Scaling of energy spectra in weakly compressible turbulence

• Published in: Acta mechanica Sinica Vol. 33; no. 3; pp. 500 - 507
• Main Authors: Dong, Yufeng, He, Guowei
• Format: Journal Article
• Language: English
• Published: Beijing The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences 01.06.2017; Springer Nature B.V; School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, China; The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, No. 15 Beisihuan Xi Road, Beijing 100190, China%The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, No. 15 Beisihuan Xi Road, Beijing 100190, China
• Edition: English ed.
• Subjects: Asymptotic properties; Classical and Continuum Physics; closure;Space–time; Compressibility; Compressible; Computational fluid dynamics; Computational Intelligence; Computer simulation; correlation; Energy spectra; Engineering; Engineering Fluid Dynamics; Jupiter; Markov processes; Ocean currents; Research Paper; Scaling; spectra;Two-point; Theoretical and Applied Mechanics; Turbulence; turbulence;Energy; Vortices; Two-point closure; Energy spectra; Space–time correlation; Compressible turbulence
• ISSN: 0567-7718; 1614-3116
• DOI: 10.1007/s10409-017-0663-x

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.