Positive- and negative-effective-viscosity phenomena in isotropic and anisotropic Beltrami flows

Bruce J Bayly, V. Yakhot

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

A field-theoretic approach, analogous to Kraichnans direct-interaction approximation, to the stability theory of complex three-dimensional flows is developed. The long-wavelength stability of a class of Beltrami flows in an unbounded, viscous fluid is considered. We examine two flows in detail, to illustrate the effects of strong isotropy versus strong anisotropy in the basic flow. The effect of the small-scale flow on the long-wavelength perturbations may be interpreted as an effective viscosity. Using diagrammatic techniques, we construct the first-order smoothing and direct-interaction approximations for the perturbation dynamics. It is argued that the effective viscosity for the isotropic flow is always positive, and approaches a value independent of the molecular viscosity in the high-Reynolds-number limit; this flow is thus stable to long-wavelength disturbances. The anisotropic flow has negative effective viscosity for some orientations of the disturbance, and is therefore unstable, when its Reynolds number exceeds 2.

Original languageEnglish (US)
Pages (from-to)381-391
Number of pages11
JournalPhysical Review A
Volume34
Issue number1
DOIs
StatePublished - 1986
Externally publishedYes

Fingerprint

Beltrami flow
viscosity
disturbances
wavelengths
perturbation
three dimensional flow
high Reynolds number
isotropy
viscous fluids
approximation
smoothing
Reynolds number
interactions
anisotropy

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Atomic and Molecular Physics, and Optics

Cite this

Positive- and negative-effective-viscosity phenomena in isotropic and anisotropic Beltrami flows. / Bayly, Bruce J; Yakhot, V.

In: Physical Review A, Vol. 34, No. 1, 1986, p. 381-391.

Research output: Contribution to journalArticle

@article{3294e63263a44e7f8b29a2bcc0686835,
title = "Positive- and negative-effective-viscosity phenomena in isotropic and anisotropic Beltrami flows",
abstract = "A field-theoretic approach, analogous to Kraichnans direct-interaction approximation, to the stability theory of complex three-dimensional flows is developed. The long-wavelength stability of a class of Beltrami flows in an unbounded, viscous fluid is considered. We examine two flows in detail, to illustrate the effects of strong isotropy versus strong anisotropy in the basic flow. The effect of the small-scale flow on the long-wavelength perturbations may be interpreted as an effective viscosity. Using diagrammatic techniques, we construct the first-order smoothing and direct-interaction approximations for the perturbation dynamics. It is argued that the effective viscosity for the isotropic flow is always positive, and approaches a value independent of the molecular viscosity in the high-Reynolds-number limit; this flow is thus stable to long-wavelength disturbances. The anisotropic flow has negative effective viscosity for some orientations of the disturbance, and is therefore unstable, when its Reynolds number exceeds 2.",
author = "Bayly, {Bruce J} and V. Yakhot",
year = "1986",
doi = "10.1103/PhysRevA.34.381",
language = "English (US)",
volume = "34",
pages = "381--391",
journal = "Physical Review A",
issn = "2469-9926",
publisher = "American Physical Society",
number = "1",

}

TY - JOUR

T1 - Positive- and negative-effective-viscosity phenomena in isotropic and anisotropic Beltrami flows

AU - Bayly, Bruce J

AU - Yakhot, V.

PY - 1986

Y1 - 1986

N2 - A field-theoretic approach, analogous to Kraichnans direct-interaction approximation, to the stability theory of complex three-dimensional flows is developed. The long-wavelength stability of a class of Beltrami flows in an unbounded, viscous fluid is considered. We examine two flows in detail, to illustrate the effects of strong isotropy versus strong anisotropy in the basic flow. The effect of the small-scale flow on the long-wavelength perturbations may be interpreted as an effective viscosity. Using diagrammatic techniques, we construct the first-order smoothing and direct-interaction approximations for the perturbation dynamics. It is argued that the effective viscosity for the isotropic flow is always positive, and approaches a value independent of the molecular viscosity in the high-Reynolds-number limit; this flow is thus stable to long-wavelength disturbances. The anisotropic flow has negative effective viscosity for some orientations of the disturbance, and is therefore unstable, when its Reynolds number exceeds 2.

AB - A field-theoretic approach, analogous to Kraichnans direct-interaction approximation, to the stability theory of complex three-dimensional flows is developed. The long-wavelength stability of a class of Beltrami flows in an unbounded, viscous fluid is considered. We examine two flows in detail, to illustrate the effects of strong isotropy versus strong anisotropy in the basic flow. The effect of the small-scale flow on the long-wavelength perturbations may be interpreted as an effective viscosity. Using diagrammatic techniques, we construct the first-order smoothing and direct-interaction approximations for the perturbation dynamics. It is argued that the effective viscosity for the isotropic flow is always positive, and approaches a value independent of the molecular viscosity in the high-Reynolds-number limit; this flow is thus stable to long-wavelength disturbances. The anisotropic flow has negative effective viscosity for some orientations of the disturbance, and is therefore unstable, when its Reynolds number exceeds 2.

UR - http://www.scopus.com/inward/record.url?scp=0037844689&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037844689&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.34.381

DO - 10.1103/PhysRevA.34.381

M3 - Article

VL - 34

SP - 381

EP - 391

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 1

ER -