Abstract

The optical path difference (OPD) of the supersonic mixing layer with convective Mach number 0.5 is measured using the nanoparticle-based planar laser scattering technique, and its short-exposure optical transfer function (OTF) is computed with the proper orthogonal decomposition (POD). The OPD is analyzed from the viewpoint of structure function, and remarkable power law behavior is found. The power exponent is computed and analyzed. Taking the advantage of POD in capturing the energy of a signal, we present a model for the temporal evolution of OPD, which combines the deterministic and random factors together. With this model, the short-exposure OTF of the mixing layer is computed and analyzed. The amplitude modulation is evident at low frequencies, and it is almost negligible at high frequencies. The imaginary part of OTF for the mixing layer with developed vortex structures is of considerable amplitude, and the phase modulation becomes important for image degradation. We compare this phenomenon with the early result in aero-optics and explain it with the non-Gaussian statistics of OPD.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  4. S. Gordeyev and E. J. Jumper, “Fluid dynamics and aero-optics of turrets,” Prog. Aerosp. Sci. 46, 388–400 (2010).
    [CrossRef]
  5. R. E. Childs, “Prediction and control of turbulent aero-optical distortion using large eddy simulation,” in Proceedings of Annual Interceptor Technology Conference (American Institute of Aeronautics and Astronautics, 1993), pp. 1993–2670.
  6. R. J. Hugo and 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]
  7. R. J. Hugo and E. J. Jumper, “Applicability of the aero-optic linking equation to a highly coherent, transitional shear layer,” Appl. Opt. 39, 4392–4401 (2000).
    [CrossRef]
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    [CrossRef]
  10. R. J. Hugo, E. J. Jumper, G. Havener, and C. Stepanek, “Time-resolved wave front measurements through a compressible free shear layer,” AIAA J. 35, 671–677 (1997).
    [CrossRef]
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  12. H. J. Catrakis and R. C. Aguirre, “New interfacial fluid thickness approach in aero-optics with applications to compressible turbulence,” AIAA J. 42, 1973–1981 (2004).
    [CrossRef]
  13. F. R. Zubair and H. J. Catrakis, “Aero-optical interaction along laser beam propagation paths in compressible turbulence,” AIAA J. 45, 1663–1674 (2007).
    [CrossRef]
  14. F. R. Zubair and H. J. Catrakis, “On separated shear layers and the fractal geometry of turbulent scalar interfaces at large Reynolds numbers,” J. Fluid Mech. 624, 389–411(2009).
    [CrossRef]
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  16. A. Mani, P. Moin, and M. Wang, “Computational study of optical distortions by separated shear layers and turbulent wakes,” J. Fluid Mech. 625, 273–298 (2009).
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  17. A. Mani, M. Wang, and P. Moin, “Statistical description of the free-space propagation of highly aberrated optical beams,” J. Opt. Soc. Am. A 23, 3027–3035 (2006).
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    [CrossRef]
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    [CrossRef]
  23. Y. X. Zhao, S. H. Yi, L. F. Tian, L. He, and Z. Y. Cheng, “Density field measurement and approximate reconstruction of supersonic mixing layer,” Chin. Sci. Bull. 55, 2004–2009 (2010).
    [CrossRef]
  24. L. F. Tian, S. H. Yi, Y. X. Zhao, L. He, and Y. Z. Cheng, “Study of density field measurement based on NPLS technique in supersonic flow,” Sci. China Ser. G 52, 1357–1363 (2009).
    [CrossRef]
  25. H. Lin, S. H. Yi, Y. X. Zhao, L. F. Tian, and Z. Chen, “Visualization of coherent structures in a supersonic flat-plate boundary layer,” Chin. Sci. Bull. 56, 489–494 (2011).
  26. H. Lin, S. H. Yi, Y. X. Zhao, L. F. Tian, and Z. Chen, “Experimental study of a supersonic turbulent boundary layer using PIV, ” Sci. China Ser. G 54, 1702–1709 (2011).
    [CrossRef]
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    [CrossRef]
  28. Q. Gao, S. H. Yi, Z. F. Jiang, Y. X. Zhao, and W. K. Xie, “Analysing the structure of the optical path length of supersonic mixing layer with wavelet methods,” Chin. Phys. B 21, 064701(2012).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  34. P. Holmes, J. L. Lumley, and G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry (Cambridge University, 1996).
  35. C. R. Truman, R. I. Zadoks, B. Staveley, and H. Barsum, “Prediction and measurement of aero-optic effects through the dynamics of a passive scalar in turbulent shear flow,” in AIAA 18th Aerospace Ground Testing Conference (American Institute of Aeronautics and Astronautics, 1994), paper 1994-2549.
  36. J. M. Cicchiello and E. J. Jumper, “Low-order representation of fluid-optic interactions associated with a shear layer,” in 39th AIAA Aerospace Sciences Meeting and Exhibit (American Institute of Aeronautics and Astronautics, 2001), paper 2001-0952.
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2012

M. Wang, A. Mani, and S. Gordeyev, “Physics and computation of aero-optics,” Ann. Rev. Fluid Mech. 44, 299–321 (2012).
[CrossRef]

Q. Gao, S. H. Yi, Z. F. Jiang, Y. X. Zhao, and W. K. Xie, “Analysing the structure of the optical path length of supersonic mixing layer with wavelet methods,” Chin. Phys. B 21, 064701(2012).
[CrossRef]

2011

H. Lin, S. H. Yi, Y. X. Zhao, L. F. Tian, and Z. Chen, “Visualization of coherent structures in a supersonic flat-plate boundary layer,” Chin. Sci. Bull. 56, 489–494 (2011).

H. Lin, S. H. Yi, Y. X. Zhao, L. F. Tian, and Z. Chen, “Experimental study of a supersonic turbulent boundary layer using PIV, ” Sci. China Ser. G 54, 1702–1709 (2011).
[CrossRef]

2010

S. Gordeyev and E. J. Jumper, “Fluid dynamics and aero-optics of turrets,” Prog. Aerosp. Sci. 46, 388–400 (2010).
[CrossRef]

S. H. Yi, L. F. Tian, Y. X. Zhao, L. He, and Z. Y. Cheng, “Aero-optical aberration measuring method based on NPLS and its application,” Chin. Sci. Bull. 55, 3545–3549 (2010).
[CrossRef]

Y. X. Zhao, S. H. Yi, L. F. Tian, L. He, and Z. Y. Cheng, “Density field measurement and approximate reconstruction of supersonic mixing layer,” Chin. Sci. Bull. 55, 2004–2009 (2010).
[CrossRef]

Q. Gao, Z. F. Jiang, S. H. Yi, and Y. X. Zhao, “Optical path difference of the supersonic mixing layer,” Appl. Opt. 49, 3786–3792 (2010).
[CrossRef]

2009

L. F. Tian, S. H. Yi, Y. X. Zhao, L. He, and Y. Z. Cheng, “Study of density field measurement based on NPLS technique in supersonic flow,” Sci. China Ser. G 52, 1357–1363 (2009).
[CrossRef]

Y. X. Zhao, S. H. Yi, L. F. Tian, and Z. Y. Cheng, “Supersonic flow imaging via nanoparticles,” Sci. China Ser. E 52, 3640–3648 (2009).
[CrossRef]

F. R. Zubair and H. J. Catrakis, “On separated shear layers and the fractal geometry of turbulent scalar interfaces at large Reynolds numbers,” J. Fluid Mech. 624, 389–411(2009).
[CrossRef]

A. Mani, P. Moin, and M. Wang, “Computational study of optical distortions by separated shear layers and turbulent wakes,” J. Fluid Mech. 625, 273–298 (2009).
[CrossRef]

2008

D. P. Rizzetta, M. R. Visbal, and P. E. Morgan, “A high-order compact finite-difference scheme for large-eddy simulation of active flow control,” Prog. Aerosp. Sci. 44, 397–426 (2008).
[CrossRef]

2007

F. R. Zubair and H. J. Catrakis, “Aero-optical interaction along laser beam propagation paths in compressible turbulence,” AIAA J. 45, 1663–1674 (2007).
[CrossRef]

2006

2004

H. J. Catrakis and R. C. Aguirre, “New interfacial fluid thickness approach in aero-optics with applications to compressible turbulence,” AIAA J. 42, 1973–1981 (2004).
[CrossRef]

2001

P. E. Dimotakis, H. J. Catrakis, and D. C. Fourguette, “Flow structure and optical beam propagation in high-Reynolds-number gas-phase shear layers and jets,” J. Fluid Mech. 433, 105–134 (2001).

E. J. Jumper and E. J. Fitzgerald, “Resent advances in aero-optics,” Prog. Aerosp. Sci. 37, 299–339 (2001).
[CrossRef]

2000

1997

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

1996

1995

M. Smith and A. Smits, “Visualization of the structure of supersonic turbulent boundary layers,” Exp. Fluids 18, 288–302 (1995).
[CrossRef]

E. J. Jumper and R. J. Hugo, “Quantification of aero-optical distortion using the small-aperture beam technique,” AIAA J. 33, 2151–2157 (1995).
[CrossRef]

1993

G. Berkooz, P. Holmes, and J. L. Lumley, “The proper orthogonal decomposition in the analysis of turbulent flows,” Annu. Rev. Fluid Mech. 25, 539–575 (1993).
[CrossRef]

1992

1990

C. R. Truman and M. J. Lee, “Effects of organized turbulent structures on the phase distortion in a coherent beam propagating through a turbulent shear flow,” Phys. Fluids A. 2, 851–857 (1990).
[CrossRef]

1989

Aguirre, R. C.

H. J. Catrakis and R. C. Aguirre, “New interfacial fluid thickness approach in aero-optics with applications to compressible turbulence,” AIAA J. 42, 1973–1981 (2004).
[CrossRef]

Barsum, H.

C. R. Truman, R. I. Zadoks, B. Staveley, and H. Barsum, “Prediction and measurement of aero-optic effects through the dynamics of a passive scalar in turbulent shear flow,” in AIAA 18th Aerospace Ground Testing Conference (American Institute of Aeronautics and Astronautics, 1994), paper 1994-2549.

Becklund, O. A.

C. S. Williams and O. A. Becklund, Introduction to the Optical Transfer Function (Wiley, 1989).

Berkooz, G.

G. Berkooz, P. Holmes, and J. L. Lumley, “The proper orthogonal decomposition in the analysis of turbulent flows,” Annu. Rev. Fluid Mech. 25, 539–575 (1993).
[CrossRef]

P. Holmes, J. L. Lumley, and G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry (Cambridge University, 1996).

Catrakis, H. J.

F. R. Zubair and H. J. Catrakis, “On separated shear layers and the fractal geometry of turbulent scalar interfaces at large Reynolds numbers,” J. Fluid Mech. 624, 389–411(2009).
[CrossRef]

F. R. Zubair and H. J. Catrakis, “Aero-optical interaction along laser beam propagation paths in compressible turbulence,” AIAA J. 45, 1663–1674 (2007).
[CrossRef]

H. J. Catrakis and R. C. Aguirre, “New interfacial fluid thickness approach in aero-optics with applications to compressible turbulence,” AIAA J. 42, 1973–1981 (2004).
[CrossRef]

P. E. Dimotakis, H. J. Catrakis, and D. C. Fourguette, “Flow structure and optical beam propagation in high-Reynolds-number gas-phase shear layers and jets,” J. Fluid Mech. 433, 105–134 (2001).

Chen, Z.

H. Lin, S. H. Yi, Y. X. Zhao, L. F. Tian, and Z. Chen, “Visualization of coherent structures in a supersonic flat-plate boundary layer,” Chin. Sci. Bull. 56, 489–494 (2011).

H. Lin, S. H. Yi, Y. X. Zhao, L. F. Tian, and Z. Chen, “Experimental study of a supersonic turbulent boundary layer using PIV, ” Sci. China Ser. G 54, 1702–1709 (2011).
[CrossRef]

Cheng, Y. Z.

L. F. Tian, S. H. Yi, Y. X. Zhao, L. He, and Y. Z. Cheng, “Study of density field measurement based on NPLS technique in supersonic flow,” Sci. China Ser. G 52, 1357–1363 (2009).
[CrossRef]

Cheng, Z. Y.

S. H. Yi, L. F. Tian, Y. X. Zhao, L. He, and Z. Y. Cheng, “Aero-optical aberration measuring method based on NPLS and its application,” Chin. Sci. Bull. 55, 3545–3549 (2010).
[CrossRef]

Y. X. Zhao, S. H. Yi, L. F. Tian, L. He, and Z. Y. Cheng, “Density field measurement and approximate reconstruction of supersonic mixing layer,” Chin. Sci. Bull. 55, 2004–2009 (2010).
[CrossRef]

Y. X. Zhao, S. H. Yi, L. F. Tian, and Z. Y. Cheng, “Supersonic flow imaging via nanoparticles,” Sci. China Ser. E 52, 3640–3648 (2009).
[CrossRef]

Childs, R. E.

R. E. Childs, “Prediction and control of turbulent aero-optical distortion using large eddy simulation,” in Proceedings of Annual Interceptor Technology Conference (American Institute of Aeronautics and Astronautics, 1993), pp. 1993–2670.

Cicchiello, J. M.

J. M. Cicchiello and E. J. Jumper, “Low-order representation of fluid-optic interactions associated with a shear layer,” in 39th AIAA Aerospace Sciences Meeting and Exhibit (American Institute of Aeronautics and Astronautics, 2001), paper 2001-0952.

Dimotakis, P. E.

P. E. Dimotakis, H. J. Catrakis, and D. C. Fourguette, “Flow structure and optical beam propagation in high-Reynolds-number gas-phase shear layers and jets,” J. Fluid Mech. 433, 105–134 (2001).

Fitzgerald, E. J.

E. J. Jumper and E. J. Fitzgerald, “Resent advances in aero-optics,” Prog. Aerosp. Sci. 37, 299–339 (2001).
[CrossRef]

Fourguette, D. C.

P. E. Dimotakis, H. J. Catrakis, and D. C. Fourguette, “Flow structure and optical beam propagation in high-Reynolds-number gas-phase shear layers and jets,” J. Fluid Mech. 433, 105–134 (2001).

Gao, Q.

Q. Gao, S. H. Yi, Z. F. Jiang, Y. X. Zhao, and W. K. Xie, “Analysing the structure of the optical path length of supersonic mixing layer with wavelet methods,” Chin. Phys. B 21, 064701(2012).
[CrossRef]

Q. Gao, Z. F. Jiang, S. H. Yi, and Y. X. Zhao, “Optical path difference of the supersonic mixing layer,” Appl. Opt. 49, 3786–3792 (2010).
[CrossRef]

Q. Gao, Z. F. Jiang, S. H. Yi, L. He, and X. H. Wang, “Universal form of the power spectrum of the aero-optical aberration caused by the supersonic turbulent boundary layer,” Opt. Express (submitted).

Gilbert, K. G.

K. G. Gilbert and L. J. Otten, Aero-Optical Phenomena(American Institute of Aeronautics and Astronautics, 1982).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2007).

Gordeyev, S.

M. Wang, A. Mani, and S. Gordeyev, “Physics and computation of aero-optics,” Ann. Rev. Fluid Mech. 44, 299–321 (2012).
[CrossRef]

S. Gordeyev and E. J. Jumper, “Fluid dynamics and aero-optics of turrets,” Prog. Aerosp. Sci. 46, 388–400 (2010).
[CrossRef]

Havener, G.

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

He, L.

Y. X. Zhao, S. H. Yi, L. F. Tian, L. He, and Z. Y. Cheng, “Density field measurement and approximate reconstruction of supersonic mixing layer,” Chin. Sci. Bull. 55, 2004–2009 (2010).
[CrossRef]

S. H. Yi, L. F. Tian, Y. X. Zhao, L. He, and Z. Y. Cheng, “Aero-optical aberration measuring method based on NPLS and its application,” Chin. Sci. Bull. 55, 3545–3549 (2010).
[CrossRef]

L. F. Tian, S. H. Yi, Y. X. Zhao, L. He, and Y. Z. Cheng, “Study of density field measurement based on NPLS technique in supersonic flow,” Sci. China Ser. G 52, 1357–1363 (2009).
[CrossRef]

Q. Gao, Z. F. Jiang, S. H. Yi, L. He, and X. H. Wang, “Universal form of the power spectrum of the aero-optical aberration caused by the supersonic turbulent boundary layer,” Opt. Express (submitted).

Holmes, P.

G. Berkooz, P. Holmes, and J. L. Lumley, “The proper orthogonal decomposition in the analysis of turbulent flows,” Annu. Rev. Fluid Mech. 25, 539–575 (1993).
[CrossRef]

P. Holmes, J. L. Lumley, and G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry (Cambridge University, 1996).

Hugo, R. J.

R. J. Hugo and E. J. Jumper, “Applicability of the aero-optic linking equation to a highly coherent, transitional shear layer,” Appl. Opt. 39, 4392–4401 (2000).
[CrossRef]

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

R. J. Hugo and 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]

E. J. Jumper and R. J. Hugo, “Quantification of aero-optical distortion using the small-aperture beam technique,” AIAA J. 33, 2151–2157 (1995).
[CrossRef]

Jiang, Z. F.

Q. Gao, S. H. Yi, Z. F. Jiang, Y. X. Zhao, and W. K. Xie, “Analysing the structure of the optical path length of supersonic mixing layer with wavelet methods,” Chin. Phys. B 21, 064701(2012).
[CrossRef]

Q. Gao, Z. F. Jiang, S. H. Yi, and Y. X. Zhao, “Optical path difference of the supersonic mixing layer,” Appl. Opt. 49, 3786–3792 (2010).
[CrossRef]

Q. Gao, Z. F. Jiang, S. H. Yi, L. He, and X. H. Wang, “Universal form of the power spectrum of the aero-optical aberration caused by the supersonic turbulent boundary layer,” Opt. Express (submitted).

Jumper, E. J.

S. Gordeyev and E. J. Jumper, “Fluid dynamics and aero-optics of turrets,” Prog. Aerosp. Sci. 46, 388–400 (2010).
[CrossRef]

E. J. Jumper and E. J. Fitzgerald, “Resent advances in aero-optics,” Prog. Aerosp. Sci. 37, 299–339 (2001).
[CrossRef]

R. J. Hugo and E. J. Jumper, “Applicability of the aero-optic linking equation to a highly coherent, transitional shear layer,” Appl. Opt. 39, 4392–4401 (2000).
[CrossRef]

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

R. J. Hugo and 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]

E. J. Jumper and R. J. Hugo, “Quantification of aero-optical distortion using the small-aperture beam technique,” AIAA J. 33, 2151–2157 (1995).
[CrossRef]

J. M. Cicchiello and E. J. Jumper, “Low-order representation of fluid-optic interactions associated with a shear layer,” in 39th AIAA Aerospace Sciences Meeting and Exhibit (American Institute of Aeronautics and Astronautics, 2001), paper 2001-0952.

Kincheloe, N.

Lee, M. J.

C. R. Truman and M. J. Lee, “Effects of organized turbulent structures on the phase distortion in a coherent beam propagating through a turbulent shear flow,” Phys. Fluids A. 2, 851–857 (1990).
[CrossRef]

Lin, H.

H. Lin, S. H. Yi, Y. X. Zhao, L. F. Tian, and Z. Chen, “Visualization of coherent structures in a supersonic flat-plate boundary layer,” Chin. Sci. Bull. 56, 489–494 (2011).

H. Lin, S. H. Yi, Y. X. Zhao, L. F. Tian, and Z. Chen, “Experimental study of a supersonic turbulent boundary layer using PIV, ” Sci. China Ser. G 54, 1702–1709 (2011).
[CrossRef]

Lumley, J. L.

G. Berkooz, P. Holmes, and J. L. Lumley, “The proper orthogonal decomposition in the analysis of turbulent flows,” Annu. Rev. Fluid Mech. 25, 539–575 (1993).
[CrossRef]

P. Holmes, J. L. Lumley, and G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry (Cambridge University, 1996).

Malley, M.

Mani, A.

M. Wang, A. Mani, and S. Gordeyev, “Physics and computation of aero-optics,” Ann. Rev. Fluid Mech. 44, 299–321 (2012).
[CrossRef]

A. Mani, P. Moin, and M. Wang, “Computational study of optical distortions by separated shear layers and turbulent wakes,” J. Fluid Mech. 625, 273–298 (2009).
[CrossRef]

A. Mani, M. Wang, and P. Moin, “Statistical description of the free-space propagation of highly aberrated optical beams,” J. Opt. Soc. Am. A 23, 3027–3035 (2006).
[CrossRef]

Miles, R.

Moin, P.

A. Mani, P. Moin, and M. Wang, “Computational study of optical distortions by separated shear layers and turbulent wakes,” J. Fluid Mech. 625, 273–298 (2009).
[CrossRef]

A. Mani, M. Wang, and P. Moin, “Statistical description of the free-space propagation of highly aberrated optical beams,” J. Opt. Soc. Am. A 23, 3027–3035 (2006).
[CrossRef]

Morgan, P. E.

D. P. Rizzetta, M. R. Visbal, and P. E. Morgan, “A high-order compact finite-difference scheme for large-eddy simulation of active flow control,” Prog. Aerosp. Sci. 44, 397–426 (2008).
[CrossRef]

Otten, L. J.

K. G. Gilbert and L. J. Otten, Aero-Optical Phenomena(American Institute of Aeronautics and Astronautics, 1982).

Rizzeta, D. P.

M. R. Visbal and D. P. Rizzeta, “Effect of flow excitation on aero-optical aberration,” in 46th AIAA Aerospace Sciences Meeting (American Institute of Aeronautics and Astronautics, 2008), paper 2008-1074.

Rizzetta, D. P.

D. P. Rizzetta, M. R. Visbal, and P. E. Morgan, “A high-order compact finite-difference scheme for large-eddy simulation of active flow control,” Prog. Aerosp. Sci. 44, 397–426 (2008).
[CrossRef]

Smith, M.

M. Smith and A. Smits, “Visualization of the structure of supersonic turbulent boundary layers,” Exp. Fluids 18, 288–302 (1995).
[CrossRef]

M. Smith, A. Smits, and R. Miles, “Compressible boundary-layer density cross section by UV Rayleigh scattering,” Opt. Lett. 14, 916–918 (1989).
[CrossRef]

Smits, A.

M. Smith and A. Smits, “Visualization of the structure of supersonic turbulent boundary layers,” Exp. Fluids 18, 288–302 (1995).
[CrossRef]

M. Smith, A. Smits, and R. Miles, “Compressible boundary-layer density cross section by UV Rayleigh scattering,” Opt. Lett. 14, 916–918 (1989).
[CrossRef]

Staveley, B.

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Steinmetz, W. J.

W. J. Steinmetz, “Second moments of optical degradation due to a thin boundary layer,” in Aero-Optical Phenomena, K. G. Gilber and L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, 1982), pp. 78–100.

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S. H. Yi, L. F. Tian, Y. X. Zhao, L. He, and Z. Y. Cheng, “Aero-optical aberration measuring method based on NPLS and its application,” Chin. Sci. Bull. 55, 3545–3549 (2010).
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L. F. Tian, S. H. Yi, Y. X. Zhao, L. He, and Y. Z. Cheng, “Study of density field measurement based on NPLS technique in supersonic flow,” Sci. China Ser. G 52, 1357–1363 (2009).
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C. R. Truman, R. I. Zadoks, B. Staveley, and H. Barsum, “Prediction and measurement of aero-optic effects through the dynamics of a passive scalar in turbulent shear flow,” in AIAA 18th Aerospace Ground Testing Conference (American Institute of Aeronautics and Astronautics, 1994), paper 1994-2549.

Visbal, M. R.

D. P. Rizzetta, M. R. Visbal, and P. E. Morgan, “A high-order compact finite-difference scheme for large-eddy simulation of active flow control,” Prog. Aerosp. Sci. 44, 397–426 (2008).
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Q. Gao, S. H. Yi, Z. F. Jiang, Y. X. Zhao, and W. K. Xie, “Analysing the structure of the optical path length of supersonic mixing layer with wavelet methods,” Chin. Phys. B 21, 064701(2012).
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H. Lin, S. H. Yi, Y. X. Zhao, L. F. Tian, and Z. Chen, “Visualization of coherent structures in a supersonic flat-plate boundary layer,” Chin. Sci. Bull. 56, 489–494 (2011).

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S. H. Yi, L. F. Tian, Y. X. Zhao, L. He, and Z. Y. Cheng, “Aero-optical aberration measuring method based on NPLS and its application,” Chin. Sci. Bull. 55, 3545–3549 (2010).
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Y. X. Zhao, S. H. Yi, L. F. Tian, and Z. Y. Cheng, “Supersonic flow imaging via nanoparticles,” Sci. China Ser. E 52, 3640–3648 (2009).
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L. F. Tian, S. H. Yi, Y. X. Zhao, L. He, and Y. Z. Cheng, “Study of density field measurement based on NPLS technique in supersonic flow,” Sci. China Ser. G 52, 1357–1363 (2009).
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C. R. Truman, R. I. Zadoks, B. Staveley, and H. Barsum, “Prediction and measurement of aero-optic effects through the dynamics of a passive scalar in turbulent shear flow,” in AIAA 18th Aerospace Ground Testing Conference (American Institute of Aeronautics and Astronautics, 1994), paper 1994-2549.

Zhao, Y. X.

Q. Gao, S. H. Yi, Z. F. Jiang, Y. X. Zhao, and W. K. Xie, “Analysing the structure of the optical path length of supersonic mixing layer with wavelet methods,” Chin. Phys. B 21, 064701(2012).
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H. Lin, S. H. Yi, Y. X. Zhao, L. F. Tian, and Z. Chen, “Visualization of coherent structures in a supersonic flat-plate boundary layer,” Chin. Sci. Bull. 56, 489–494 (2011).

H. Lin, S. H. Yi, Y. X. Zhao, L. F. Tian, and Z. Chen, “Experimental study of a supersonic turbulent boundary layer using PIV, ” Sci. China Ser. G 54, 1702–1709 (2011).
[CrossRef]

S. H. Yi, L. F. Tian, Y. X. Zhao, L. He, and Z. Y. Cheng, “Aero-optical aberration measuring method based on NPLS and its application,” Chin. Sci. Bull. 55, 3545–3549 (2010).
[CrossRef]

Y. X. Zhao, S. H. Yi, L. F. Tian, L. He, and Z. Y. Cheng, “Density field measurement and approximate reconstruction of supersonic mixing layer,” Chin. Sci. Bull. 55, 2004–2009 (2010).
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Q. Gao, Z. F. Jiang, S. H. Yi, and Y. X. Zhao, “Optical path difference of the supersonic mixing layer,” Appl. Opt. 49, 3786–3792 (2010).
[CrossRef]

Y. X. Zhao, S. H. Yi, L. F. Tian, and Z. Y. Cheng, “Supersonic flow imaging via nanoparticles,” Sci. China Ser. E 52, 3640–3648 (2009).
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L. F. Tian, S. H. Yi, Y. X. Zhao, L. He, and Y. Z. Cheng, “Study of density field measurement based on NPLS technique in supersonic flow,” Sci. China Ser. G 52, 1357–1363 (2009).
[CrossRef]

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[CrossRef]

Ann. Rev. Fluid Mech.

M. Wang, A. Mani, and S. Gordeyev, “Physics and computation of aero-optics,” Ann. Rev. Fluid Mech. 44, 299–321 (2012).
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Chin. Phys. B

Q. Gao, S. H. Yi, Z. F. Jiang, Y. X. Zhao, and W. K. Xie, “Analysing the structure of the optical path length of supersonic mixing layer with wavelet methods,” Chin. Phys. B 21, 064701(2012).
[CrossRef]

Chin. Sci. Bull.

S. H. Yi, L. F. Tian, Y. X. Zhao, L. He, and Z. Y. Cheng, “Aero-optical aberration measuring method based on NPLS and its application,” Chin. Sci. Bull. 55, 3545–3549 (2010).
[CrossRef]

Y. X. Zhao, S. H. Yi, L. F. Tian, L. He, and Z. Y. Cheng, “Density field measurement and approximate reconstruction of supersonic mixing layer,” Chin. Sci. Bull. 55, 2004–2009 (2010).
[CrossRef]

H. Lin, S. H. Yi, Y. X. Zhao, L. F. Tian, and Z. Chen, “Visualization of coherent structures in a supersonic flat-plate boundary layer,” Chin. Sci. Bull. 56, 489–494 (2011).

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A. Mani, P. Moin, and M. Wang, “Computational study of optical distortions by separated shear layers and turbulent wakes,” J. Fluid Mech. 625, 273–298 (2009).
[CrossRef]

F. R. Zubair and H. J. Catrakis, “On separated shear layers and the fractal geometry of turbulent scalar interfaces at large Reynolds numbers,” J. Fluid Mech. 624, 389–411(2009).
[CrossRef]

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Opt. Lett.

Phys. Fluids A.

C. R. Truman and M. J. Lee, “Effects of organized turbulent structures on the phase distortion in a coherent beam propagating through a turbulent shear flow,” Phys. Fluids A. 2, 851–857 (1990).
[CrossRef]

Prog. Aerosp. Sci.

D. P. Rizzetta, M. R. Visbal, and P. E. Morgan, “A high-order compact finite-difference scheme for large-eddy simulation of active flow control,” Prog. Aerosp. Sci. 44, 397–426 (2008).
[CrossRef]

S. Gordeyev and E. J. Jumper, “Fluid dynamics and aero-optics of turrets,” Prog. Aerosp. Sci. 46, 388–400 (2010).
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Y. X. Zhao, S. H. Yi, L. F. Tian, and Z. Y. Cheng, “Supersonic flow imaging via nanoparticles,” Sci. China Ser. E 52, 3640–3648 (2009).
[CrossRef]

Sci. China Ser. G

L. F. Tian, S. H. Yi, Y. X. Zhao, L. He, and Y. Z. Cheng, “Study of density field measurement based on NPLS technique in supersonic flow,” Sci. China Ser. G 52, 1357–1363 (2009).
[CrossRef]

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Q. Gao, Z. F. Jiang, S. H. Yi, L. He, and X. H. Wang, “Universal form of the power spectrum of the aero-optical aberration caused by the supersonic turbulent boundary layer,” Opt. Express (submitted).

M. R. Visbal and D. P. Rizzeta, “Effect of flow excitation on aero-optical aberration,” in 46th AIAA Aerospace Sciences Meeting (American Institute of Aeronautics and Astronautics, 2008), paper 2008-1074.

M. R. Visbal, “Numerical simulation of aero-optical aberration through weakly-compressible shear layers,” in Proceedings of 39th AIAA Fluid Dynamics Conference (American Institute of Aeronautics and Astronautics, 2009), paper 2009-4298.

R. E. Childs, “Prediction and control of turbulent aero-optical distortion using large eddy simulation,” in Proceedings of Annual Interceptor Technology Conference (American Institute of Aeronautics and Astronautics, 1993), pp. 1993–2670.

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J. M. Cicchiello and E. J. Jumper, “Low-order representation of fluid-optic interactions associated with a shear layer,” in 39th AIAA Aerospace Sciences Meeting and Exhibit (American Institute of Aeronautics and Astronautics, 2001), paper 2001-0952.

C. S. Williams and O. A. Becklund, Introduction to the Optical Transfer Function (Wiley, 1989).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

W. J. Steinmetz, “Second moments of optical degradation due to a thin boundary layer,” in Aero-Optical Phenomena, K. G. Gilber and L. J. Otten, eds. (American Institute of Aeronautics and Astronautics, 1982), pp. 78–100.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2007).

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Figures (7)

Fig. 1.
Fig. 1.

Sketch of the experimental setup used in the present study. The main components are the supersonic mixing layer wind tunnel and the NPLS system.

Fig. 2.
Fig. 2.

(a) and (b) NPLS images of the mixing flow in the middle region and (c) the relevant OPD: red solid curve, (a); black dashed curve, (b). These images have been enhanced by gamma transform with γ=0.6. (The images used in our computation below are the original ones.)

Fig. 3.
Fig. 3.

(a) and (b) NPLS images of the mixing flow in the latter region and (c) the relevant OPD: red solid curve, (a); black dashed curve, (b). These images have been enhanced by gamma transform with γ=0.6. (The images used in our computation are the original ones.)

Fig. 4.
Fig. 4.

SF of OPD in the (a) middle and (b) latter regions of the supersonic mixing layer.

Fig. 5.
Fig. 5.

POD analysis of the OPD in the (a) and (b) middle and (c) and (d) latter regions of the supersonic mixing layer. The mean OPD of each ensemble is subtracted before the analysis.

Fig. 6.
Fig. 6.

Cumulative energy of the POD eigenvalues relevant to the middle and latter regions of the supersonic mixing layer.

Fig. 7.
Fig. 7.

Short-exposure OTF of the supersonic mixing layer in the (a) and (b) middle and (c) and (d) latter regions. Find details in the text.

Tables (1)

Tables Icon

Table 1 Important Parameters of the Supersonic Mixing Layer Wind Tunnel with Mc=0.50

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

Mc=(U2U1)/(a1+a2)=0.50,
OPL(x)=yaybn(x,y)dy=yayb[1+KGDρ(x,y)]dy,
OPD(x)=OPL(x)OPL(x),
D(x)=(OPD(x+x0)OPD(x0))2,
ψ=k=1MckLk,
1Mk=1M(Li,Lk)ck=λci,i=1,2,,M,
L=jajψj.
ajak=δjkλj,
tc=l/ΔU=l/(U2U1),
L(t1)=jaj(t1)ψj,L(t2)=jaj(t2)ψj,
W(t,x)=2πL(t,x)/λ¯,
H(t,fx)=l(fx)exp{i[W(t,x+λ¯dfx/2)W(t,xλ¯dfx/2)]}dxl(0)dx,
p(x+λ¯dfx),p(xλ¯dfx).
p(x)=rect(x2w)={1,|x|<w0,else,
f0=w/λ¯d,f^x=fx/2f0.
H(f^x)=1f^x,f^x1.
e(k)=i=1kλ/iλi.

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