### Abstract

A vexing problem occurs in certain flows when long, but finite, time-average estimates of the mean flow fail to exhibit the symmetry properties imposed by boundary conditions and physics. The mean field becomes suspect, making it difficult, or even incorrect to apply Reynolds decomposition. The problem occurs when the flow exhibits "super-coherent" states, i.e. states of flow having coherence times much longer than the averaging times used in typical turbulence experiments. Turbulent Rayleigh-Benard convection (RBC) is one such flow, and it will be used here as an example to illustrate and explain this phenomenon. The study focuses on a turbulent RBC experiment (Fernandes, 2001) in a 6.3:1 (diameter: depth) aspect-ratio vertical cylinder that supplemented time averaging with true ensemble averaging to achieve almost zero mean flow. To obtain a three-dimensional time-varying picture of the mechanisms at work, the experiment is simulated by direct numerical simulation of the Boussinesq equations (Sakievich et al., 2016). Three types of super-coherent states, associated with the symmetries of the flow, are found to bias the mean flow, unless steps are taken to sample each state with equal probability. They are azimuthal composition and orientation of the large-scale structures, the direction of azimuthal drift, and the preferential direction of the large-scale central motions.

Original language | English (US) |
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Title of host publication | 10th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2017 |

Publisher | International Symposium on Turbulence and Shear Flow Phenomena, TSFP10 |

Volume | 1 |

ISBN (Electronic) | 9780000000002 |

State | Published - 2017 |

Event | 10th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2017 - Chicago, United States Duration: Jul 6 2017 → Jul 9 2017 |

### Other

Other | 10th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2017 |
---|---|

Country | United States |

City | Chicago |

Period | 7/6/17 → 7/9/17 |

### Fingerprint

### ASJC Scopus subject areas

- Atmospheric Science
- Aerospace Engineering

### Cite this

*10th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2017*(Vol. 1). International Symposium on Turbulence and Shear Flow Phenomena, TSFP10.

**Reynolds decomposition of turbulence containing super-coherent states.** / Adrian, Ronald; Sakievich, P. J.; Peet, Yulia.

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

*10th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2017.*vol. 1, International Symposium on Turbulence and Shear Flow Phenomena, TSFP10, 10th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2017, Chicago, United States, 7/6/17.

}

TY - GEN

T1 - Reynolds decomposition of turbulence containing super-coherent states

AU - Adrian, Ronald

AU - Sakievich, P. J.

AU - Peet, Yulia

PY - 2017

Y1 - 2017

N2 - A vexing problem occurs in certain flows when long, but finite, time-average estimates of the mean flow fail to exhibit the symmetry properties imposed by boundary conditions and physics. The mean field becomes suspect, making it difficult, or even incorrect to apply Reynolds decomposition. The problem occurs when the flow exhibits "super-coherent" states, i.e. states of flow having coherence times much longer than the averaging times used in typical turbulence experiments. Turbulent Rayleigh-Benard convection (RBC) is one such flow, and it will be used here as an example to illustrate and explain this phenomenon. The study focuses on a turbulent RBC experiment (Fernandes, 2001) in a 6.3:1 (diameter: depth) aspect-ratio vertical cylinder that supplemented time averaging with true ensemble averaging to achieve almost zero mean flow. To obtain a three-dimensional time-varying picture of the mechanisms at work, the experiment is simulated by direct numerical simulation of the Boussinesq equations (Sakievich et al., 2016). Three types of super-coherent states, associated with the symmetries of the flow, are found to bias the mean flow, unless steps are taken to sample each state with equal probability. They are azimuthal composition and orientation of the large-scale structures, the direction of azimuthal drift, and the preferential direction of the large-scale central motions.

AB - A vexing problem occurs in certain flows when long, but finite, time-average estimates of the mean flow fail to exhibit the symmetry properties imposed by boundary conditions and physics. The mean field becomes suspect, making it difficult, or even incorrect to apply Reynolds decomposition. The problem occurs when the flow exhibits "super-coherent" states, i.e. states of flow having coherence times much longer than the averaging times used in typical turbulence experiments. Turbulent Rayleigh-Benard convection (RBC) is one such flow, and it will be used here as an example to illustrate and explain this phenomenon. The study focuses on a turbulent RBC experiment (Fernandes, 2001) in a 6.3:1 (diameter: depth) aspect-ratio vertical cylinder that supplemented time averaging with true ensemble averaging to achieve almost zero mean flow. To obtain a three-dimensional time-varying picture of the mechanisms at work, the experiment is simulated by direct numerical simulation of the Boussinesq equations (Sakievich et al., 2016). Three types of super-coherent states, associated with the symmetries of the flow, are found to bias the mean flow, unless steps are taken to sample each state with equal probability. They are azimuthal composition and orientation of the large-scale structures, the direction of azimuthal drift, and the preferential direction of the large-scale central motions.

UR - http://www.scopus.com/inward/record.url?scp=85033216606&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85033216606&partnerID=8YFLogxK

M3 - Conference contribution

VL - 1

BT - 10th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2017

PB - International Symposium on Turbulence and Shear Flow Phenomena, TSFP10

ER -