### Abstract

A theoretical model of harmonic perturbations in turbulent wakes is considered. The proposed model is based on the triple decomposition method. It is assumed that the instantaneous velocities and pressures consist of three distinctive components: the mean (time average), the coherent (phase average) and the random (turbulent) motion. The interaction between incoherent turbulent fluctuations and large- scale coherent disturbances is incorporated by means of a Newtonian eddy viscosity model. A slight divergence of the flow is also taken into account. For high-amplitude perturbations, the nonlinear feedback to the mean flow is taken into account by means of the coherent Reynolds stresses. The equations for the mean flow are coupled with the linearized equations for the disturbances taking account of the mean flow non-parallel effects. The model resolves uncertainties noticed in previous theories and provides a correct comparison with available experimental data. The results demonstrate the effect of harmonic perturbations on the turbulent wake growth parameter G=LqUJ6 u_{0}, where L_{0} is the half-width of the wake; uq is the centreline velocity deficit; Q is the momentum thickness and U_{x} is the free stream velocity. At the initial stage of disturbance amplification, the amplitude parameter G increases. At high levels of the amplitude, downstream of the neutral point of the induced disturbance, G has a plateau or even decreases, and further downstream a growth of the parameter is recovered.

Original language | English (US) |
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Title of host publication | Fluids 2000 Conference and Exhibit |

State | Published - 2000 |

Externally published | Yes |

Event | Fluids 2000 Conference and Exhibit - Denver, CO, United States Duration: Jun 19 2000 → Jun 22 2000 |

### Other

Other | Fluids 2000 Conference and Exhibit |
---|---|

Country | United States |

City | Denver, CO |

Period | 6/19/00 → 6/22/00 |

### Fingerprint

### ASJC Scopus subject areas

- Fluid Flow and Transfer Processes
- Energy Engineering and Power Technology
- Aerospace Engineering
- Mechanical Engineering

### Cite this

*Fluids 2000 Conference and Exhibit*

**On harmonic perturbations in turbulent wakes.** / Reau, Nicolas; Tumin, Anatoli.

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

*Fluids 2000 Conference and Exhibit.*Fluids 2000 Conference and Exhibit, Denver, CO, United States, 6/19/00.

}

TY - GEN

T1 - On harmonic perturbations in turbulent wakes

AU - Reau, Nicolas

AU - Tumin, Anatoli

PY - 2000

Y1 - 2000

N2 - A theoretical model of harmonic perturbations in turbulent wakes is considered. The proposed model is based on the triple decomposition method. It is assumed that the instantaneous velocities and pressures consist of three distinctive components: the mean (time average), the coherent (phase average) and the random (turbulent) motion. The interaction between incoherent turbulent fluctuations and large- scale coherent disturbances is incorporated by means of a Newtonian eddy viscosity model. A slight divergence of the flow is also taken into account. For high-amplitude perturbations, the nonlinear feedback to the mean flow is taken into account by means of the coherent Reynolds stresses. The equations for the mean flow are coupled with the linearized equations for the disturbances taking account of the mean flow non-parallel effects. The model resolves uncertainties noticed in previous theories and provides a correct comparison with available experimental data. The results demonstrate the effect of harmonic perturbations on the turbulent wake growth parameter G=LqUJ6 u0, where L0 is the half-width of the wake; uq is the centreline velocity deficit; Q is the momentum thickness and Ux is the free stream velocity. At the initial stage of disturbance amplification, the amplitude parameter G increases. At high levels of the amplitude, downstream of the neutral point of the induced disturbance, G has a plateau or even decreases, and further downstream a growth of the parameter is recovered.

AB - A theoretical model of harmonic perturbations in turbulent wakes is considered. The proposed model is based on the triple decomposition method. It is assumed that the instantaneous velocities and pressures consist of three distinctive components: the mean (time average), the coherent (phase average) and the random (turbulent) motion. The interaction between incoherent turbulent fluctuations and large- scale coherent disturbances is incorporated by means of a Newtonian eddy viscosity model. A slight divergence of the flow is also taken into account. For high-amplitude perturbations, the nonlinear feedback to the mean flow is taken into account by means of the coherent Reynolds stresses. The equations for the mean flow are coupled with the linearized equations for the disturbances taking account of the mean flow non-parallel effects. The model resolves uncertainties noticed in previous theories and provides a correct comparison with available experimental data. The results demonstrate the effect of harmonic perturbations on the turbulent wake growth parameter G=LqUJ6 u0, where L0 is the half-width of the wake; uq is the centreline velocity deficit; Q is the momentum thickness and Ux is the free stream velocity. At the initial stage of disturbance amplification, the amplitude parameter G increases. At high levels of the amplitude, downstream of the neutral point of the induced disturbance, G has a plateau or even decreases, and further downstream a growth of the parameter is recovered.

UR - http://www.scopus.com/inward/record.url?scp=84894562324&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894562324&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84894562324

BT - Fluids 2000 Conference and Exhibit

ER -