Abstract

We investigate the validity of applying a simplified (under the assumptions of isotropic and homogeneous turbulence) aero-optic linking equation to a flow field that is known to consist of anisotropic and nonhomogeneous turbulence. The investigation is performed in the near-nozzle region of a heated two-dimensional jet, and the study makes use of a conditional-sampling experiment to acquire a spatiotemporal temperature field database for the heated-jet flow field. After compensating for the bandwidth limitations of constant-current wire temperature measurements, the temperature field database is applied to the computation of optical degradation through both direct and indirect methods, relying on the aero-optic linking equation. The simplified version of the linking equation was found to provide good agreement with direct calculations, provided that the length scale of the density fluctuations was interpreted as being the integral scale, with the limits of integration being the first two zero crossings of the covariance coefficient function.

© 2000 Optical Society of America

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References

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  1. J. D. Trolinger, “Aero-optical characterization of aircraft optical turrets by holography, interferometry, and shadowgraph,” in Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 200–217.
  2. D. Kelsall, “Optical seeing through the atmosphere by an interferometric technique,” J. Opt. Soc. Am. 63, 1472–1484 (1973).
    [CrossRef]
  3. K. G. Gilbert, “Lear jet boundary-layer/shear-layer laser propagation measurements,” in Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 249–260.
  4. D. R. Neal, T. J. O’Hern, J. R. Torczynski, M. E. Warren, R. Shul, T. S. McKechnie, “Wavefront sensors for optical diagnostics in fluid mechanics: application to heated flow, turbulence and droplet evaporation,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds. Proc. SPIE2005, 194–203 (1993).
    [CrossRef]
  5. L. McMackin, B. Masson, N. Clark, K. Bishop, R. Pierson, E. Chen, “Hartmann wave front sensor studies of dynamic organized structures in flowfields,” AIAA J. 33, 2158–2164 (1995).
    [CrossRef]
  6. M. Malley, G. W. Sutton, N. Kincheloe, “Beam-jitter measurements of turbulent aero-optical path differences,” Appl. Opt. 31, 4440–4443 (1992).
    [CrossRef] [PubMed]
  7. R. J. Hugo, E. J. Jumper, “Experimental measurement of a time-varying optical path difference by the small-aperture beam technique,” Appl. Opt. 35, 4436–4447 (1996).
    [CrossRef] [PubMed]
  8. J. M. Cicchiello, E. J. Jumper, “Far-field optical degradation due to near-field transmission through a turbulent heated jet,” Appl. Opt. 36, 6441–6452 (1997).
    [CrossRef]
  9. G. Havener, “Optical wave front variance: a study on analytic models in use today,” Paper AIAA-92-0654, presented at the 30th Aerospace Sciences Meeting, Reno, Nev., 6–9 January 1992 (American Institute of Aeronautics and Astronautics, Reston, Va., 1992).
  10. R. J. Hugo, E. J. Jumper, G. Havener, S. A. Stepanek, “Time-resolved wave front measurements through a compressible free shear layer,” AIAA J. 35, 671–677 (1997).
    [CrossRef]
  11. C. A. Atwood, W. R. Van Dalsem, “Flowfield simulation about the SOFIA Airborne Observatory,” Paper AIAA-92-0656, presented at the 30th Aerospace Sciences Meeting, Reno, Nev., 6–9 January 1992 (American Institute of Aeronautics and Astronautics, Reston, Va., 1992).
  12. G. W. Sutton, “Effect of turbulent fluctuations in an optically active fluid medium,” AIAA J. 7, 1737–1743 (1969).
    [CrossRef]
  13. W. J. Steinmetz, “Second moments of optical degradation due to a thin turbulent layer,” in Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 78–100.
  14. G. W. Sutton, “Optical imaging through aircraft turbulent boundary layers,” in Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 15–39.
  15. R. J. Hugo, “Quantifying the spatio-temporal effects of optically-active turbulent flowfields on a coherent optical wave,” Ph.D. dissertation (University of Notre Dame, Notre Dame, Ind., 1995).
  16. M. V. Klein, Optics (Wiley, New York, 1970).
  17. D. E. Wroblewski, P. A. Eibeck, “A frequency response compensation technique for cold wires and its application to a heat flux probe,” Exp. Therm. Fluid Sci. 4, 452–463 (1991).
    [CrossRef]
  18. T. Tsuji, Y. Nagano, M. Tagawa, “Frequency response and instantaneous temperature profile of cold-wire sensors for fluid temperature fluctuation measurements,” Exp. Fluids 13, 171–178 (1992).
    [CrossRef]
  19. Y. Nagano, T. Tsuji, “Recent developments in hot- and cold-wire techniques for measurements in turbulent shear flows near walls,” Exp. Therm. Fluid Sci. 9, 94–110 (1994).
    [CrossRef]
  20. P. Paranthoen, C. Petit, J. C. Lecordier, “The effect of the thermal prong-wire interaction on the response of a cold wire in gaseous flows (air, argon, and helium),” J. Fluid Mech. 124, 457–473 (1982).
    [CrossRef]
  21. J. M. Cimbala, W. J. Park, “A direct hot-wire calibration technique to account for ambient temperature drift in incompressible flow,” Exp. Fluids 8, 299–300 (1990).
    [CrossRef]
  22. G. Cardell, “A note on the temperature-dependent hot-wire calibration method of Cimbala and Park,” Exp. Fluids 14, 283–285 (1993).
    [CrossRef]
  23. R. J. Hugo, S. R. Nowlin, F. D. Eaton, K. A. McCrae, K. P. Bishop, “Hot-wire calibration in a non-isothermal incompressible pressure variant flow,” in Airborne Laser Advanced Technology II, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3706, 11–22 (1999).
    [CrossRef]
  24. L. V. King, “On the convection of heat from small cylinders in a stream of fluid: determination of the convection constants of small platinum wires with applications to hot-wire anemometry,” Philos. Trans. R. Soc. London Ser. A 214, 373–432 (1914).
    [CrossRef]
  25. R. S. Figliola, D. E. Beasley, Theory and Design for Mechanical Measurements (Wiley, New York, 1991).
  26. J. O. Hinze, Turbulence, 2nd ed. (McGraw-Hill Classic Textbook Reissue, New York, 1975).

1997

J. M. Cicchiello, E. J. Jumper, “Far-field optical degradation due to near-field transmission through a turbulent heated jet,” Appl. Opt. 36, 6441–6452 (1997).
[CrossRef]

R. J. Hugo, E. J. Jumper, G. Havener, S. A. Stepanek, “Time-resolved wave front measurements through a compressible free shear layer,” AIAA J. 35, 671–677 (1997).
[CrossRef]

1996

1995

L. McMackin, B. Masson, N. Clark, K. Bishop, R. Pierson, E. Chen, “Hartmann wave front sensor studies of dynamic organized structures in flowfields,” AIAA J. 33, 2158–2164 (1995).
[CrossRef]

1994

Y. Nagano, T. Tsuji, “Recent developments in hot- and cold-wire techniques for measurements in turbulent shear flows near walls,” Exp. Therm. Fluid Sci. 9, 94–110 (1994).
[CrossRef]

1993

G. Cardell, “A note on the temperature-dependent hot-wire calibration method of Cimbala and Park,” Exp. Fluids 14, 283–285 (1993).
[CrossRef]

1992

M. Malley, G. W. Sutton, N. Kincheloe, “Beam-jitter measurements of turbulent aero-optical path differences,” Appl. Opt. 31, 4440–4443 (1992).
[CrossRef] [PubMed]

T. Tsuji, Y. Nagano, M. Tagawa, “Frequency response and instantaneous temperature profile of cold-wire sensors for fluid temperature fluctuation measurements,” Exp. Fluids 13, 171–178 (1992).
[CrossRef]

1991

D. E. Wroblewski, P. A. Eibeck, “A frequency response compensation technique for cold wires and its application to a heat flux probe,” Exp. Therm. Fluid Sci. 4, 452–463 (1991).
[CrossRef]

1990

J. M. Cimbala, W. J. Park, “A direct hot-wire calibration technique to account for ambient temperature drift in incompressible flow,” Exp. Fluids 8, 299–300 (1990).
[CrossRef]

1982

P. Paranthoen, C. Petit, J. C. Lecordier, “The effect of the thermal prong-wire interaction on the response of a cold wire in gaseous flows (air, argon, and helium),” J. Fluid Mech. 124, 457–473 (1982).
[CrossRef]

1973

1969

G. W. Sutton, “Effect of turbulent fluctuations in an optically active fluid medium,” AIAA J. 7, 1737–1743 (1969).
[CrossRef]

1914

L. V. King, “On the convection of heat from small cylinders in a stream of fluid: determination of the convection constants of small platinum wires with applications to hot-wire anemometry,” Philos. Trans. R. Soc. London Ser. A 214, 373–432 (1914).
[CrossRef]

Atwood, C. A.

C. A. Atwood, W. R. Van Dalsem, “Flowfield simulation about the SOFIA Airborne Observatory,” Paper AIAA-92-0656, presented at the 30th Aerospace Sciences Meeting, Reno, Nev., 6–9 January 1992 (American Institute of Aeronautics and Astronautics, Reston, Va., 1992).

Beasley, D. E.

R. S. Figliola, D. E. Beasley, Theory and Design for Mechanical Measurements (Wiley, New York, 1991).

Bishop, K.

L. McMackin, B. Masson, N. Clark, K. Bishop, R. Pierson, E. Chen, “Hartmann wave front sensor studies of dynamic organized structures in flowfields,” AIAA J. 33, 2158–2164 (1995).
[CrossRef]

Bishop, K. P.

R. J. Hugo, S. R. Nowlin, F. D. Eaton, K. A. McCrae, K. P. Bishop, “Hot-wire calibration in a non-isothermal incompressible pressure variant flow,” in Airborne Laser Advanced Technology II, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3706, 11–22 (1999).
[CrossRef]

Cardell, G.

G. Cardell, “A note on the temperature-dependent hot-wire calibration method of Cimbala and Park,” Exp. Fluids 14, 283–285 (1993).
[CrossRef]

Chen, E.

L. McMackin, B. Masson, N. Clark, K. Bishop, R. Pierson, E. Chen, “Hartmann wave front sensor studies of dynamic organized structures in flowfields,” AIAA J. 33, 2158–2164 (1995).
[CrossRef]

Cicchiello, J. M.

Cimbala, J. M.

J. M. Cimbala, W. J. Park, “A direct hot-wire calibration technique to account for ambient temperature drift in incompressible flow,” Exp. Fluids 8, 299–300 (1990).
[CrossRef]

Clark, N.

L. McMackin, B. Masson, N. Clark, K. Bishop, R. Pierson, E. Chen, “Hartmann wave front sensor studies of dynamic organized structures in flowfields,” AIAA J. 33, 2158–2164 (1995).
[CrossRef]

Eaton, F. D.

R. J. Hugo, S. R. Nowlin, F. D. Eaton, K. A. McCrae, K. P. Bishop, “Hot-wire calibration in a non-isothermal incompressible pressure variant flow,” in Airborne Laser Advanced Technology II, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3706, 11–22 (1999).
[CrossRef]

Eibeck, P. A.

D. E. Wroblewski, P. A. Eibeck, “A frequency response compensation technique for cold wires and its application to a heat flux probe,” Exp. Therm. Fluid Sci. 4, 452–463 (1991).
[CrossRef]

Figliola, R. S.

R. S. Figliola, D. E. Beasley, Theory and Design for Mechanical Measurements (Wiley, New York, 1991).

Gilbert, K. G.

K. G. Gilbert, “Lear jet boundary-layer/shear-layer laser propagation measurements,” in Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 249–260.

Havener, G.

R. J. Hugo, E. J. Jumper, G. Havener, S. A. Stepanek, “Time-resolved wave front measurements through a compressible free shear layer,” AIAA J. 35, 671–677 (1997).
[CrossRef]

G. Havener, “Optical wave front variance: a study on analytic models in use today,” Paper AIAA-92-0654, presented at the 30th Aerospace Sciences Meeting, Reno, Nev., 6–9 January 1992 (American Institute of Aeronautics and Astronautics, Reston, Va., 1992).

Hinze, J. O.

J. O. Hinze, Turbulence, 2nd ed. (McGraw-Hill Classic Textbook Reissue, New York, 1975).

Hugo, R. J.

R. J. Hugo, E. J. Jumper, G. Havener, S. A. Stepanek, “Time-resolved wave front measurements through a compressible free shear layer,” AIAA J. 35, 671–677 (1997).
[CrossRef]

R. J. Hugo, E. J. Jumper, “Experimental measurement of a time-varying optical path difference by the small-aperture beam technique,” Appl. Opt. 35, 4436–4447 (1996).
[CrossRef] [PubMed]

R. J. Hugo, “Quantifying the spatio-temporal effects of optically-active turbulent flowfields on a coherent optical wave,” Ph.D. dissertation (University of Notre Dame, Notre Dame, Ind., 1995).

R. J. Hugo, S. R. Nowlin, F. D. Eaton, K. A. McCrae, K. P. Bishop, “Hot-wire calibration in a non-isothermal incompressible pressure variant flow,” in Airborne Laser Advanced Technology II, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3706, 11–22 (1999).
[CrossRef]

Jumper, E. J.

Kelsall, D.

Kincheloe, N.

King, L. V.

L. V. King, “On the convection of heat from small cylinders in a stream of fluid: determination of the convection constants of small platinum wires with applications to hot-wire anemometry,” Philos. Trans. R. Soc. London Ser. A 214, 373–432 (1914).
[CrossRef]

Klein, M. V.

M. V. Klein, Optics (Wiley, New York, 1970).

Lecordier, J. C.

P. Paranthoen, C. Petit, J. C. Lecordier, “The effect of the thermal prong-wire interaction on the response of a cold wire in gaseous flows (air, argon, and helium),” J. Fluid Mech. 124, 457–473 (1982).
[CrossRef]

Malley, M.

Masson, B.

L. McMackin, B. Masson, N. Clark, K. Bishop, R. Pierson, E. Chen, “Hartmann wave front sensor studies of dynamic organized structures in flowfields,” AIAA J. 33, 2158–2164 (1995).
[CrossRef]

McCrae, K. A.

R. J. Hugo, S. R. Nowlin, F. D. Eaton, K. A. McCrae, K. P. Bishop, “Hot-wire calibration in a non-isothermal incompressible pressure variant flow,” in Airborne Laser Advanced Technology II, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3706, 11–22 (1999).
[CrossRef]

McKechnie, T. S.

D. R. Neal, T. J. O’Hern, J. R. Torczynski, M. E. Warren, R. Shul, T. S. McKechnie, “Wavefront sensors for optical diagnostics in fluid mechanics: application to heated flow, turbulence and droplet evaporation,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds. Proc. SPIE2005, 194–203 (1993).
[CrossRef]

McMackin, L.

L. McMackin, B. Masson, N. Clark, K. Bishop, R. Pierson, E. Chen, “Hartmann wave front sensor studies of dynamic organized structures in flowfields,” AIAA J. 33, 2158–2164 (1995).
[CrossRef]

Nagano, Y.

Y. Nagano, T. Tsuji, “Recent developments in hot- and cold-wire techniques for measurements in turbulent shear flows near walls,” Exp. Therm. Fluid Sci. 9, 94–110 (1994).
[CrossRef]

T. Tsuji, Y. Nagano, M. Tagawa, “Frequency response and instantaneous temperature profile of cold-wire sensors for fluid temperature fluctuation measurements,” Exp. Fluids 13, 171–178 (1992).
[CrossRef]

Neal, D. R.

D. R. Neal, T. J. O’Hern, J. R. Torczynski, M. E. Warren, R. Shul, T. S. McKechnie, “Wavefront sensors for optical diagnostics in fluid mechanics: application to heated flow, turbulence and droplet evaporation,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds. Proc. SPIE2005, 194–203 (1993).
[CrossRef]

Nowlin, S. R.

R. J. Hugo, S. R. Nowlin, F. D. Eaton, K. A. McCrae, K. P. Bishop, “Hot-wire calibration in a non-isothermal incompressible pressure variant flow,” in Airborne Laser Advanced Technology II, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3706, 11–22 (1999).
[CrossRef]

O’Hern, T. J.

D. R. Neal, T. J. O’Hern, J. R. Torczynski, M. E. Warren, R. Shul, T. S. McKechnie, “Wavefront sensors for optical diagnostics in fluid mechanics: application to heated flow, turbulence and droplet evaporation,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds. Proc. SPIE2005, 194–203 (1993).
[CrossRef]

Paranthoen, P.

P. Paranthoen, C. Petit, J. C. Lecordier, “The effect of the thermal prong-wire interaction on the response of a cold wire in gaseous flows (air, argon, and helium),” J. Fluid Mech. 124, 457–473 (1982).
[CrossRef]

Park, W. J.

J. M. Cimbala, W. J. Park, “A direct hot-wire calibration technique to account for ambient temperature drift in incompressible flow,” Exp. Fluids 8, 299–300 (1990).
[CrossRef]

Petit, C.

P. Paranthoen, C. Petit, J. C. Lecordier, “The effect of the thermal prong-wire interaction on the response of a cold wire in gaseous flows (air, argon, and helium),” J. Fluid Mech. 124, 457–473 (1982).
[CrossRef]

Pierson, R.

L. McMackin, B. Masson, N. Clark, K. Bishop, R. Pierson, E. Chen, “Hartmann wave front sensor studies of dynamic organized structures in flowfields,” AIAA J. 33, 2158–2164 (1995).
[CrossRef]

Shul, R.

D. R. Neal, T. J. O’Hern, J. R. Torczynski, M. E. Warren, R. Shul, T. S. McKechnie, “Wavefront sensors for optical diagnostics in fluid mechanics: application to heated flow, turbulence and droplet evaporation,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds. Proc. SPIE2005, 194–203 (1993).
[CrossRef]

Steinmetz, W. J.

W. J. Steinmetz, “Second moments of optical degradation due to a thin turbulent layer,” in Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 78–100.

Stepanek, S. A.

R. J. Hugo, E. J. Jumper, G. Havener, S. A. Stepanek, “Time-resolved wave front measurements through a compressible free shear layer,” AIAA J. 35, 671–677 (1997).
[CrossRef]

Sutton, G. W.

M. Malley, G. W. Sutton, N. Kincheloe, “Beam-jitter measurements of turbulent aero-optical path differences,” Appl. Opt. 31, 4440–4443 (1992).
[CrossRef] [PubMed]

G. W. Sutton, “Effect of turbulent fluctuations in an optically active fluid medium,” AIAA J. 7, 1737–1743 (1969).
[CrossRef]

G. W. Sutton, “Optical imaging through aircraft turbulent boundary layers,” in Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 15–39.

Tagawa, M.

T. Tsuji, Y. Nagano, M. Tagawa, “Frequency response and instantaneous temperature profile of cold-wire sensors for fluid temperature fluctuation measurements,” Exp. Fluids 13, 171–178 (1992).
[CrossRef]

Torczynski, J. R.

D. R. Neal, T. J. O’Hern, J. R. Torczynski, M. E. Warren, R. Shul, T. S. McKechnie, “Wavefront sensors for optical diagnostics in fluid mechanics: application to heated flow, turbulence and droplet evaporation,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds. Proc. SPIE2005, 194–203 (1993).
[CrossRef]

Trolinger, J. D.

J. D. Trolinger, “Aero-optical characterization of aircraft optical turrets by holography, interferometry, and shadowgraph,” in Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 200–217.

Tsuji, T.

Y. Nagano, T. Tsuji, “Recent developments in hot- and cold-wire techniques for measurements in turbulent shear flows near walls,” Exp. Therm. Fluid Sci. 9, 94–110 (1994).
[CrossRef]

T. Tsuji, Y. Nagano, M. Tagawa, “Frequency response and instantaneous temperature profile of cold-wire sensors for fluid temperature fluctuation measurements,” Exp. Fluids 13, 171–178 (1992).
[CrossRef]

Van Dalsem, W. R.

C. A. Atwood, W. R. Van Dalsem, “Flowfield simulation about the SOFIA Airborne Observatory,” Paper AIAA-92-0656, presented at the 30th Aerospace Sciences Meeting, Reno, Nev., 6–9 January 1992 (American Institute of Aeronautics and Astronautics, Reston, Va., 1992).

Warren, M. E.

D. R. Neal, T. J. O’Hern, J. R. Torczynski, M. E. Warren, R. Shul, T. S. McKechnie, “Wavefront sensors for optical diagnostics in fluid mechanics: application to heated flow, turbulence and droplet evaporation,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds. Proc. SPIE2005, 194–203 (1993).
[CrossRef]

Wroblewski, D. E.

D. E. Wroblewski, P. A. Eibeck, “A frequency response compensation technique for cold wires and its application to a heat flux probe,” Exp. Therm. Fluid Sci. 4, 452–463 (1991).
[CrossRef]

AIAA J.

L. McMackin, B. Masson, N. Clark, K. Bishop, R. Pierson, E. Chen, “Hartmann wave front sensor studies of dynamic organized structures in flowfields,” AIAA J. 33, 2158–2164 (1995).
[CrossRef]

R. J. Hugo, E. J. Jumper, G. Havener, S. A. Stepanek, “Time-resolved wave front measurements through a compressible free shear layer,” AIAA J. 35, 671–677 (1997).
[CrossRef]

G. W. Sutton, “Effect of turbulent fluctuations in an optically active fluid medium,” AIAA J. 7, 1737–1743 (1969).
[CrossRef]

Appl. Opt.

Exp. Fluids

T. Tsuji, Y. Nagano, M. Tagawa, “Frequency response and instantaneous temperature profile of cold-wire sensors for fluid temperature fluctuation measurements,” Exp. Fluids 13, 171–178 (1992).
[CrossRef]

J. M. Cimbala, W. J. Park, “A direct hot-wire calibration technique to account for ambient temperature drift in incompressible flow,” Exp. Fluids 8, 299–300 (1990).
[CrossRef]

G. Cardell, “A note on the temperature-dependent hot-wire calibration method of Cimbala and Park,” Exp. Fluids 14, 283–285 (1993).
[CrossRef]

Exp. Therm. Fluid Sci.

Y. Nagano, T. Tsuji, “Recent developments in hot- and cold-wire techniques for measurements in turbulent shear flows near walls,” Exp. Therm. Fluid Sci. 9, 94–110 (1994).
[CrossRef]

D. E. Wroblewski, P. A. Eibeck, “A frequency response compensation technique for cold wires and its application to a heat flux probe,” Exp. Therm. Fluid Sci. 4, 452–463 (1991).
[CrossRef]

J. Fluid Mech.

P. Paranthoen, C. Petit, J. C. Lecordier, “The effect of the thermal prong-wire interaction on the response of a cold wire in gaseous flows (air, argon, and helium),” J. Fluid Mech. 124, 457–473 (1982).
[CrossRef]

J. Opt. Soc. Am.

Philos. Trans. R. Soc. London Ser. A

L. V. King, “On the convection of heat from small cylinders in a stream of fluid: determination of the convection constants of small platinum wires with applications to hot-wire anemometry,” Philos. Trans. R. Soc. London Ser. A 214, 373–432 (1914).
[CrossRef]

Other

R. S. Figliola, D. E. Beasley, Theory and Design for Mechanical Measurements (Wiley, New York, 1991).

J. O. Hinze, Turbulence, 2nd ed. (McGraw-Hill Classic Textbook Reissue, New York, 1975).

R. J. Hugo, S. R. Nowlin, F. D. Eaton, K. A. McCrae, K. P. Bishop, “Hot-wire calibration in a non-isothermal incompressible pressure variant flow,” in Airborne Laser Advanced Technology II, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3706, 11–22 (1999).
[CrossRef]

K. G. Gilbert, “Lear jet boundary-layer/shear-layer laser propagation measurements,” in Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 249–260.

D. R. Neal, T. J. O’Hern, J. R. Torczynski, M. E. Warren, R. Shul, T. S. McKechnie, “Wavefront sensors for optical diagnostics in fluid mechanics: application to heated flow, turbulence and droplet evaporation,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds. Proc. SPIE2005, 194–203 (1993).
[CrossRef]

C. A. Atwood, W. R. Van Dalsem, “Flowfield simulation about the SOFIA Airborne Observatory,” Paper AIAA-92-0656, presented at the 30th Aerospace Sciences Meeting, Reno, Nev., 6–9 January 1992 (American Institute of Aeronautics and Astronautics, Reston, Va., 1992).

G. Havener, “Optical wave front variance: a study on analytic models in use today,” Paper AIAA-92-0654, presented at the 30th Aerospace Sciences Meeting, Reno, Nev., 6–9 January 1992 (American Institute of Aeronautics and Astronautics, Reston, Va., 1992).

J. D. Trolinger, “Aero-optical characterization of aircraft optical turrets by holography, interferometry, and shadowgraph,” in Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 200–217.

W. J. Steinmetz, “Second moments of optical degradation due to a thin turbulent layer,” in Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 78–100.

G. W. Sutton, “Optical imaging through aircraft turbulent boundary layers,” in Vol. 80 of Progress in Astronautics and Aeronautics: Aero-Optical Phenomena, K. Gilbert, L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, New York, 1982), pp. 15–39.

R. J. Hugo, “Quantifying the spatio-temporal effects of optically-active turbulent flowfields on a coherent optical wave,” Ph.D. dissertation (University of Notre Dame, Notre Dame, Ind., 1995).

M. V. Klein, Optics (Wiley, New York, 1970).

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Figures (11)

Fig. 1
Fig. 1

Schematic of the heated-jet facility.

Fig. 2
Fig. 2

Instantaneous temperature field from a conditionally sampled database (compensated).

Fig. 3
Fig. 3

Variance of density fluctuations.

Fig. 4
Fig. 4

Variance of density fluctuations.

Fig. 5
Fig. 5

Covariance coefficient function of the density fluctuations: x/ D = 2.0.

Fig. 6
Fig. 6

Covariance coefficient function of the density fluctuations: x/ D = 3.0.

Fig. 7
Fig. 7

Optical degradation estimated by use of the linking equation.

Fig. 8
Fig. 8

Relationship between the integral length scale and the covariance coefficient function.

Fig. 9
Fig. 9

Typical slice of the covariance coefficient function.

Fig. 10
Fig. 10

Optical degradation estimated by use of the linking equation.

Fig. 11
Fig. 11

Slices of the covariance coefficient function.

Equations (19)

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σΦ2L=β20L0Lcovρy1, y2dy1dy2,
σΓ2=σΦ2/k2.
covρy1, y2=Eρy1-ρ¯y1ρy2-ρ¯y2,
ρ=P/RT,
covρx1, y1, z1; x2, y2, z2=σρ2 exp-x2-x1lρ2+y2-y1lρ2+z2-z1lρ21/2,
covρx1, y1, z1; x2, y2, z2=σρ2 exp-x2-x1lρ2+y2-y1lρ2+z2-z1lρ2,
σΦ2L=2β20L σρ2ylρydy,
σΦ2L=π β20L σρ2ylρydy,
OPLt, x=y1y2 nt, x, ydy,
n=KGDρ.
σΓ2=OPLt, x-OPLt, x¯2,
η=1-1lwkwdwh1/2,
τ=ρCdw/4h,
Nu=0.2+0.4Re0.45,
Mf=11+2πfτ21/2,
ϕ*f=-arctan2πfτ,
Hf=ηMfexp-iϕ*f.
I=OHH*H*=OH*|H|2,
Λy2=12-covρy1, y2ρ1ρ2dy1,

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