–530 (1977).

R. M. Williams, Jr. and C. A. Paulson, "Microscale temperature and velocity spectra in the atmospheric boundary layer," J. Fluid Mech. 83, 547–567 (1977).

1973

1970

C. H. Gibson, R. R. Lyon, and I. Hirschsohn, "Reaction product fluctuations in a sphere wake," AIAA J. 8, 1859–1863 (1970).

1968

H. L. Grant, B. A. Hughes, W. M. Vogel, and A. Moilliet, "The spectrum of temperature fluctuations in turbulent flow," J. Fluid Mech. 34, 423–492 (1968).

1959

G. K. Batchelor, "Small-scale variation of convected quantities like temperature in turbulent fluid, Part I, General discussion and the case of small conductivity," J. Fluid Mech. 5, 113–133 (1959).

1951

S. Corrsin, "On the spectrum of isotropic temperature fluctuations in isotropic turbulence," J. Appl. Phys. 22, 469–473 (1951).

Batchelor, G. K.

G. K. Batchelor, "Small-scale variation of convected quantities like temperature in turbulent fluid, Part I, General discussion and the case of small conductivity," J. Fluid Mech. 5, 113–133 (1959).

Champagne, F. H.

F. H. Champagne, C. A. Friehe, J. C. LaRue, and J. C. Wyngaard, "Flux measurements, flux-estimation techniques, and fine-scale turbulence measurements in the unstable surface layer over land," J. Atmos. Sci. 34, 515–530 (1977).

Clifford, S. F.

Consortini, A.

Corrsin, S.

S. Corrsin, "On the spectrum of isotropic temperature fluctuations in isotropic turbulence," J. Appl. Phys. 22, 469–473 (1951).

Friehe, C. A.

F. H. Champagne, C. A. Friehe, J. C. LaRue, and J. C. Wyngaard, "Flux measurements, flux-estimation techniques, and fine-scale turbulence measurements in the unstable surface layer over land," J. Atmos. Sci. 34, 515–530 (1977).

Gibson, C. H.

C. H. Gibson, R. R. Lyon, and I. Hirschsohn, "Reaction product fluctuations in a sphere wake," AIAA J. 8, 1859–1863 (1970).

Grant, H. L.

H. L. Grant, B. A. Hughes, W. M. Vogel, and A. Moilliet, "The spectrum of temperature fluctuations in turbulent flow," J. Fluid Mech. 34, 423–492 (1968).

Hill, R. J.

R. J. Hill and S. F. Clifford, "The modified spectrum at atmospheric temperature fluctuations and its application to optical propagation," J. Opt. Soc. Am. 68, 892–899 (1978).

R. J. Hill, "Spectra of fluctuations in refractivity, temperature, humidity, and the temperature-humidity cospectrum in the inertial and dissipation ranges," Radio Sci. (to be published).

R. J. Hill, "Models of the scalar spectrum for turbulent advection," J. Fluid Mech. (to be published).

Hirschsohn, I.

C. H. Gibson, R. R. Lyon, and I. Hirschsohn, "Reaction product fluctuations in a sphere wake," AIAA J. 8, 1859–1863 (1970).

Hughes, B. A.

H. L. Grant, B. A. Hughes, W. M. Vogel, and A. Moilliet, "The spectrum of temperature fluctuations in turbulent flow," J. Fluid Mech. 34, 423–492 (1968).

LaRue, J. C.

F. H. Champagne, C. A. Friehe, J. C. LaRue, and J. C. Wyngaard, "Flux measurements, flux-estimation techniques, and fine-scale turbulence measurements in the unstable surface layer over land," J. Atmos. Sci. 34, 515–530 (1977).

Lawrence, R. S.

R. S. Lawrence and J. W. Strohbehn, "A survey of clear-air propagation effects relevant to optical communications," Proc. IEEE 58, 1523–1545 (1970).

Lyon, R. R.

C. H. Gibson, R. R. Lyon, and I. Hirschsohn, "Reaction product fluctuations in a sphere wake," AIAA J. 8, 1859–1863 (1970).

Moilliet, A.

H. L. Grant, B. A. Hughes, W. M. Vogel, and A. Moilliet, "The spectrum of temperature fluctuations in turbulent flow," J. Fluid Mech. 34, 423–492 (1968).

Moroder, E.

Paulson, C. A.

R. M. Williams, Jr. and C. A. Paulson, "Microscale temperature and velocity spectra in the atmospheric boundary layer," J. Fluid Mech. 83, 547–567 (1977).

Ronchi, L.

Strohbehn, J. W.

R. S. Lawrence and J. W. Strohbehn, "A survey of clear-air propagation effects relevant to optical communications," Proc. IEEE 58, 1523–1545 (1970).

Vogel, W. M.

H. L. Grant, B. A. Hughes, W. M. Vogel, and A. Moilliet, "The spectrum of temperature fluctuations in turbulent flow," J. Fluid Mech. 34, 423–492 (1968).

Williams, Jr., R. M.

R. M. Williams, Jr. and C. A. Paulson, "Microscale temperature and velocity spectra in the atmospheric boundary layer," J. Fluid Mech. 83, 547–567 (1977).

Wyngaard, J. C.

F. H. Champagne, C. A. Friehe, J. C. LaRue, and J. C. Wyngaard, "Flux measurements, flux-estimation techniques, and fine-scale turbulence measurements in the unstable surface layer over land," J. Atmos. Sci. 34, 515–530 (1977).

Yura, H. T.

AIAA J.

C. H. Gibson, R. R. Lyon, and I. Hirschsohn, "Reaction product fluctuations in a sphere wake," AIAA J. 8, 1859–1863 (1970).

J. Appl. Phys.

S. Corrsin, "On the spectrum of isotropic temperature fluctuations in isotropic turbulence," J. Appl. Phys. 22, 469–473 (1951).

J. Atmos. Sci.

F. H. Champagne, C. A. Friehe, J. C. LaRue, and J. C. Wyngaard, "Flux measurements, flux-estimation techniques, and fine-scale turbulence measurements in the unstable surface layer over land," J. Atmos. Sci. 34, 515–530 (1977).

J. Fluid Mech.

R. M. Williams, Jr. and C. A. Paulson, "Microscale temperature and velocity spectra in the atmospheric boundary layer," J. Fluid Mech. 83, 547–567 (1977).

G. K. Batchelor, "Small-scale variation of convected quantities like temperature in turbulent fluid, Part I, General discussion and the case of small conductivity," J. Fluid Mech. 5, 113–133 (1959).

H. L. Grant, B. A. Hughes, W. M. Vogel, and A. Moilliet, "The spectrum of temperature fluctuations in turbulent flow," J. Fluid Mech. 34, 423–492 (1968).

J. Opt. Soc. Am.

Other

R. J. Hill, "Spectra of fluctuations in refractivity, temperature, humidity, and the temperature-humidity cospectrum in the inertial and dissipation ranges," Radio Sci. (to be published).

R. S. Lawrence and J. W. Strohbehn, "A survey of clear-air propagation effects relevant to optical communications," Proc. IEEE 58, 1523–1545 (1970).

R. J. Hill, "Models of the scalar spectrum for turbulent advection," J. Fluid Mech. (to be published).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.