Universal form of the power spectrum of the aero-optical aberration caused by the supersonic turbulent boundary layer

doi:10.1088/1674-1056/23/10/104201

Abstract Based on the measurement of one-dimensional (1D) optical path difference (OPD) of the supersonic turbulent boundary layer, an analytical form for the power spectrum of the two-dimensional (2D) OPD is obtained with its structure function and under the locally homogeneous isotropic assumption. The universality of this spectrum is argued, and its validity is checked by the comparison with experimental result. The potential applications of this model in theoretical and numerical studies are emphasized. Another contribution of this work is around the application of correlation function to analyzing the statistics of OPD. Based on our results and other results published elsewhere, we show that the OPD is often not stationary, and one should be cautious about using this tool.

Keywords: aero-optics supersonic turbulent boundary layer optical path difference power spectrum

Received: 05 December 2013
Revised: 10 February 2014
Accepted manuscript online:

PACS:	42.25.Dd	(Wave propagation in random media)
	47.40.Ki	(Supersonic and hypersonic flows)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 61008037) and the National Basic Research Program of China (Grant No. 2009CB724100).

Corresponding Authors: Gao Qiong
E-mail: gaoqiong1980@126.com

About author: 42.25.Dd; 47.40.Ki

Cite this article:

Gao Qiong (高穹), Yi Shi-He (易仕和), Jiang Zong-Fu (姜宗福) Universal form of the power spectrum of the aero-optical aberration caused by the supersonic turbulent boundary layer 2014 Chin. Phys. B 23 104201


[1]	Gilbert K G and Otten L J 1982 Aero-Optical Phenomena (New York: AIAA)

[2]	Sutton G W 1985 AIAA J. 23 1525

[3]	Jumper E J and Fitzgerald E J 2001 Prog. Aerospace. Sci. 37 299

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

[5]	Gordeyev S, Jumper E J, Ng T T and Cain A B 2003 AIAA Paper 2003-3606

[6]	Malley M, Sutton G W and Kincheloe N 1992 Appl. Opt. 31 4440

[7]	Wittich D, Gordeyev S and Jumper E 2007 AIAA Paper 2007-4009

[8]	Smith A E, Gordeyev S and Jumper E 2012 Proc. SPIE 8395 83950C

[9]	Wang K and Wang M 2012 J. Fluid Mech. 696 122

[10]	Wyckham C M and Smits A J 2007 AIAA Paper 2006-3067

[11]	Gordeyev S, Jumper E and Hayden T E 2012 AIAA J. 50 682

[12]	Zhao Y X, Yi S H, Tian L F and Cheng Z Y 2009 Sci. China Ser. E 52 3640

[13]	He L, Yi S H, Zhao Y X, Tian L F and Chen Z 2011 Sci. China Ser. G 54 1702

[14]	He L, Yi S H, Zhao Y X, Tian L F and Chen Z 2011 Chin. Sci. Bull. 56 489

[15]	Gao Q, Yi S H, Jiang Z F, He L and Zhao Y X 2012 Opt. Express 20 16494

[16]	Tian L F, Yi S H, Zhao Y X, He L and Cheng Z Y 2009 Sci. China Ser. G 52 1357

[17]	Ye Q X and Shen Y H (ed.) 2006 Practical Handbook of Mathematics (Beijing, Science Press)

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

[19]	Hutchins N and Marusic I 2007 J. Fluid Mech. 579 1

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

[21]	Tatarski V I 1961 Wave Propagation in a Turbulent Medium (New York: McGraw-Hill) pp. 9-43

[22]	Cliff S F 1978 Laser Beam Propagation in the Atmosphere, Strohbehn J W (ed.) (Berlin: Springer-Verlag) pp. 3-26

[23]	Lane R G, Glindemann A and Dainty J C 1992 Waves Rand. Media 2 209

[24]	Frehlich R 2000 Appl. Opt. 39 393

[25]	Smits A and Dussauge J 2006 Turbulent Shear Layers in Supersonic Flow (New York: Springer)

[26]	Ganapathisubramani B, Hutchins N, Hambleton W T, Longmire E K and Marusic I 2005 J. Fluid Mech. 524 57

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Universal form of the power spectrum of the aero-optical aberration caused by the supersonic turbulent boundary layer

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