| ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS |
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Longitudinal and transverse structure functions in decaying nearly homogeneous and isotropic turbulence |
| Imtiaz Ahmada 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 |
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Abstract Streamwise evolution of longitudinal and transverse velocity structure functions in a decaying homogeneous and nearly isotropic turbulence is reported for Reynolds numbers Reλ 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.
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Received: 19 March 2013
Revised: 23 June 2013
Accepted manuscript online:
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PACS:
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47.10.ad
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(Navier-Stokes equations)
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47.27.Jv
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(High-Reynolds-number turbulence)
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| Fund: 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). |
Corresponding Authors:
Lu Zhi-Ming
E-mail: zmlu@shu.edu.cn
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Cite this article:
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 2014 Chin. Phys. B 23 014701
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