Spectral analysis of structure functions and their scaling exponents in forced isotropic turbulence

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

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The pseudospectral method, in conjunction with a technique for obtaining scaling exponents ζn from the structure functions Sn(r), is presented as an alternative to the extended self-similarity (ESS) method and the use of generalized structure functions. We propose plotting the ratio ∣∣Sn(r)/S3(r)∣∣ against the separation r in accordance with a standard technique for analyzing experimental data. This method differs from the ESS technique, which plots Sn(r) against S3(r), with the assumption S3(r)∼r. Using our method for the particular case of S2(r) we obtain the result that the exponent ζ2 decreases as the Taylor-Reynolds number increases, with ζ2 → 0.679±0.013 as Rλ→∞. This supports the idea of finite-viscosity corrections to the K41 prediction for S2, and is the opposite of the result obtained by ESS. The pseudospectral method also permits the forcing to be taken into account exactly through the calculation of the energy input in real space from the work spectrum of the stirring forces.
LanguageEnglish
Article number053010
Number of pages12
JournalPhysical Review E
Volume90
Issue number5
DOIs
Publication statusPublished - 20 Nov 2014

Fingerprint

isotropic turbulence
Scaling Exponent
Structure-function
Self-similarity
Spectral Analysis
spectrum analysis
Turbulence
Pseudospectral Method
exponents
scaling
plotting
stirring
Forcing
Reynolds number
Viscosity
plots
Exponent
Experimental Data
viscosity
Decrease

Keywords

  • spectral analysis
  • structure functions
  • isotropic turbulence
  • extended self-similarity
  • ESS

Cite this

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title = "Spectral analysis of structure functions and their scaling exponents in forced isotropic turbulence",
abstract = "The pseudospectral method, in conjunction with a technique for obtaining scaling exponents ζn from the structure functions Sn(r), is presented as an alternative to the extended self-similarity (ESS) method and the use of generalized structure functions. We propose plotting the ratio ∣∣Sn(r)/S3(r)∣∣ against the separation r in accordance with a standard technique for analyzing experimental data. This method differs from the ESS technique, which plots Sn(r) against S3(r), with the assumption S3(r)∼r. Using our method for the particular case of S2(r) we obtain the result that the exponent ζ2 decreases as the Taylor-Reynolds number increases, with ζ2 → 0.679±0.013 as Rλ→∞. This supports the idea of finite-viscosity corrections to the K41 prediction for S2, and is the opposite of the result obtained by ESS. The pseudospectral method also permits the forcing to be taken into account exactly through the calculation of the energy input in real space from the work spectrum of the stirring forces.",
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Spectral analysis of structure functions and their scaling exponents in forced isotropic turbulence. / McComb, W. D.; Yoffe, S. R.; Linkmann, M. F.; Berera, A.

In: Physical Review E, Vol. 90, No. 5, 053010, 20.11.2014.

Research output: Contribution to journalArticle

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AU - Yoffe, S. R.

AU - Linkmann, M. F.

AU - Berera, A.

N1 - (c) American Physical Society

PY - 2014/11/20

Y1 - 2014/11/20

N2 - The pseudospectral method, in conjunction with a technique for obtaining scaling exponents ζn from the structure functions Sn(r), is presented as an alternative to the extended self-similarity (ESS) method and the use of generalized structure functions. We propose plotting the ratio ∣∣Sn(r)/S3(r)∣∣ against the separation r in accordance with a standard technique for analyzing experimental data. This method differs from the ESS technique, which plots Sn(r) against S3(r), with the assumption S3(r)∼r. Using our method for the particular case of S2(r) we obtain the result that the exponent ζ2 decreases as the Taylor-Reynolds number increases, with ζ2 → 0.679±0.013 as Rλ→∞. This supports the idea of finite-viscosity corrections to the K41 prediction for S2, and is the opposite of the result obtained by ESS. The pseudospectral method also permits the forcing to be taken into account exactly through the calculation of the energy input in real space from the work spectrum of the stirring forces.

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