### Abstract

How to design an artificial inflow condition in simulations of the Navier-Stokes equation that is already fully turbulent? This is the turbulent inflow problem. This first question is followed by: How much of the true turbulence must be reproduced at the inflow? We present a technique able to produce a random field with the exact two-point two-time covariance of a given reference turbulent flow. It is obtained as the output of a linear filter fed with white noise. The method is illustrated on the simulation of a turbulent free shear layer. The filter coefficients are obtained from the solution of the Yule-Walker equation, and the computation can be performed efficiently using a recursive solution procedure. The method should also be useful in the study of flow receptivity, when the processes of transition to turbulence are sensitive to the perturbation environment.

Original language | English |
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Pages (from-to) | 54-80 |

Number of pages | 27 |

Journal | Journal of Fluid Mechanics |

Volume | 676 |

DOIs | |

Publication status | Published - 2011 Jun 10 |

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### Keywords

- shear layer turbulence
- turbulence simulation

### ASJC Scopus subject areas

- Mechanical Engineering
- Mechanics of Materials
- Condensed Matter Physics

### Cite this

*Journal of Fluid Mechanics*,

*676*, 54-80. https://doi.org/10.1017/jfm.2011.32

**Realizing turbulent statistics.** / Hepffner, Jérôme; Naka, Yoshitsugu; Fukagata, Koji.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, vol. 676, pp. 54-80. https://doi.org/10.1017/jfm.2011.32

}

TY - JOUR

T1 - Realizing turbulent statistics

AU - Hepffner, Jérôme

AU - Naka, Yoshitsugu

AU - Fukagata, Koji

PY - 2011/6/10

Y1 - 2011/6/10

N2 - How to design an artificial inflow condition in simulations of the Navier-Stokes equation that is already fully turbulent? This is the turbulent inflow problem. This first question is followed by: How much of the true turbulence must be reproduced at the inflow? We present a technique able to produce a random field with the exact two-point two-time covariance of a given reference turbulent flow. It is obtained as the output of a linear filter fed with white noise. The method is illustrated on the simulation of a turbulent free shear layer. The filter coefficients are obtained from the solution of the Yule-Walker equation, and the computation can be performed efficiently using a recursive solution procedure. The method should also be useful in the study of flow receptivity, when the processes of transition to turbulence are sensitive to the perturbation environment.

AB - How to design an artificial inflow condition in simulations of the Navier-Stokes equation that is already fully turbulent? This is the turbulent inflow problem. This first question is followed by: How much of the true turbulence must be reproduced at the inflow? We present a technique able to produce a random field with the exact two-point two-time covariance of a given reference turbulent flow. It is obtained as the output of a linear filter fed with white noise. The method is illustrated on the simulation of a turbulent free shear layer. The filter coefficients are obtained from the solution of the Yule-Walker equation, and the computation can be performed efficiently using a recursive solution procedure. The method should also be useful in the study of flow receptivity, when the processes of transition to turbulence are sensitive to the perturbation environment.

KW - shear layer turbulence

KW - turbulence simulation

UR - http://www.scopus.com/inward/record.url?scp=79959251889&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79959251889&partnerID=8YFLogxK

U2 - 10.1017/jfm.2011.32

DO - 10.1017/jfm.2011.32

M3 - Article

AN - SCOPUS:79959251889

VL - 676

SP - 54

EP - 80

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -