### Abstract

We present a fundamentally new approach for the modeling of the subgrid-scale stresses for the large-eddy simulation (LES) of turbulent flows, based directly on the spatial distribution of vorticity within the subgrid field. Drawing on a substantial body of theoretical, experimental and computational evidence, we demonstrate that the enstrophy field Q(x, t) ≡ 1/2 ω·ω(x, t) exhibits multifractal scale-similarity in the inertial range of high Reynolds-number turbulence. A multifractal cascade can then be used to describe the spatial distribution of vorticity magnitudes within the subgrid field. An additive cascade can be used to describe the spatial distribution of vorticity orientations, which isotropically decorrelate through the subgrid field from the orientations of the smallest resolved scale Δ in the flow. It is then possible to recast the subgrid velocity contributions to the subgrid stress tensor T_{ij} as Biot-Savart integrals over the subgrid vorticity field, which permits direct calculation of T_{ij}. The integral can be simplified using central-limit concepts, and in the high Reynolds-number limit, the subgrid-velocity field reduces to a simple algebraic expression based on quantities available from the resolved scales of the flow. Results from a priori tests are presented indicating good spatial and magnitude agreement for the filtered subgrid velocities u^{s9s}, the subgrid stress tensor T_{ij} and the subgrid energy production, P*. The multifractal approach presented here can be extended to model the filtered scalar transport equation and the Reynolds stresses in the Reynolds Averaged Navier-Stokes equation.

Original language | English (US) |
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Title of host publication | 40th AIAA Aerospace Sciences Meeting and Exhibit |

State | Published - 2002 |

Externally published | Yes |

Event | 40th AIAA Aerospace Sciences Meeting and Exhibit 2002 - Reno, NV, United States Duration: Jan 14 2002 → Jan 17 2002 |

### Other

Other | 40th AIAA Aerospace Sciences Meeting and Exhibit 2002 |
---|---|

Country | United States |

City | Reno, NV |

Period | 1/14/02 → 1/17/02 |

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### ASJC Scopus subject areas

- Space and Planetary Science
- Aerospace Engineering

### Cite this

*40th AIAA Aerospace Sciences Meeting and Exhibit*

**A new multifractal subgrid-scale model for large-eddy simulation.** / Burton, Gregory C.; Dahm, Werner; Dowling, David R.; Powell, Kenneth G.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*40th AIAA Aerospace Sciences Meeting and Exhibit.*40th AIAA Aerospace Sciences Meeting and Exhibit 2002, Reno, NV, United States, 1/14/02.

}

TY - GEN

T1 - A new multifractal subgrid-scale model for large-eddy simulation

AU - Burton, Gregory C.

AU - Dahm, Werner

AU - Dowling, David R.

AU - Powell, Kenneth G.

PY - 2002

Y1 - 2002

N2 - We present a fundamentally new approach for the modeling of the subgrid-scale stresses for the large-eddy simulation (LES) of turbulent flows, based directly on the spatial distribution of vorticity within the subgrid field. Drawing on a substantial body of theoretical, experimental and computational evidence, we demonstrate that the enstrophy field Q(x, t) ≡ 1/2 ω·ω(x, t) exhibits multifractal scale-similarity in the inertial range of high Reynolds-number turbulence. A multifractal cascade can then be used to describe the spatial distribution of vorticity magnitudes within the subgrid field. An additive cascade can be used to describe the spatial distribution of vorticity orientations, which isotropically decorrelate through the subgrid field from the orientations of the smallest resolved scale Δ in the flow. It is then possible to recast the subgrid velocity contributions to the subgrid stress tensor Tij as Biot-Savart integrals over the subgrid vorticity field, which permits direct calculation of Tij. The integral can be simplified using central-limit concepts, and in the high Reynolds-number limit, the subgrid-velocity field reduces to a simple algebraic expression based on quantities available from the resolved scales of the flow. Results from a priori tests are presented indicating good spatial and magnitude agreement for the filtered subgrid velocities us9s, the subgrid stress tensor Tij and the subgrid energy production, P*. The multifractal approach presented here can be extended to model the filtered scalar transport equation and the Reynolds stresses in the Reynolds Averaged Navier-Stokes equation.

AB - We present a fundamentally new approach for the modeling of the subgrid-scale stresses for the large-eddy simulation (LES) of turbulent flows, based directly on the spatial distribution of vorticity within the subgrid field. Drawing on a substantial body of theoretical, experimental and computational evidence, we demonstrate that the enstrophy field Q(x, t) ≡ 1/2 ω·ω(x, t) exhibits multifractal scale-similarity in the inertial range of high Reynolds-number turbulence. A multifractal cascade can then be used to describe the spatial distribution of vorticity magnitudes within the subgrid field. An additive cascade can be used to describe the spatial distribution of vorticity orientations, which isotropically decorrelate through the subgrid field from the orientations of the smallest resolved scale Δ in the flow. It is then possible to recast the subgrid velocity contributions to the subgrid stress tensor Tij as Biot-Savart integrals over the subgrid vorticity field, which permits direct calculation of Tij. The integral can be simplified using central-limit concepts, and in the high Reynolds-number limit, the subgrid-velocity field reduces to a simple algebraic expression based on quantities available from the resolved scales of the flow. Results from a priori tests are presented indicating good spatial and magnitude agreement for the filtered subgrid velocities us9s, the subgrid stress tensor Tij and the subgrid energy production, P*. The multifractal approach presented here can be extended to model the filtered scalar transport equation and the Reynolds stresses in the Reynolds Averaged Navier-Stokes equation.

UR - http://www.scopus.com/inward/record.url?scp=84894317824&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894317824&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84894317824

BT - 40th AIAA Aerospace Sciences Meeting and Exhibit

ER -