On harmonic perturbations in a turbulent mixing layer

Nicolas Reau, Anatoli Tumin

Research output: Contribution to journalArticle

43 Citations (Scopus)

Abstract

A theoretical model of harmonic perturbations in a turbulent mixing layer is proposed. The model based on the triple decomposition method. It is assumed that the instantaneous velocities and pressure 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 the Newtonian eddy viscosity model. A slight divergence of the flow is also taken into account, and the results are compared with experimental data. For a high amplitude of the perturbations, the nonlinear feedback to the mean flow is taken into account by means of the coherent Reynolds stresses. The results reveal the possibility of a negative spreading rate of the mixing layer. A simultaneous consideration of the mean flow divergence and nonlinear self-interaction results in Landau-like amplitude equations. It is observed that the nonlinear term in the amplitude equation is not significant at the levels of amplitude considered. The velocity disturbance profiles of the second harmonic are also presented and, at low-level amplitude, they are in good agreement with experiments.

Original languageEnglish (US)
Pages (from-to)143-155
Number of pages13
JournalEuropean Journal of Mechanics, B/Fluids
Volume21
Issue number2
DOIs
StatePublished - Mar 2002

Fingerprint

Turbulent Mixing
Mixing Layer
turbulent mixing
Amplitude Equations
Harmonic
Perturbation
harmonics
perturbation
Divergence
Disturbance
Eddy Viscosity
Nonlinear feedback
Reynolds Stress
Time-average
Decomposition Method
divergence
Interaction
disturbances
Theoretical Model
Instantaneous

Keywords

  • Harmonic perturbations
  • Mixing layer
  • Stability

ASJC Scopus subject areas

  • Mechanical Engineering

Cite this

On harmonic perturbations in a turbulent mixing layer. / Reau, Nicolas; Tumin, Anatoli.

In: European Journal of Mechanics, B/Fluids, Vol. 21, No. 2, 03.2002, p. 143-155.

Research output: Contribution to journalArticle

@article{a20730f28ea647c99cbe3d39973bcb39,
title = "On harmonic perturbations in a turbulent mixing layer",
abstract = "A theoretical model of harmonic perturbations in a turbulent mixing layer is proposed. The model based on the triple decomposition method. It is assumed that the instantaneous velocities and pressure 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 the Newtonian eddy viscosity model. A slight divergence of the flow is also taken into account, and the results are compared with experimental data. For a high amplitude of the perturbations, the nonlinear feedback to the mean flow is taken into account by means of the coherent Reynolds stresses. The results reveal the possibility of a negative spreading rate of the mixing layer. A simultaneous consideration of the mean flow divergence and nonlinear self-interaction results in Landau-like amplitude equations. It is observed that the nonlinear term in the amplitude equation is not significant at the levels of amplitude considered. The velocity disturbance profiles of the second harmonic are also presented and, at low-level amplitude, they are in good agreement with experiments.",
keywords = "Harmonic perturbations, Mixing layer, Stability",
author = "Nicolas Reau and Anatoli Tumin",
year = "2002",
month = "3",
doi = "10.1016/S0997-7546(01)01170-0",
language = "English (US)",
volume = "21",
pages = "143--155",
journal = "European Journal of Mechanics, B/Fluids",
issn = "0997-7546",
publisher = "Elsevier BV",
number = "2",

}

TY - JOUR

T1 - On harmonic perturbations in a turbulent mixing layer

AU - Reau, Nicolas

AU - Tumin, Anatoli

PY - 2002/3

Y1 - 2002/3

N2 - A theoretical model of harmonic perturbations in a turbulent mixing layer is proposed. The model based on the triple decomposition method. It is assumed that the instantaneous velocities and pressure 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 the Newtonian eddy viscosity model. A slight divergence of the flow is also taken into account, and the results are compared with experimental data. For a high amplitude of the perturbations, the nonlinear feedback to the mean flow is taken into account by means of the coherent Reynolds stresses. The results reveal the possibility of a negative spreading rate of the mixing layer. A simultaneous consideration of the mean flow divergence and nonlinear self-interaction results in Landau-like amplitude equations. It is observed that the nonlinear term in the amplitude equation is not significant at the levels of amplitude considered. The velocity disturbance profiles of the second harmonic are also presented and, at low-level amplitude, they are in good agreement with experiments.

AB - A theoretical model of harmonic perturbations in a turbulent mixing layer is proposed. The model based on the triple decomposition method. It is assumed that the instantaneous velocities and pressure 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 the Newtonian eddy viscosity model. A slight divergence of the flow is also taken into account, and the results are compared with experimental data. For a high amplitude of the perturbations, the nonlinear feedback to the mean flow is taken into account by means of the coherent Reynolds stresses. The results reveal the possibility of a negative spreading rate of the mixing layer. A simultaneous consideration of the mean flow divergence and nonlinear self-interaction results in Landau-like amplitude equations. It is observed that the nonlinear term in the amplitude equation is not significant at the levels of amplitude considered. The velocity disturbance profiles of the second harmonic are also presented and, at low-level amplitude, they are in good agreement with experiments.

KW - Harmonic perturbations

KW - Mixing layer

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=0036502867&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036502867&partnerID=8YFLogxK

U2 - 10.1016/S0997-7546(01)01170-0

DO - 10.1016/S0997-7546(01)01170-0

M3 - Article

AN - SCOPUS:0036502867

VL - 21

SP - 143

EP - 155

JO - European Journal of Mechanics, B/Fluids

JF - European Journal of Mechanics, B/Fluids

SN - 0997-7546

IS - 2

ER -