Rapidly rotating precessing cylinder flows: Forced triadic resonances

Juan Lopez, Francisco Marques

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Rapidly rotating cylinder flows subjected to low-amplitude precessional forcing are studied numerically over a range of cylinder and precessional rotation rates. For sufficiently small rotation rates, viscous effects lead to a forced overturning flow that is steady in the precession (table) frame of reference. Increasing the rotation rates, this forced flow loses stability in a Hopf bifurcation, which can be either supercritical or subcritical, and may preserve or break the symmetry of the system, depending on the parameter regime studied. Regardless of these details of the Hopf bifurcation, it is found that the Hopf instability is associated with a slightly detuned triadic resonance between the forced overturning flow and two free Kelvin modes (inviscid eigenmodes of the rotating cylinder). Further increases in rotation rates lead to a sequence of secondary instabilities which also follow a generic pattern irrespective of the parameter regime investigated. The relationship between this sequence of instabilities and the resultant nonlinear dynamics with the experimentally observed phenomenon of resonant collapse is discussed.

Original languageEnglish (US)
Pages (from-to)239-270
Number of pages32
JournalJournal of Fluid Mechanics
Volume839
DOIs
StatePublished - Mar 25 2018

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rotating cylinders
Hopf bifurcation
precession
symmetry

Keywords

  • nonlinear dynamical systems
  • nonlinear instability
  • waves in rotating fluids

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Rapidly rotating precessing cylinder flows : Forced triadic resonances. / Lopez, Juan; Marques, Francisco.

In: Journal of Fluid Mechanics, Vol. 839, 25.03.2018, p. 239-270.

Research output: Contribution to journalArticle

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