### Abstract

*ζ*from the structure functions

_{n}*S*, is presented as an alternative to the extended self-similarity (ESS) method and the use of generalized structure functions. We propose plotting the ratio ∣∣

_{n}(r)*S*∣∣ against the separation

_{n}(r)/S_{3}(r)*r*in accordance with a standard technique for analyzing experimental data. This method differs from the ESS technique, which plots

*S*against

_{n}(r)*S*, with the assumption

_{3}(r)*S*. Using our method for the particular case of

_{3}(r)∼r*S*we obtain the result that the exponent

_{2}(r)*ζ*decreases as the Taylor-Reynolds number increases, with

_{2}*ζ*→ 0.679±0.013 as

_{2}*R*→∞. This supports the idea of finite-viscosity corrections to the K41 prediction for

_{λ}*S*, 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.

_{2}Language | English |
---|---|

Article number | 053010 |

Number of pages | 12 |

Journal | Physical Review E |

Volume | 90 |

Issue number | 5 |

DOIs | |

Publication status | Published - 20 Nov 2014 |

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### Keywords

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

### Cite this

*Physical Review E*,

*90*(5), [053010]. https://doi.org/10.1103/PhysRevE.90.053010

}

*Physical Review E*, vol. 90, no. 5, 053010. https://doi.org/10.1103/PhysRevE.90.053010

**Spectral analysis of structure functions and their scaling exponents in forced isotropic turbulence.** / McComb, W. D.; Yoffe, S. R.; Linkmann, M. F.; Berera, A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Spectral analysis of structure functions and their scaling exponents in forced isotropic turbulence

AU - McComb, W. D.

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.

AB - 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.

KW - spectral analysis

KW - structure functions

KW - isotropic turbulence

KW - extended self-similarity

KW - ESS

UR - http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.053010

U2 - 10.1103/PhysRevE.90.053010

DO - 10.1103/PhysRevE.90.053010

M3 - Article

VL - 90

JO - Physical Review E

T2 - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 5

M1 - 053010

ER -