### Abstract

The temporal dynamics of large-scale structures in a plane turbulent mixing layer are studied through the development of a low-order dynamical system of ordinary differential equations (ODEs). This model is derived by projecting Navier-Strokes equations onto an empirical basis set from the proper orthogonal decomposition (POD) using a Galerkin method. To obtain this low-dimensional set of equations, a truncation is performed that only includes the first POD mode for selected streamwise/ spanwise (k_{1}/k_{3}) modes. The initial truncations are for k_{3} = 0; however, once these truncations are evaluated, non-zero spanwise wavenumbers are added. These truncated systems of equations are then examined in the pseudo-Fourier space in which they are solved and by reconstructing the velocity field. Two different methods for closing the mean streamwise velocity are evaluated that show the importance of introducing, into the low-order dynamical system, a term allowing feedback between the turbulent and mean flows. The results of the numerical simulations show a strongly periodic flow indicative of the spanwise vorticity. The simulated flow had the correct energy distributions in the cross-stream direction. These models also indicated that the events associated with the centre of the mixing layer lead the temporal dynamics. For truncations involving both spanwise and streamwise wavenumbers, the reconstructed velocity field exhibits the main spanwise and streamwise vortical structures known to exist in this flow. The streamwise aligned vorticity is shown to connect spanwise vortex tubes.

Original language | English (US) |
---|---|

Pages (from-to) | 67-108 |

Number of pages | 42 |

Journal | Journal of Fluid Mechanics |

Volume | 441 |

DOIs | |

State | Published - Aug 25 2001 |

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### ASJC Scopus subject areas

- Mechanics of Materials
- Computational Mechanics
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Journal of Fluid Mechanics*,

*441*, 67-108. https://doi.org/10.1017/S0022112001004803

**Examination of large-scale structures in a turbulent plane mixing layer. Part 2. Dynamical systems model.** / Ukeiley, L.; Cordier, L.; Manceau, R.; Delville, J.; Glauser, Mark N; Bonnet, J. P.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, vol. 441, pp. 67-108. https://doi.org/10.1017/S0022112001004803

}

TY - JOUR

T1 - Examination of large-scale structures in a turbulent plane mixing layer. Part 2. Dynamical systems model

AU - Ukeiley, L.

AU - Cordier, L.

AU - Manceau, R.

AU - Delville, J.

AU - Glauser, Mark N

AU - Bonnet, J. P.

PY - 2001/8/25

Y1 - 2001/8/25

N2 - The temporal dynamics of large-scale structures in a plane turbulent mixing layer are studied through the development of a low-order dynamical system of ordinary differential equations (ODEs). This model is derived by projecting Navier-Strokes equations onto an empirical basis set from the proper orthogonal decomposition (POD) using a Galerkin method. To obtain this low-dimensional set of equations, a truncation is performed that only includes the first POD mode for selected streamwise/ spanwise (k1/k3) modes. The initial truncations are for k3 = 0; however, once these truncations are evaluated, non-zero spanwise wavenumbers are added. These truncated systems of equations are then examined in the pseudo-Fourier space in which they are solved and by reconstructing the velocity field. Two different methods for closing the mean streamwise velocity are evaluated that show the importance of introducing, into the low-order dynamical system, a term allowing feedback between the turbulent and mean flows. The results of the numerical simulations show a strongly periodic flow indicative of the spanwise vorticity. The simulated flow had the correct energy distributions in the cross-stream direction. These models also indicated that the events associated with the centre of the mixing layer lead the temporal dynamics. For truncations involving both spanwise and streamwise wavenumbers, the reconstructed velocity field exhibits the main spanwise and streamwise vortical structures known to exist in this flow. The streamwise aligned vorticity is shown to connect spanwise vortex tubes.

AB - The temporal dynamics of large-scale structures in a plane turbulent mixing layer are studied through the development of a low-order dynamical system of ordinary differential equations (ODEs). This model is derived by projecting Navier-Strokes equations onto an empirical basis set from the proper orthogonal decomposition (POD) using a Galerkin method. To obtain this low-dimensional set of equations, a truncation is performed that only includes the first POD mode for selected streamwise/ spanwise (k1/k3) modes. The initial truncations are for k3 = 0; however, once these truncations are evaluated, non-zero spanwise wavenumbers are added. These truncated systems of equations are then examined in the pseudo-Fourier space in which they are solved and by reconstructing the velocity field. Two different methods for closing the mean streamwise velocity are evaluated that show the importance of introducing, into the low-order dynamical system, a term allowing feedback between the turbulent and mean flows. The results of the numerical simulations show a strongly periodic flow indicative of the spanwise vorticity. The simulated flow had the correct energy distributions in the cross-stream direction. These models also indicated that the events associated with the centre of the mixing layer lead the temporal dynamics. For truncations involving both spanwise and streamwise wavenumbers, the reconstructed velocity field exhibits the main spanwise and streamwise vortical structures known to exist in this flow. The streamwise aligned vorticity is shown to connect spanwise vortex tubes.

UR - http://www.scopus.com/inward/record.url?scp=0035949148&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035949148&partnerID=8YFLogxK

U2 - 10.1017/S0022112001004803

DO - 10.1017/S0022112001004803

M3 - Article

VL - 441

SP - 67

EP - 108

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -