### Abstract

A new fundamentally based formulation of nonlocal effects in the rapid pressure-strain correlation in turbulent flows has been obtained. The resulting explicit form for the rapid pressure-strain correlation accounts for nonlocal effects produced by spatial variations in the mean-flow velocity gradients and is derived through Taylor expansion of the mean velocity gradients appearing in the exact integral relation for the rapid pressure-strain correlation. The integrals in the resulting series expansion are solved for high- and low-Reynolds number forms of the longitudinal correlation function f (r), and the resulting nonlocal rapid pressure-strain correlation is expressed as an infinite series in terms of Laplacians of the mean strain rate tensor. This formulation is used to obtain a nonlocal transport equation for the turbulence anisotropy that is expected to provide improved predictions of the anisotropy in strongly inhomogeneous flows.

Original language | English (US) |
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Article number | 046311 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 80 |

Issue number | 4 |

DOIs | |

State | Published - Oct 15 2009 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Statistics and Probability

### Cite this

**Nonlocal form of the rapid pressure-strain correlation in turbulent flows.** / Hamlington, Peter E.; Dahm, Werner.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 80, no. 4, 046311. https://doi.org/10.1103/PhysRevE.80.046311

}

TY - JOUR

T1 - Nonlocal form of the rapid pressure-strain correlation in turbulent flows

AU - Hamlington, Peter E.

AU - Dahm, Werner

PY - 2009/10/15

Y1 - 2009/10/15

N2 - A new fundamentally based formulation of nonlocal effects in the rapid pressure-strain correlation in turbulent flows has been obtained. The resulting explicit form for the rapid pressure-strain correlation accounts for nonlocal effects produced by spatial variations in the mean-flow velocity gradients and is derived through Taylor expansion of the mean velocity gradients appearing in the exact integral relation for the rapid pressure-strain correlation. The integrals in the resulting series expansion are solved for high- and low-Reynolds number forms of the longitudinal correlation function f (r), and the resulting nonlocal rapid pressure-strain correlation is expressed as an infinite series in terms of Laplacians of the mean strain rate tensor. This formulation is used to obtain a nonlocal transport equation for the turbulence anisotropy that is expected to provide improved predictions of the anisotropy in strongly inhomogeneous flows.

AB - A new fundamentally based formulation of nonlocal effects in the rapid pressure-strain correlation in turbulent flows has been obtained. The resulting explicit form for the rapid pressure-strain correlation accounts for nonlocal effects produced by spatial variations in the mean-flow velocity gradients and is derived through Taylor expansion of the mean velocity gradients appearing in the exact integral relation for the rapid pressure-strain correlation. The integrals in the resulting series expansion are solved for high- and low-Reynolds number forms of the longitudinal correlation function f (r), and the resulting nonlocal rapid pressure-strain correlation is expressed as an infinite series in terms of Laplacians of the mean strain rate tensor. This formulation is used to obtain a nonlocal transport equation for the turbulence anisotropy that is expected to provide improved predictions of the anisotropy in strongly inhomogeneous flows.

UR - http://www.scopus.com/inward/record.url?scp=70350521606&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350521606&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.80.046311

DO - 10.1103/PhysRevE.80.046311

M3 - Article

VL - 80

JO - Physical review. E

JF - Physical review. E

SN - 1539-3755

IS - 4

M1 - 046311

ER -