Abstract

The tilt of the aero-optical aberration caused by the supersonic turbulent boundary layer is obtained by analyzing the center wandering of the far-field optical pattern, and its characteristics are examined from the viewpoint of statistics. When the diameter of the beam propagating through the flow is small compared with the boundary layer thickness, the probability density function (PDF) of the tilt coefficient is centered and can be approximated with a Gaussian distribution. For a larger beam diameter, the PDF of the tilt in the spanwise direction can still be regarded as centered and Gaussian, but the tilt in the streamwise direction clearly deviates from a Gaussian distribution. The correlation of the tilts in the two directions is investigated by computing the correlation coefficient, and the results indicate that the correlation is negative and strong for a small beam diameter and becomes positive and weak for a large beam diameter. These characteristics are explained by the hairpin vortex structures in the boundary layer, which prevail and meander for a very long distance streamwise.

© 2013 Optical Society of America

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References

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  1. K. G. Gilbert and L. J. Otten, eds., Aero-Optical Phenomena (American Institute of Aeronautics and Astronautics, 1982).
  2. E. J. Jumper and E. J. Fitzgerald, Prog. Aerospace Sci. 37, 299 (2001).
    [CrossRef]
  3. W. Wang, A. Mani, and S. Gordeyev, Ann. Rev. Fluid Mech. 44, 299 (2012).
    [CrossRef]
  4. D. L. Fried, J. Opt. Soc. Am. 55, 1427 (1965).
    [CrossRef]
  5. D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).
    [CrossRef]
  6. J. W. Goodman, Statistical Optics (Wiley, 2000).
  7. W. J. Yanta, W. C. Spring, J. F. Lafferty, A. S. Collier, R. L. Bell, D. R. Neal, D. R. Hamrick, R. J. Copland, L. Pezzaniti, M. Banish, and R. Shaw, “Near- and far-field measurements of aero-optical effects due to propagation through hypersonic flows,” AIAA Tech. Rep. 2000–2357 (American Institute of Aeronautics and Astronautics, 2000).
  8. A. Mani, M. Wang, and P. Moin, J. Opt. Soc. Am. A 23, 3027 (2006).
    [CrossRef]
  9. B. Ganapathisubramani, N. T. Clemens, and D. S. Dolling, J. Fluid Mech. 556, 271 (2006).
    [CrossRef]
  10. M. J. Ringuette, M. Wu, and M. P. Martin, J. Fluid Mech. 594, 59 (2008).
    [CrossRef]
  11. G. E. Elsinga, R. J. Adrian, B. W. Oudheusden, and F. Scarano, J. Fluid Mech. 644, 35 (2010).
    [CrossRef]

2012

W. Wang, A. Mani, and S. Gordeyev, Ann. Rev. Fluid Mech. 44, 299 (2012).
[CrossRef]

2010

G. E. Elsinga, R. J. Adrian, B. W. Oudheusden, and F. Scarano, J. Fluid Mech. 644, 35 (2010).
[CrossRef]

2008

M. J. Ringuette, M. Wu, and M. P. Martin, J. Fluid Mech. 594, 59 (2008).
[CrossRef]

2006

A. Mani, M. Wang, and P. Moin, J. Opt. Soc. Am. A 23, 3027 (2006).
[CrossRef]

B. Ganapathisubramani, N. T. Clemens, and D. S. Dolling, J. Fluid Mech. 556, 271 (2006).
[CrossRef]

2001

E. J. Jumper and E. J. Fitzgerald, Prog. Aerospace Sci. 37, 299 (2001).
[CrossRef]

1966

1965

Adrian, R. J.

G. E. Elsinga, R. J. Adrian, B. W. Oudheusden, and F. Scarano, J. Fluid Mech. 644, 35 (2010).
[CrossRef]

Banish, M.

W. J. Yanta, W. C. Spring, J. F. Lafferty, A. S. Collier, R. L. Bell, D. R. Neal, D. R. Hamrick, R. J. Copland, L. Pezzaniti, M. Banish, and R. Shaw, “Near- and far-field measurements of aero-optical effects due to propagation through hypersonic flows,” AIAA Tech. Rep. 2000–2357 (American Institute of Aeronautics and Astronautics, 2000).

Bell, R. L.

W. J. Yanta, W. C. Spring, J. F. Lafferty, A. S. Collier, R. L. Bell, D. R. Neal, D. R. Hamrick, R. J. Copland, L. Pezzaniti, M. Banish, and R. Shaw, “Near- and far-field measurements of aero-optical effects due to propagation through hypersonic flows,” AIAA Tech. Rep. 2000–2357 (American Institute of Aeronautics and Astronautics, 2000).

Clemens, N. T.

B. Ganapathisubramani, N. T. Clemens, and D. S. Dolling, J. Fluid Mech. 556, 271 (2006).
[CrossRef]

Collier, A. S.

W. J. Yanta, W. C. Spring, J. F. Lafferty, A. S. Collier, R. L. Bell, D. R. Neal, D. R. Hamrick, R. J. Copland, L. Pezzaniti, M. Banish, and R. Shaw, “Near- and far-field measurements of aero-optical effects due to propagation through hypersonic flows,” AIAA Tech. Rep. 2000–2357 (American Institute of Aeronautics and Astronautics, 2000).

Copland, R. J.

W. J. Yanta, W. C. Spring, J. F. Lafferty, A. S. Collier, R. L. Bell, D. R. Neal, D. R. Hamrick, R. J. Copland, L. Pezzaniti, M. Banish, and R. Shaw, “Near- and far-field measurements of aero-optical effects due to propagation through hypersonic flows,” AIAA Tech. Rep. 2000–2357 (American Institute of Aeronautics and Astronautics, 2000).

Dolling, D. S.

B. Ganapathisubramani, N. T. Clemens, and D. S. Dolling, J. Fluid Mech. 556, 271 (2006).
[CrossRef]

Elsinga, G. E.

G. E. Elsinga, R. J. Adrian, B. W. Oudheusden, and F. Scarano, J. Fluid Mech. 644, 35 (2010).
[CrossRef]

Fitzgerald, E. J.

E. J. Jumper and E. J. Fitzgerald, Prog. Aerospace Sci. 37, 299 (2001).
[CrossRef]

Fried, D. L.

Ganapathisubramani, B.

B. Ganapathisubramani, N. T. Clemens, and D. S. Dolling, J. Fluid Mech. 556, 271 (2006).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 2000).

Gordeyev, S.

W. Wang, A. Mani, and S. Gordeyev, Ann. Rev. Fluid Mech. 44, 299 (2012).
[CrossRef]

Hamrick, D. R.

W. J. Yanta, W. C. Spring, J. F. Lafferty, A. S. Collier, R. L. Bell, D. R. Neal, D. R. Hamrick, R. J. Copland, L. Pezzaniti, M. Banish, and R. Shaw, “Near- and far-field measurements of aero-optical effects due to propagation through hypersonic flows,” AIAA Tech. Rep. 2000–2357 (American Institute of Aeronautics and Astronautics, 2000).

Jumper, E. J.

E. J. Jumper and E. J. Fitzgerald, Prog. Aerospace Sci. 37, 299 (2001).
[CrossRef]

Lafferty, J. F.

W. J. Yanta, W. C. Spring, J. F. Lafferty, A. S. Collier, R. L. Bell, D. R. Neal, D. R. Hamrick, R. J. Copland, L. Pezzaniti, M. Banish, and R. Shaw, “Near- and far-field measurements of aero-optical effects due to propagation through hypersonic flows,” AIAA Tech. Rep. 2000–2357 (American Institute of Aeronautics and Astronautics, 2000).

Mani, A.

W. Wang, A. Mani, and S. Gordeyev, Ann. Rev. Fluid Mech. 44, 299 (2012).
[CrossRef]

A. Mani, M. Wang, and P. Moin, J. Opt. Soc. Am. A 23, 3027 (2006).
[CrossRef]

Martin, M. P.

M. J. Ringuette, M. Wu, and M. P. Martin, J. Fluid Mech. 594, 59 (2008).
[CrossRef]

Moin, P.

Neal, D. R.

W. J. Yanta, W. C. Spring, J. F. Lafferty, A. S. Collier, R. L. Bell, D. R. Neal, D. R. Hamrick, R. J. Copland, L. Pezzaniti, M. Banish, and R. Shaw, “Near- and far-field measurements of aero-optical effects due to propagation through hypersonic flows,” AIAA Tech. Rep. 2000–2357 (American Institute of Aeronautics and Astronautics, 2000).

Oudheusden, B. W.

G. E. Elsinga, R. J. Adrian, B. W. Oudheusden, and F. Scarano, J. Fluid Mech. 644, 35 (2010).
[CrossRef]

Pezzaniti, L.

W. J. Yanta, W. C. Spring, J. F. Lafferty, A. S. Collier, R. L. Bell, D. R. Neal, D. R. Hamrick, R. J. Copland, L. Pezzaniti, M. Banish, and R. Shaw, “Near- and far-field measurements of aero-optical effects due to propagation through hypersonic flows,” AIAA Tech. Rep. 2000–2357 (American Institute of Aeronautics and Astronautics, 2000).

Ringuette, M. J.

M. J. Ringuette, M. Wu, and M. P. Martin, J. Fluid Mech. 594, 59 (2008).
[CrossRef]

Scarano, F.

G. E. Elsinga, R. J. Adrian, B. W. Oudheusden, and F. Scarano, J. Fluid Mech. 644, 35 (2010).
[CrossRef]

Shaw, R.

W. J. Yanta, W. C. Spring, J. F. Lafferty, A. S. Collier, R. L. Bell, D. R. Neal, D. R. Hamrick, R. J. Copland, L. Pezzaniti, M. Banish, and R. Shaw, “Near- and far-field measurements of aero-optical effects due to propagation through hypersonic flows,” AIAA Tech. Rep. 2000–2357 (American Institute of Aeronautics and Astronautics, 2000).

Spring, W. C.

W. J. Yanta, W. C. Spring, J. F. Lafferty, A. S. Collier, R. L. Bell, D. R. Neal, D. R. Hamrick, R. J. Copland, L. Pezzaniti, M. Banish, and R. Shaw, “Near- and far-field measurements of aero-optical effects due to propagation through hypersonic flows,” AIAA Tech. Rep. 2000–2357 (American Institute of Aeronautics and Astronautics, 2000).

Wang, M.

Wang, W.

W. Wang, A. Mani, and S. Gordeyev, Ann. Rev. Fluid Mech. 44, 299 (2012).
[CrossRef]

Wu, M.

M. J. Ringuette, M. Wu, and M. P. Martin, J. Fluid Mech. 594, 59 (2008).
[CrossRef]

Yanta, W. J.

W. J. Yanta, W. C. Spring, J. F. Lafferty, A. S. Collier, R. L. Bell, D. R. Neal, D. R. Hamrick, R. J. Copland, L. Pezzaniti, M. Banish, and R. Shaw, “Near- and far-field measurements of aero-optical effects due to propagation through hypersonic flows,” AIAA Tech. Rep. 2000–2357 (American Institute of Aeronautics and Astronautics, 2000).

Ann. Rev. Fluid Mech.

W. Wang, A. Mani, and S. Gordeyev, Ann. Rev. Fluid Mech. 44, 299 (2012).
[CrossRef]

J. Fluid Mech.

B. Ganapathisubramani, N. T. Clemens, and D. S. Dolling, J. Fluid Mech. 556, 271 (2006).
[CrossRef]

M. J. Ringuette, M. Wu, and M. P. Martin, J. Fluid Mech. 594, 59 (2008).
[CrossRef]

G. E. Elsinga, R. J. Adrian, B. W. Oudheusden, and F. Scarano, J. Fluid Mech. 644, 35 (2010).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Prog. Aerospace Sci.

E. J. Jumper and E. J. Fitzgerald, Prog. Aerospace Sci. 37, 299 (2001).
[CrossRef]

Other

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

J. W. Goodman, Statistical Optics (Wiley, 2000).

W. J. Yanta, W. C. Spring, J. F. Lafferty, A. S. Collier, R. L. Bell, D. R. Neal, D. R. Hamrick, R. J. Copland, L. Pezzaniti, M. Banish, and R. Shaw, “Near- and far-field measurements of aero-optical effects due to propagation through hypersonic flows,” AIAA Tech. Rep. 2000–2357 (American Institute of Aeronautics and Astronautics, 2000).

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Figures (4)

Fig. 1.
Fig. 1.

Sketch of the experimental setup.

Fig. 2.
Fig. 2.

(a) Center wandering of far-field optical pattern and the PDFs of the shifts in the (b) u and (c) v directions. The aperture diameter da is 30 mm and exposure time Δt is 100 μs.

Fig. 3.
Fig. 3.

Skewness of the shift in the (a) u direction and (b) v direction and flatness of the shift in the (c) u direction and (d) v direction.

Fig. 4.
Fig. 4.

Correlation coefficients between the shifts in the u and v directions.

Equations (8)

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

Ui(x,y)=A(x,y)exp[jkΦ(x,y)],
If(u,v)=|Ui(x,y)exp[jk(xu+yv)/f]dxdy|2,
Φ(x,y)=Φ0+kxx+kyy+Φr(x,y),
If(u+fkx,v+fky)=|A(x,y)exp[jkΦr(x,y)]×exp[jk(xu+yv)/f]dxdy|2.
uc=i,juiI(ui,vj)/i,jI(ui,vj),vc=i,jvjI(ui,vj)/i,jI(ui,vj),
α=μu/f,β=μv/f,γ=1α2β2.
S=x3/(x2)3/2,F=x4/(x2)2,
Cuv=(Δucμu)(Δvcμv)/σuσv,

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