### Abstract

*C*was derived from the dimensionless Kármán-Howarth equation, resulting in

_{ε}*C*, where

_{ε}= C_{ε,∞}+C/R_{L}+ O(1/R_{L})*R*is the integral scale Reynolds number. The coefficients

_{L}*C*and

*C*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

_{ε,∞}*R*= 5875 (

_{L}*R*= 435), which were used to establish that the decay of dimensionless dissipation with increasing Reynolds number took the form of a power law

_{λ}*R*with exponent value

_{L}^{n}*n*= −1.000 ± 0.009, and that this decay of

*C*was actually due to the increase in the Taylor surrogate

_{ε}*U*. The model equation was fitted to data from the DNS which resulted in the value

^{3}/L*C*= 18.9 ± 1.3 and in an asymptotic value for

*C*in the infinite Reynolds number limit of

_{ε}*C*= 0.468 ± 0.006.

_{ε,∞}Language | English |
---|---|

Article number | 043013 |

Number of pages | 10 |

Journal | Physical Review E |

Volume | 91 |

Issue number | 4 |

DOIs | |

Publication status | Published - 21 Apr 2015 |

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### Keywords

- energy transfer
- isotropic turbulence
- direct numerical simulation

### Cite this

*Physical Review E*,

*91*(4), [043013]. https://doi.org/10.1103/PhysRevE.91.043013

}

*Physical Review E*, vol. 91, no. 4, 043013. https://doi.org/10.1103/PhysRevE.91.043013

**Energy transfer and dissipation in forced isotropic turbulence.** / McComb, W. D.; Berera, A.; Yoffe, S. R.; Linkmann, M. F.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Energy transfer and dissipation in forced isotropic turbulence

AU - McComb, W. D.

AU - Berera, A.

AU - Yoffe, S. R.

AU - Linkmann, M. F.

PY - 2015/4/21

Y1 - 2015/4/21

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.

KW - energy transfer

KW - isotropic turbulence

KW - direct numerical simulation

UR - http://link.aps.org/doi/10.1103/PhysRevE.91.043013

U2 - 10.1103/PhysRevE.91.043013

DO - 10.1103/PhysRevE.91.043013

M3 - Article

VL - 91

JO - Physical Review E

T2 - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 4

M1 - 043013

ER -