On triadic resonance as an instability mechanism in precessing cylinder flow

Thomas Albrecht, Hugh M. Blackburn, Juan Lopez, Richard Manasseh, Patrice Meunier

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Contained rotating flows subject to precessional forcing are well known to exhibit rapid and energetic transitions to disorder. Triadic resonance of inertial modes has been previously proposed as an instability mechanism in such flows, and that idea was developed into a successful model for predicting instability in a cylindrical container when departures from solid-body rotation are sufficiently small. Using direct numerical simulation and dynamic mode decomposition, we analyse instabilities of precessing cylinder flows whose three-dimensional basic states, steady in the gimbal frame of reference, may depart substantially from solid-body rotation. In the gimbal frame, the instability can be interpreted as resulting from a supercritical Hopf bifurcation that results in a limit-cycle flow. In the cylinder frame of reference, the basic state is a rotating wave with azimuthal wavenumber , and the instability satisfies triadic-resonance conditions with the instability mode maintaining a fixed orientation with respect to the basic state. Thus, we are able to demonstrate the existence of two alternative but congruent explanations for the instability. Additionally, we show that basic states may depart substantially from solid-body rotation even with modest cylinder tilt angles, and growth rates for instabilities may be sufficiently large that nonlinear saturation to disordered states can occur within approximately ten cylinder revolutions, in agreement with experimental observations.

Original languageEnglish (US)
Article numberR3
JournalJournal of Fluid Mechanics
Volume841
DOIs
StatePublished - Apr 25 2018

Fingerprint

gimbals
three dimensional flow
Hopf bifurcation
Direct numerical simulation
containers
direct numerical simulation
Containers
disorders
Decomposition
saturation
decomposition
cycles

Keywords

  • geophysical and geological flows
  • transition to turbulence
  • waves in rotating fluids

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

On triadic resonance as an instability mechanism in precessing cylinder flow. / Albrecht, Thomas; Blackburn, Hugh M.; Lopez, Juan; Manasseh, Richard; Meunier, Patrice.

In: Journal of Fluid Mechanics, Vol. 841, R3, 25.04.2018.

Research output: Contribution to journalArticle

Albrecht, Thomas ; Blackburn, Hugh M. ; Lopez, Juan ; Manasseh, Richard ; Meunier, Patrice. / On triadic resonance as an instability mechanism in precessing cylinder flow. In: Journal of Fluid Mechanics. 2018 ; Vol. 841.
@article{e4678494c17f4ce68cf0ee6e388ea8d2,
title = "On triadic resonance as an instability mechanism in precessing cylinder flow",
abstract = "Contained rotating flows subject to precessional forcing are well known to exhibit rapid and energetic transitions to disorder. Triadic resonance of inertial modes has been previously proposed as an instability mechanism in such flows, and that idea was developed into a successful model for predicting instability in a cylindrical container when departures from solid-body rotation are sufficiently small. Using direct numerical simulation and dynamic mode decomposition, we analyse instabilities of precessing cylinder flows whose three-dimensional basic states, steady in the gimbal frame of reference, may depart substantially from solid-body rotation. In the gimbal frame, the instability can be interpreted as resulting from a supercritical Hopf bifurcation that results in a limit-cycle flow. In the cylinder frame of reference, the basic state is a rotating wave with azimuthal wavenumber , and the instability satisfies triadic-resonance conditions with the instability mode maintaining a fixed orientation with respect to the basic state. Thus, we are able to demonstrate the existence of two alternative but congruent explanations for the instability. Additionally, we show that basic states may depart substantially from solid-body rotation even with modest cylinder tilt angles, and growth rates for instabilities may be sufficiently large that nonlinear saturation to disordered states can occur within approximately ten cylinder revolutions, in agreement with experimental observations.",
keywords = "geophysical and geological flows, transition to turbulence, waves in rotating fluids",
author = "Thomas Albrecht and Blackburn, {Hugh M.} and Juan Lopez and Richard Manasseh and Patrice Meunier",
year = "2018",
month = "4",
day = "25",
doi = "10.1017/jfm.2018.145",
language = "English (US)",
volume = "841",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",

}

TY - JOUR

T1 - On triadic resonance as an instability mechanism in precessing cylinder flow

AU - Albrecht, Thomas

AU - Blackburn, Hugh M.

AU - Lopez, Juan

AU - Manasseh, Richard

AU - Meunier, Patrice

PY - 2018/4/25

Y1 - 2018/4/25

N2 - Contained rotating flows subject to precessional forcing are well known to exhibit rapid and energetic transitions to disorder. Triadic resonance of inertial modes has been previously proposed as an instability mechanism in such flows, and that idea was developed into a successful model for predicting instability in a cylindrical container when departures from solid-body rotation are sufficiently small. Using direct numerical simulation and dynamic mode decomposition, we analyse instabilities of precessing cylinder flows whose three-dimensional basic states, steady in the gimbal frame of reference, may depart substantially from solid-body rotation. In the gimbal frame, the instability can be interpreted as resulting from a supercritical Hopf bifurcation that results in a limit-cycle flow. In the cylinder frame of reference, the basic state is a rotating wave with azimuthal wavenumber , and the instability satisfies triadic-resonance conditions with the instability mode maintaining a fixed orientation with respect to the basic state. Thus, we are able to demonstrate the existence of two alternative but congruent explanations for the instability. Additionally, we show that basic states may depart substantially from solid-body rotation even with modest cylinder tilt angles, and growth rates for instabilities may be sufficiently large that nonlinear saturation to disordered states can occur within approximately ten cylinder revolutions, in agreement with experimental observations.

AB - Contained rotating flows subject to precessional forcing are well known to exhibit rapid and energetic transitions to disorder. Triadic resonance of inertial modes has been previously proposed as an instability mechanism in such flows, and that idea was developed into a successful model for predicting instability in a cylindrical container when departures from solid-body rotation are sufficiently small. Using direct numerical simulation and dynamic mode decomposition, we analyse instabilities of precessing cylinder flows whose three-dimensional basic states, steady in the gimbal frame of reference, may depart substantially from solid-body rotation. In the gimbal frame, the instability can be interpreted as resulting from a supercritical Hopf bifurcation that results in a limit-cycle flow. In the cylinder frame of reference, the basic state is a rotating wave with azimuthal wavenumber , and the instability satisfies triadic-resonance conditions with the instability mode maintaining a fixed orientation with respect to the basic state. Thus, we are able to demonstrate the existence of two alternative but congruent explanations for the instability. Additionally, we show that basic states may depart substantially from solid-body rotation even with modest cylinder tilt angles, and growth rates for instabilities may be sufficiently large that nonlinear saturation to disordered states can occur within approximately ten cylinder revolutions, in agreement with experimental observations.

KW - geophysical and geological flows

KW - transition to turbulence

KW - waves in rotating fluids

UR - http://www.scopus.com/inward/record.url?scp=85042704441&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042704441&partnerID=8YFLogxK

U2 - 10.1017/jfm.2018.145

DO - 10.1017/jfm.2018.145

M3 - Article

AN - SCOPUS:85042704441

VL - 841

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

M1 - R3

ER -