Examination of large-scale structures in a turbulent plane mixing layer. Part 1. Proper orthogonal decomposition

J. Delville, L. Ukeiley, L. Cordier, J. P. Bonnet, Mark N Glauser

Research output: Contribution to journalArticle

122 Citations (Scopus)

Abstract

Large-scale structures in a plane turbulent mixing layer are studied through the use of the proper orthogonal decomposition (POD). Extensive experimental measurements are obtained in a turbulent plane mixing layer by means of two cross-wire rakes aligned normal to the direction of the mean shear and perpendicular to the mean flow direction. The measurements are acquired well into the asymptotic region. From the measured velocities the two-point spectral tensor is calculated as a function of separation in the cross-stream direction and spanwise and streamwise wavenumbers. The continuity equation is then used for the calculation of the non-measured components of the tensor. The POD is applied using the cross-spectral tensor as its kernel. This decomposition yields an optimal basis set in the mean square sense. The energy contained in the POD modes converges rapidly with the first mode being dominant (49% of the turbulent kinetic energy). Examination of these modes shows that the first mode contains evidence of both known flow organizations in the mixing layer, i.e. quasi-two-dimensional spanwise structures and streamwise aligned vortices. Using the shot-noise theory the dominant mode of the POD is transformed back into physical space. This structure is also indicative of the known flow organizations.

Original languageEnglish (US)
Pages (from-to)91-122
Number of pages32
JournalJournal of Fluid Mechanics
Volume391
StatePublished - Jul 25 1999
Externally publishedYes

Fingerprint

examination
Decomposition
decomposition
Tensors
tensors
rakes
Shot noise
turbulent mixing
continuity equation
shot noise
Kinetic energy
Vortex flow
kinetic energy
wire
Wire
vortices
shear
energy

ASJC Scopus subject areas

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

Cite this

Examination of large-scale structures in a turbulent plane mixing layer. Part 1. Proper orthogonal decomposition. / Delville, J.; Ukeiley, L.; Cordier, L.; Bonnet, J. P.; Glauser, Mark N.

In: Journal of Fluid Mechanics, Vol. 391, 25.07.1999, p. 91-122.

Research output: Contribution to journalArticle

@article{8f373b34998040a7be50bd6f13aba1f3,
title = "Examination of large-scale structures in a turbulent plane mixing layer. Part 1. Proper orthogonal decomposition",
abstract = "Large-scale structures in a plane turbulent mixing layer are studied through the use of the proper orthogonal decomposition (POD). Extensive experimental measurements are obtained in a turbulent plane mixing layer by means of two cross-wire rakes aligned normal to the direction of the mean shear and perpendicular to the mean flow direction. The measurements are acquired well into the asymptotic region. From the measured velocities the two-point spectral tensor is calculated as a function of separation in the cross-stream direction and spanwise and streamwise wavenumbers. The continuity equation is then used for the calculation of the non-measured components of the tensor. The POD is applied using the cross-spectral tensor as its kernel. This decomposition yields an optimal basis set in the mean square sense. The energy contained in the POD modes converges rapidly with the first mode being dominant (49{\%} of the turbulent kinetic energy). Examination of these modes shows that the first mode contains evidence of both known flow organizations in the mixing layer, i.e. quasi-two-dimensional spanwise structures and streamwise aligned vortices. Using the shot-noise theory the dominant mode of the POD is transformed back into physical space. This structure is also indicative of the known flow organizations.",
author = "J. Delville and L. Ukeiley and L. Cordier and Bonnet, {J. P.} and Glauser, {Mark N}",
year = "1999",
month = "7",
day = "25",
language = "English (US)",
volume = "391",
pages = "91--122",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",

}

TY - JOUR

T1 - Examination of large-scale structures in a turbulent plane mixing layer. Part 1. Proper orthogonal decomposition

AU - Delville, J.

AU - Ukeiley, L.

AU - Cordier, L.

AU - Bonnet, J. P.

AU - Glauser, Mark N

PY - 1999/7/25

Y1 - 1999/7/25

N2 - Large-scale structures in a plane turbulent mixing layer are studied through the use of the proper orthogonal decomposition (POD). Extensive experimental measurements are obtained in a turbulent plane mixing layer by means of two cross-wire rakes aligned normal to the direction of the mean shear and perpendicular to the mean flow direction. The measurements are acquired well into the asymptotic region. From the measured velocities the two-point spectral tensor is calculated as a function of separation in the cross-stream direction and spanwise and streamwise wavenumbers. The continuity equation is then used for the calculation of the non-measured components of the tensor. The POD is applied using the cross-spectral tensor as its kernel. This decomposition yields an optimal basis set in the mean square sense. The energy contained in the POD modes converges rapidly with the first mode being dominant (49% of the turbulent kinetic energy). Examination of these modes shows that the first mode contains evidence of both known flow organizations in the mixing layer, i.e. quasi-two-dimensional spanwise structures and streamwise aligned vortices. Using the shot-noise theory the dominant mode of the POD is transformed back into physical space. This structure is also indicative of the known flow organizations.

AB - Large-scale structures in a plane turbulent mixing layer are studied through the use of the proper orthogonal decomposition (POD). Extensive experimental measurements are obtained in a turbulent plane mixing layer by means of two cross-wire rakes aligned normal to the direction of the mean shear and perpendicular to the mean flow direction. The measurements are acquired well into the asymptotic region. From the measured velocities the two-point spectral tensor is calculated as a function of separation in the cross-stream direction and spanwise and streamwise wavenumbers. The continuity equation is then used for the calculation of the non-measured components of the tensor. The POD is applied using the cross-spectral tensor as its kernel. This decomposition yields an optimal basis set in the mean square sense. The energy contained in the POD modes converges rapidly with the first mode being dominant (49% of the turbulent kinetic energy). Examination of these modes shows that the first mode contains evidence of both known flow organizations in the mixing layer, i.e. quasi-two-dimensional spanwise structures and streamwise aligned vortices. Using the shot-noise theory the dominant mode of the POD is transformed back into physical space. This structure is also indicative of the known flow organizations.

UR - http://www.scopus.com/inward/record.url?scp=0032677711&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032677711&partnerID=8YFLogxK

M3 - Article

VL - 391

SP - 91

EP - 122

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -