## Abstract

The properties of acceleration fluctuations in isotropic turbulence are studied in direct numerical simulations (DNS) by decomposing the acceleration as the sum of local and convective contributions (a_{L} = ∂u/∂t and a_{C} = u. ∇u), or alternatively as the sum of irrotational and solenoidal contributions [a_{1} = - ∇(p/p) and a_{s} =ν∇^{2}u]. The main emphasis is on the nature of the mutual cancellation between a_{L} and a_{c} which must occur in order for the acceleration (a) to be small as predicted by the "random Taylor hypothesis" [Tennekes, J. Fluid Mech. 67, 561 (1975)] of small eddies in turbulent flow being passively "swept" past a stationary Eulerian observer. Results at Taylor-scale Reynolds number up to 240 show that the random-Taylor scenario 〈a^{2}〉≪〈a^{2}_{c}〉 ≈〈a^{2}_{L}〉, accompanied by strong antialignment between the vectors a_{L} and a_{C}, is indeed increasingly valid at higher Reynolds number. Mutual cancellation between a_{L} and a_{C} also leads to the solenoidal part of a being small compared to its irrotational part. Results for spectra in wave number space indicate that, at a given Reynolds number, the random Taylor hypothesis has greater validity at decreasing scale sizes. Finally, comparisons with DNS data in Gaussian random fields show that the mutual cancellation between a_{L} and a_{C} is essentially a kinematic effect, although the Reynolds number trends are made stronger by the dynamics implied in the Navier-Stokes equations.

Original language | English |
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Pages (from-to) | 1974-1984 |

Number of pages | 11 |

Journal | Physics of Fluids |

Volume | 13 |

Issue number | 7 |

DOIs | |

State | Published - Jul 2001 |