### Abstract

A model for the Reynolds number dependence of the dimensionless dissipation rate

*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,∞}Original language | English |
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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

McComb, W. D., Berera, A., Yoffe, S. R., & Linkmann, M. F. (2015). Energy transfer and dissipation in forced isotropic turbulence.

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