Acta Mechanica Sinica

, Volume 33, Issue 3, pp 500–507 | Cite as

Scaling of energy spectra in weakly compressible turbulence

Research Paper


We find an asymptotic expression for the characteristic timescales of decorrelation processes in weakly compressible and isothermal turbulence. This result is used in the Eddy-Damped Quasi-Normal Markovian equation to derive the scalings of compressible energy spectra: (1) if the acoustic waves are dominant, the compressible energy spectra exhibit \(-7/3\) scaling; (2) if local eddy straining is dominant, the compressible energy spectra are scaled as \(-3\). Meanwhile, the energy spectra of incompressible components display the same scaling of \(-5/3\) as those in incompressible turbulence. The direct numerical simulations of weakly compressible turbulence are used to examine the scaling.


Compressible turbulence Energy spectra Two-point closure Space–time correlation 



This work was supported by the National Natural Science Foundation of China (Grants 11302238, 11232011, 11572331, and 11490551). The authors would like to acknowledge the support from the Strategic Priority Research Program (Grant XDB22040104) and the Key Research Program of Frontier Sciences of Chinese Academy of Sciences and the National Basic Research Program of China (973 Program) (Grant 2013CB834100: Nonlinear science).


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.The State Key Laboratory of Nonlinear Mechanics, Institute of MechanicsChinese Academy of SciencesBeijingChina
  2. 2.School of Engineering SciencesUniversity of Chinese Academy of SciencesBeijingChina

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