### 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 |

### Keywords

- shear layer turbulence
- turbulence simulation

### ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

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## Cite this

*Journal of Fluid Mechanics*,

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