## Hierarchical structure of the optical path length of the supersonic turbulent boundary layer |

Optics Express, Vol. 20, Issue 15, pp. 16494-16503 (2012)

http://dx.doi.org/10.1364/OE.20.016494

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### Abstract

The optical path length (OPL) of supersonic turbulent boundary layer of Mach number 3.0 is obtained with the nanoparticle-based planar laser scattering technique, and its structure is analyzed within the framework of hierarchical symmetry assumption. Our result offers reasonable evidence for that the OPL obeys this assumption with parameter *β* depending on *q*. The scaling exponent *ζ*(*q*) of structure function is computed and compared with the theoretical prediction of She-Leveque model. The curve *ζ*(*q*) we obtained is convex and smaller than the theoretical value for small *q*, which is attributed to the large scale structure of the OPL.

© 2012 OSA

**OCIS Codes**

(030.6600) Coherence and statistical optics : Statistical optics

(030.7060) Coherence and statistical optics : Turbulence

**ToC Category:**

Coherence and Statistical Optics

**History**

Original Manuscript: June 20, 2012

Manuscript Accepted: June 22, 2012

Published: July 5, 2012

**Citation**

Qiong Gao, Shihe Yi, Zongfu Jiang, Lin He, and Yuxin Zhao, "Hierarchical structure of the optical path length of the supersonic turbulent boundary layer," Opt. Express **20**, 16494-16503 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-15-16494

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### References

- K. G. Gilbert and L. J. Otten, eds., Aero-Optical Phenomena (American Institute of Aeronautics and Astronautics, 1982).
- E. J. Jumper and E. J. Fitzgerald, “Resent advances in aero-optics,” Prog. Aerosp. Sci.37(3), 299–339 (2001). [CrossRef]
- M. Wang, A. Mani, and S. Gordeyev, “Physics and computation of aero-optics,” Annu. Rev. Fluid Mech.44(1), 299–321 (2012). [CrossRef]
- M. M. Malley, G. W. Sutton, and N. Kincheloe, “Beam-jitter measurements of turbulent aero-optical path differences,” Appl. Opt.31(22), 4440–4443 (1992). [CrossRef] [PubMed]
- 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(22), 4436–4447 (1996). [CrossRef] [PubMed]
- A. Mani, M. Wang, and P. Moin, “Statistical description of the free-space propagation of highly aberrated optical beams,” J. Opt. Soc. Am. A23(12), 3027–3035 (2006). [CrossRef] [PubMed]
- H. A. Stine and W. Winovitch, “Light diffusion through high-speed turbulent boundary layers,” NACA Res. Mem. A56B21 (NACA, 1956).
- S. Gordeyev, E. J. Jumper, T. T. Ng, and A. B. Cain, “Aero-optical characteristics of compressible, subsonic turbulent boundary layer,” AIAA paper 2003–3606 (American Institute of Aeronautics and Astronautics, 2003).
- S. Gordeyev, J. A. Cress, and E. J. Jumper, “Aero-optical properties of subsonic, turbulent boundary layers,” Preprint.
- S. Gordeyev, E. J. Jumper, and T. E. Hayden, “Aero-optics of supersonic boundary layers,” AIAA paper 2011–1325 (American Institute of Aeronautics and Astronautics, 2011).
- C. M. Wyckham and A. J. Smith, “Comparison of aero-optics distortions in hypersonic and transonic, turbulent boundary layers with gas injection,” AIAA paper 2006–3067 (American Institute of Aeronautics and Astronautics, 2006).
- C. R. Truman and M. J. Lee, “Effects of organized turbulence structures on the phase distortion in a coherent beam propagating through a turbulent shear flow,” Phys. Fluids A2(5), 851–857 (1990). [CrossRef]
- E. Tromeur, E. Garnier, and P. Sagaut, “Large eddy simulations of aero-optical effects in a spatially developing turbulent boundary layer,” J. Turbul.7, N1– N28 (2006). [CrossRef]
- K. Wang and M. Wang, “Aero-optics of subsonic turbulent boundary layers,” J. Fluid Mech.696, 122–151 (2012). [CrossRef]
- G. W. Sutton, “Aero-optical foundations and applications,” AIAA J.23(10), 1525–1537 (1985). [CrossRef]
- A. P. Freeman and H. J. Catrakis, “Direct reduction of aero-optical aberrations by large structure suppression control in turbulence,” AIAA J.46(10), 2582–2590 (2008). [CrossRef]
- V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).
- Q. Gao, Z. F. Jiang, S. H. Yi, L. He, and Y. X. Zhao, “Structure function of the refractive index of the supersonic turbulent boundary layer,” Submitted.
- U. Frisch, Turbulence (Cambridge University Press, 1995).
- G. Parisi and U. Frisch, “On the singularity structure of fully developed turbulence,” in Proc. of Int. School on Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, M. Ghil, R. Benzi, and G. Parisi eds. (Amsterdam, 1985), pp. 84–87.
- Z. S. She and E. Leveque, “Universal scaling laws in fully developed turbulence,” Phys. Rev. Lett.72(3), 336–339 (1994). [CrossRef] [PubMed]
- G. Ruiz-Chavarria, C. Baudet, and S. Ciliberto, “Scaling laws and dissipation scales of a passive scalar in fully developed turbulence,” Physica D99(2-3), 369–380 (1996). [CrossRef]
- C. Sun, Q. Zhou, and K. Q. Xia, “Cascades of velocity and temperature fluctuations in buoyancy-driven thermal turbulence,” Phys. Rev. Lett.97(14), 144504 (2006). [CrossRef] [PubMed]
- A. Smits and J. Dussauge, Turbulent Shear Layers in Supersonic Flow (Springer, 2006).
- Y. X. Zhao, S. H. Yi, L. F. Tian, and Z. Y. Cheng, “Supersonic flow imaging via nanoparticles,” Sci. China Ser. E52(12), 3640–3648 (2009). [CrossRef]
- L. He, 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. G54(9), 1702–1709 (2011). [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(6), 489–494 (2011). [CrossRef]
- M. Smith, A. Smits, and R. Miles, “Compressible boundary-layer density cross sections by UV Rayleigh scattering,” Opt. Lett.14(17), 916–918 (1989). [CrossRef] [PubMed]
- M. Smith and A. Smits, “Visualization of the structure of supersonic turbulent boundary layers,” Exp. Fluids18(4), 288–302 (1995). [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. G52(9), 1357–1363 (2009). [CrossRef]
- G. R. Osche, Optical Detection Theory for Laser Applications (Wiley-Interscience, 2002).
- R. J. Adrian, “Particle-imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech.23(1), 261–304 (1991). [CrossRef]
- Z. S. She and Z. X. Zhang, “Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems,” Acta Mech. Sin.25(3), 279–294 (2009). [CrossRef]
- R. Benzi, S. Ciliberto, R. Tripiccione, C. Baudet, F. Massaioli, and S. Succi, “Extended self-similarity in turbulent flows,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics48(1), R29–R32 (1993). [CrossRef] [PubMed]
- B. Davidovitch, M. H. Jensen, A. Levermann, J. Mathiesen, and I. Procaccia, “Thermodynamic formalism of the harmonic measure of diffusion limited aggregates: phase transition,” Phys. Rev. Lett.87(16), 164101 (2001). [CrossRef] [PubMed]
- K. R. Sreenivasan, “Fractals and multifractals in fluid turbulence,” Annu. Rev. Fluid Mech.23(1), 539–604 (1991). [CrossRef]
- B. Ganapathisubramani, N. T. Clemens, and D. S. Dolling, “Large-scale motions in a supersonic turbulent boundary layer,” J. Fluid Mech.556, 271–282 (2006). [CrossRef]
- M. J. Ringuette, M. Wu, and M. P. Martin, “Coherent structures in direct numerical simulation of turbulent boundary layer at Mach 3,” J. Fluid Mech.594, 59–69 (2008). [CrossRef]
- G. E. Elsinga, R. J. Adrian, B. W. Van Oudheusden, and F. Scarano, “Three-dimensional vortex organization in a high-Reynolds-number supersonic turbulent boundary layer,” J. Fluid Mech.644, 35–60 (2010). [CrossRef]

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