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Acta Mechanica Sinica
Published in: Acta Mechanica Sinica 3/2017

02-05-2017 | Research Paper

Scaling of energy spectra in weakly compressible turbulence

Authors: Yufeng Dong, Guowei He

Published in: Acta Mechanica Sinica | Issue 3/2017

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Abstract

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.
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Appendix
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Literature
1.
Frisch, U.: Turbulence. The legacy of A. N. Kolmogorov. Cambridge University Press, Cambridge (1995)MATH
2.
Sagaut, P., Cambon, C.: Homogeneous Turbulence Dynamics. Cambridge University Press, Cambridge (2008)CrossRefMATH
3.
4.
Galtier, S., Banerjee, S.: Exact relation for correlation functions in compressible isothermal turbulence. Phys. Rev. Lett. 107, 134501 (2011)CrossRef
5.
Kritsuk, A.G., Wagner, R., Norman, M.L.: Energy cascade and scaling in supersonic isothermal turbulence. J. Fluid Mech. 729, R1 (2013)MathSciNetCrossRefMATH
6.
Falkovich, G., Fouxon, I., Oz, Y.: New relations for correlation functions in Navier–Stokes turbulence. J. Fluid Mech. 644, 465–472 (2010)MathSciNetCrossRefMATH
7.
Wagner, R., Falkovich, G., Kritsuk, A.G., et al.: Flux correlations in supersonic isothermal turbulence. J. Fluid Mech. 713, 482–490 (2012)MathSciNetCrossRefMATH
8.
Aluie, H.: Compressible turbulence: the cascade and its locality. Phys. Rev. Lett. 106, 1745902 (2011)CrossRef
9.
Fauchet, G., Bertoglio, J.P.: A two-point closure for compressible turbulence. C. R. Acad. Sci. Ser. IIB Mech. Phys. Astron. 327, 665–671 (1999)MATH
10.
Fauchet, G., Bertoglio, J.P.: Pseudo-sound and acoustic regimes in compressible turbulence. C. R. Acad. Sci. Ser. IIB Mech. Phys. Astron. 327, 673–678 (1999)MATH
11.
Bertoglio, J.P., Bataille, F., Marion, J.D.: Two-point closures for weakly compressible turbulence. Phys. Fluids 13, 290–310 (2001)CrossRefMATH
12.
He, G.W., Jin, G.D., Yang, Y.: Space–time correlations and dynamic coupling in turbulent Flows. Annu. Rev. Fluid Mech. 49, 51–70 (2017)CrossRefMATH
13.
14.
Leslie, D.C.: Developments in the Theory of Turbulence. Clarendon Press, Oxford (1973)MATH
15.
Bos, W.J.T., Bertoglio, J.P.: Lagrangian markovianized field approximation for turbulence. J. Turbul. 14, 99–120 (2013)MathSciNetCrossRef
16.
17.
Li, D., Zhang, X., He, G.W.: Temporal decorrelations in compressible isotropic turbulence. Phys. Rev. E 88, 021001(R) (2013)CrossRef
18.
Yang, Y., Pullin, D.I., Bermejo-Moreno, I.: Multi-scale geometric analysis of Lagrangian structures in isotropic turbulence. J. Fluid Mech. 654, 230–277 (2010)MathSciNetCrossRefMATH
19.
Fang, L., Bos, W.J.T., Jin, G.D.: Short-time evolution of Lagrangian velocity gradient correlations in isotropic turbulence. Phys. Fluids 27, 125102 (2015)
20.
Chen, J.C., Jin, G.D., Zhang, J.: Large eddy simulation of orientation and rotation of ellipsoidal particles in isotropic turbulent flows. J. Turbul. 17, 308–326 (2016)MathSciNetCrossRef
21.
Sarkar, S., Erlebacher, G., Hussaini, M.Y., et al.: The analysis and modeling of dilatational terms in compressible turbulence. J. Fluid Mech. 227, 473–493 (1991)CrossRefMATH
22.
Li, D., Guo, L., Zhang, X., et al.: A numerical study of a turbulent mixing layer and its generated noise. Sci. China Phys. Mech. 56, 1157–1164 (2013)CrossRef
23.
Porter, D., Pouquet, A., Woodward, P.: Measures of intermittency in driven supersonic flows. Phys. Rev. E 66, 026301 (2002)CrossRef
24.
Kritsuk, A.G., Norman, M.L., Padoan, P., et al.: The statistics of supersonic isothermal turbulence. Astrophys. J. 665, 416–431 (2007)CrossRef
25.
Wang, J.C., Yang, Y.T., Shi, Y.P., et al.: Cascade of kinetic energy in three-dimensional compressible turbulence. Phys. Rev. Lett. 110, 214505 (2013)CrossRef
26.
Bachelor, G.K.: The Theory of Homogeneous Turbulence. Cambridge University Press, Cambridge (1971)
27.
Bataille, F., Zhou, Y.: Nature of the energy transfer process in compressible turbulence. Phys. Rev. E 59, 5417–5426 (1999)CrossRef
28.
Pan, L.B., Padoan, P., Kritsuk, A.G.: Dissipative structures in supersonic turbulence. Phys. Rev. Lett. 102, 034501 (2009)CrossRef
Metadata
Title
Scaling of energy spectra in weakly compressible turbulence
Authors
Yufeng Dong
Guowei He
Publication date
02-05-2017
Publisher
The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences
Published in
Acta Mechanica Sinica / Issue 3/2017
Print ISSN: 0567-7718
Electronic ISSN: 1614-3116
DOI
https://doi.org/10.1007/s10409-017-0663-x

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