Longitudinal and transverse structure functions in decaying nearly homogeneous and isotropic turbulence

doi:10.1088/1674-1056/23/1/014701

Chin. Phys. B ›› 2014, Vol. 23 ›› Issue (1): 14701-014701.doi: 10.1088/1674-1056/23/1/014701

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Longitudinal and transverse structure functions in decaying nearly homogeneous and isotropic turbulence

Imtiaz Ahmad^{a b}, 卢志明^a, 刘宇陆^a

a Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
b Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan

收稿日期:2013-03-19 修回日期:2013-06-23 出版日期:2013-11-12 发布日期:2013-11-12
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11272196, 11002085, and 11032007) and the Key Project of Education Commission of Shanghai Municipal, China (Grant No. 11ZZ87).

Longitudinal and transverse structure functions in decaying nearly homogeneous and isotropic turbulence

Imtiaz Ahmad^{a b}, Lu Zhi-Ming (卢志明)^a, Liu Yu-Lu (刘宇陆)^a

a Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
b Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan

Received:2013-03-19 Revised:2013-06-23 Online:2013-11-12 Published:2013-11-12
Contact: Lu Zhi-Ming E-mail:zmlu@shu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11272196, 11002085, and 11032007) and the Key Project of Education Commission of Shanghai Municipal, China (Grant No. 11ZZ87).

摘要/Abstract

摘要： Streamwise evolution of longitudinal and transverse velocity structure functions in a decaying homogeneous and nearly isotropic turbulence is reported for Reynolds numbers Re_λ up to 720. First, two theoretical relations between longitudinal and transverse structure functions are examined in the light of recently derived relations and the results show that the low-order transverse structure functions can be well approximated by longitudinal ones within the sub-inertial range. Reconstruction of fourth-order transverse structure functions with a recently proposed relation by Grauer et al. is comparatively less valid than the relation already proposed by Antonia et al. Secondly, extended self-similarity methods are used to measure the scaling exponents up to order eight and the streamwise evolution of scaling exponents is explored. The scaling exponents of longitudinal structure functions are, at first location, close to Zybin’s model, and at the fourth location, close to She–Leveque model. No obvious trend is found for the streamwise evolution of longitudinal scaling exponents, whereas, on the contrary, transverse scaling exponents become slightly smaller with the development of a steamwise direction. Finally, the stremwise variation of the order-dependent isotropy ratio indicates the turbulence at the last location is closer to isotropic than the other three locations.

关键词: fully developed turbulence, longitudinal and transverse structure functions, scaling exponents, intermittency

Abstract: Streamwise evolution of longitudinal and transverse velocity structure functions in a decaying homogeneous and nearly isotropic turbulence is reported for Reynolds numbers Re_λ up to 720. First, two theoretical relations between longitudinal and transverse structure functions are examined in the light of recently derived relations and the results show that the low-order transverse structure functions can be well approximated by longitudinal ones within the sub-inertial range. Reconstruction of fourth-order transverse structure functions with a recently proposed relation by Grauer et al. is comparatively less valid than the relation already proposed by Antonia et al. Secondly, extended self-similarity methods are used to measure the scaling exponents up to order eight and the streamwise evolution of scaling exponents is explored. The scaling exponents of longitudinal structure functions are, at first location, close to Zybin’s model, and at the fourth location, close to She–Leveque model. No obvious trend is found for the streamwise evolution of longitudinal scaling exponents, whereas, on the contrary, transverse scaling exponents become slightly smaller with the development of a steamwise direction. Finally, the stremwise variation of the order-dependent isotropy ratio indicates the turbulence at the last location is closer to isotropic than the other three locations.

Key words: fully developed turbulence, longitudinal and transverse structure functions, scaling exponents, intermittency

中图分类号: (Navier-Stokes equations)

47.10.ad

47.27.Jv (High-Reynolds-number turbulence)

Imtiaz Ahmad, 卢志明, 刘宇陆. Longitudinal and transverse structure functions in decaying nearly homogeneous and isotropic turbulence[J]. Chin. Phys. B, 2014, 23(1): 14701-014701.

Imtiaz Ahmad, Lu Zhi-Ming (卢志明), Liu Yu-Lu (刘宇陆). Longitudinal and transverse structure functions in decaying nearly homogeneous and isotropic turbulence[J]. Chin. Phys. B, 2014, 23(1): 14701-014701.

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Longitudinal and transverse structure functions in decaying nearly homogeneous and isotropic turbulence

Longitudinal and transverse structure functions in decaying nearly homogeneous and isotropic turbulence

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