Energy transfer and dissipation in forced isotropic turbulence

W. D. McComb, A. Berera, S. R. Yoffe, M. F. Linkmann

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

A model for the Reynolds number dependence of the dimensionless dissipation rate Cε was derived from the dimensionless Kármán-Howarth equation, resulting in Cε = Cε,∞ +C/RL + O(1/RL ), where RL is the integral scale Reynolds number. The coefficients C and Cε,∞ arise from asymptotic expansions of the dimensionless second- and third-order structure functions. This theoretical work was supplemented by direct numerical simulations (DNS) of forced isotropic turbulence for integral scale Reynolds numbers up to RL = 5875 (Rλ = 435), which were used to establish that the decay of dimensionless dissipation with increasing Reynolds number took the form of a power law RLn with exponent value n = −1.000 ± 0.009, and that this decay of Cε was actually due to the increase in the Taylor surrogate U3/L. The model equation was fitted to data from the DNS which resulted in the value C = 18.9 ± 1.3 and in an asymptotic value for Cε in the infinite Reynolds number limit of Cε,∞ = 0.468 ± 0.006.
LanguageEnglish
Article number043013
Number of pages10
JournalPhysical Review E
Volume91
Issue number4
DOIs
Publication statusPublished - 21 Apr 2015

Fingerprint

isotropic turbulence
Energy Transfer
Energy Dissipation
Dimensionless
Reynolds number
Turbulence
energy dissipation
energy transfer
direct numerical simulation
Dissipation
dissipation
Decay
decay
Structure-function
Asymptotic Expansion
Power Law
Exponent
exponents
expansion
Coefficient

Keywords

  • energy transfer
  • isotropic turbulence
  • direct numerical simulation

Cite this

McComb, W. D. ; Berera, A. ; Yoffe, S. R. ; Linkmann, M. F. / Energy transfer and dissipation in forced isotropic turbulence. In: Physical Review E. 2015 ; Vol. 91, No. 4.
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Energy transfer and dissipation in forced isotropic turbulence. / McComb, W. D.; Berera, A.; Yoffe, S. R.; Linkmann, M. F.

In: Physical Review E, Vol. 91, No. 4, 043013, 21.04.2015.

Research output: Contribution to journalArticle

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N2 - A model for the Reynolds number dependence of the dimensionless dissipation rate Cε was derived from the dimensionless Kármán-Howarth equation, resulting in Cε = Cε,∞ +C/RL + O(1/RL ), where RL is the integral scale Reynolds number. The coefficients C and Cε,∞ arise from asymptotic expansions of the dimensionless second- and third-order structure functions. This theoretical work was supplemented by direct numerical simulations (DNS) of forced isotropic turbulence for integral scale Reynolds numbers up to RL = 5875 (Rλ = 435), which were used to establish that the decay of dimensionless dissipation with increasing Reynolds number took the form of a power law RLn with exponent value n = −1.000 ± 0.009, and that this decay of Cε was actually due to the increase in the Taylor surrogate U3/L. The model equation was fitted to data from the DNS which resulted in the value C = 18.9 ± 1.3 and in an asymptotic value for Cε in the infinite Reynolds number limit of Cε,∞ = 0.468 ± 0.006.

AB - A model for the Reynolds number dependence of the dimensionless dissipation rate Cε was derived from the dimensionless Kármán-Howarth equation, resulting in Cε = Cε,∞ +C/RL + O(1/RL ), where RL is the integral scale Reynolds number. The coefficients C and Cε,∞ arise from asymptotic expansions of the dimensionless second- and third-order structure functions. This theoretical work was supplemented by direct numerical simulations (DNS) of forced isotropic turbulence for integral scale Reynolds numbers up to RL = 5875 (Rλ = 435), which were used to establish that the decay of dimensionless dissipation with increasing Reynolds number took the form of a power law RLn with exponent value n = −1.000 ± 0.009, and that this decay of Cε was actually due to the increase in the Taylor surrogate U3/L. The model equation was fitted to data from the DNS which resulted in the value C = 18.9 ± 1.3 and in an asymptotic value for Cε in the infinite Reynolds number limit of Cε,∞ = 0.468 ± 0.006.

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