Instability and mode interactions in a differentially driven rotating cylinder

Juan Lopez, J. E. Hart, F. Marques, S. Kittelman, J. Shen

Research output: Contribution to journalArticle

49 Citations (Scopus)

Abstract

The flow in a completely filled rotating cylinder driven by the counter-rotation of the top endwall is investigated both numerically and experimentally. The basic state of this system is steady and axisymmetric, but has a rich structure in the radial and axial directions. The most striking feature, when the counter-rotation is sufficiently large, is the separation of the Ekman layer on the top endwall, producing a free shear layer that separates regions of flow with opposite senses of azimuthal velocity. This shear layer is unstable to azimuthal disturbances and a supercritical symmetry-breaking Hopf bifurcation to a rotating wave state results. For height-to-radius ratio of 0.5 and Reynolds number (based on cylinder radius and base rotation) of 1000, rotating waves with azimuthal wavenumbers 4 and 5 co-exist and are stable over an extensive range of the ratio of top to base rotation. Mixed modes and period doublings are also found, and a bifurcation diagram is determined. The agreement between the Navier-Stokes computations and the experimental measurements is excellent. The simulations not only capture the qualitative features of the multiple states observed in the laboratory, but also quantitatively replicate the parameter values over which they are stable, and produce accurate precession frequencies of the various rotating waves.

Original languageEnglish (US)
Pages (from-to)383-409
Number of pages27
JournalJournal of Fluid Mechanics
Volume462
DOIs
StatePublished - Jul 10 2002

Fingerprint

rotating cylinders
counter rotation
shear layers
interactions
Hopf bifurcation
Ekman layer
radii
period doubling
Reynolds number
precession
broken symmetry
disturbances
diagrams
simulation

ASJC Scopus subject areas

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

Cite this

Instability and mode interactions in a differentially driven rotating cylinder. / Lopez, Juan; Hart, J. E.; Marques, F.; Kittelman, S.; Shen, J.

In: Journal of Fluid Mechanics, Vol. 462, 10.07.2002, p. 383-409.

Research output: Contribution to journalArticle

Lopez, Juan ; Hart, J. E. ; Marques, F. ; Kittelman, S. ; Shen, J. / Instability and mode interactions in a differentially driven rotating cylinder. In: Journal of Fluid Mechanics. 2002 ; Vol. 462. pp. 383-409.
@article{1e1cc21fd76a46aea9169c1622501f3f,
title = "Instability and mode interactions in a differentially driven rotating cylinder",
abstract = "The flow in a completely filled rotating cylinder driven by the counter-rotation of the top endwall is investigated both numerically and experimentally. The basic state of this system is steady and axisymmetric, but has a rich structure in the radial and axial directions. The most striking feature, when the counter-rotation is sufficiently large, is the separation of the Ekman layer on the top endwall, producing a free shear layer that separates regions of flow with opposite senses of azimuthal velocity. This shear layer is unstable to azimuthal disturbances and a supercritical symmetry-breaking Hopf bifurcation to a rotating wave state results. For height-to-radius ratio of 0.5 and Reynolds number (based on cylinder radius and base rotation) of 1000, rotating waves with azimuthal wavenumbers 4 and 5 co-exist and are stable over an extensive range of the ratio of top to base rotation. Mixed modes and period doublings are also found, and a bifurcation diagram is determined. The agreement between the Navier-Stokes computations and the experimental measurements is excellent. The simulations not only capture the qualitative features of the multiple states observed in the laboratory, but also quantitatively replicate the parameter values over which they are stable, and produce accurate precession frequencies of the various rotating waves.",
author = "Juan Lopez and Hart, {J. E.} and F. Marques and S. Kittelman and J. Shen",
year = "2002",
month = "7",
day = "10",
doi = "10.1017/S0022112002008649",
language = "English (US)",
volume = "462",
pages = "383--409",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",

}

TY - JOUR

T1 - Instability and mode interactions in a differentially driven rotating cylinder

AU - Lopez, Juan

AU - Hart, J. E.

AU - Marques, F.

AU - Kittelman, S.

AU - Shen, J.

PY - 2002/7/10

Y1 - 2002/7/10

N2 - The flow in a completely filled rotating cylinder driven by the counter-rotation of the top endwall is investigated both numerically and experimentally. The basic state of this system is steady and axisymmetric, but has a rich structure in the radial and axial directions. The most striking feature, when the counter-rotation is sufficiently large, is the separation of the Ekman layer on the top endwall, producing a free shear layer that separates regions of flow with opposite senses of azimuthal velocity. This shear layer is unstable to azimuthal disturbances and a supercritical symmetry-breaking Hopf bifurcation to a rotating wave state results. For height-to-radius ratio of 0.5 and Reynolds number (based on cylinder radius and base rotation) of 1000, rotating waves with azimuthal wavenumbers 4 and 5 co-exist and are stable over an extensive range of the ratio of top to base rotation. Mixed modes and period doublings are also found, and a bifurcation diagram is determined. The agreement between the Navier-Stokes computations and the experimental measurements is excellent. The simulations not only capture the qualitative features of the multiple states observed in the laboratory, but also quantitatively replicate the parameter values over which they are stable, and produce accurate precession frequencies of the various rotating waves.

AB - The flow in a completely filled rotating cylinder driven by the counter-rotation of the top endwall is investigated both numerically and experimentally. The basic state of this system is steady and axisymmetric, but has a rich structure in the radial and axial directions. The most striking feature, when the counter-rotation is sufficiently large, is the separation of the Ekman layer on the top endwall, producing a free shear layer that separates regions of flow with opposite senses of azimuthal velocity. This shear layer is unstable to azimuthal disturbances and a supercritical symmetry-breaking Hopf bifurcation to a rotating wave state results. For height-to-radius ratio of 0.5 and Reynolds number (based on cylinder radius and base rotation) of 1000, rotating waves with azimuthal wavenumbers 4 and 5 co-exist and are stable over an extensive range of the ratio of top to base rotation. Mixed modes and period doublings are also found, and a bifurcation diagram is determined. The agreement between the Navier-Stokes computations and the experimental measurements is excellent. The simulations not only capture the qualitative features of the multiple states observed in the laboratory, but also quantitatively replicate the parameter values over which they are stable, and produce accurate precession frequencies of the various rotating waves.

UR - http://www.scopus.com/inward/record.url?scp=0037055082&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037055082&partnerID=8YFLogxK

U2 - 10.1017/S0022112002008649

DO - 10.1017/S0022112002008649

M3 - Article

AN - SCOPUS:0037055082

VL - 462

SP - 383

EP - 409

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -