Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (6): 765-778.doi: https://doi.org/10.1007/s10483-017-2204-8

• 论文 •    下一篇

Scaling laws of compressible turbulence

Bohua SUN   

  1. Department of Mechanical Engineering, Cape Peninsula University of Technology, Cape Town 7535, South Africa
  • 收稿日期:2016-05-30 修回日期:2017-01-05 出版日期:2017-06-01 发布日期:2017-06-01
  • 通讯作者: Bohua SUN E-mail:sunb@cput.ac.za
  • 基金资助:

    Project supported by the National Research Foundation of South Africa (No. 93918)

Scaling laws of compressible turbulence

Bohua SUN   

  1. Department of Mechanical Engineering, Cape Peninsula University of Technology, Cape Town 7535, South Africa
  • Received:2016-05-30 Revised:2017-01-05 Online:2017-06-01 Published:2017-06-01
  • Contact: Bohua SUN E-mail:sunb@cput.ac.za
  • Supported by:

    Project supported by the National Research Foundation of South Africa (No. 93918)

摘要:

Spatial scaling laws of velocity kinetic energy spectra for the compressible turbulence flow and the density-weighted counterparts are formulated in terms of the wavenumber, dissipation rate, and Mach number by using a dimensional analysis. We apply the Barenblatt's incomplete similarity theory to both kinetic and density-weighted energy spectra. It shows that, within the initial subrange, both energy spectra approach the -5/3 and -2 power laws of the wavenumber when the Mach number tends to unity and infinity, respectively.

关键词: dimensional analysis, non-linear non-holonomic constraints, quasi-coordinates, fundamental equations of dynamics, spatial scaling law, incomplete similarity, compressible turbulence

Abstract:

Spatial scaling laws of velocity kinetic energy spectra for the compressible turbulence flow and the density-weighted counterparts are formulated in terms of the wavenumber, dissipation rate, and Mach number by using a dimensional analysis. We apply the Barenblatt's incomplete similarity theory to both kinetic and density-weighted energy spectra. It shows that, within the initial subrange, both energy spectra approach the -5/3 and -2 power laws of the wavenumber when the Mach number tends to unity and infinity, respectively.

Key words: non-linear non-holonomic constraints, quasi-coordinates, fundamental equations of dynamics, spatial scaling law, dimensional analysis, incomplete similarity, compressible turbulence

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