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Rapidly rotating precessing cylinder flows: forced triadic resonances

Published online by Cambridge University Press:  25 January 2018

Juan M. Lopez Open the ORCID record for Juan M. Lopez [Opens in a new window]  and
Francisco Marques
Juan M. Lopez*
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
Francisco Marques
Affiliation:
Departament de Fisica Aplicada, Univ. Politècnica de Catalunya, Barcelona 08034, Spain
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Instability: Nonlinear instability Geophysical and Geological Flows: Waves in rotating fluids
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 839 , 25 March 2018 , pp. 239 - 270
Copyright
© 2018 Cambridge University Press 

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Lopez et al. supplementary movie 1

Helcity isosurfaces of LCa (Po=-0.3745).

Download Lopez et al. supplementary movie 1(Video)
Video 3.1 MB

Lopez et al. supplementary movie 2

Helicity isosurfaces of unstable LCs, computed in symmetry subspace (Po=-0.3745)

Download Lopez et al. supplementary movie 2(Video)
Video 3.1 MB

Lopez et al. supplementary movie 3

Helicity isosurfaces of LCs (Po=-0.4).

Download Lopez et al. supplementary movie 3(Video)
Video 3.6 MB

Lopez et al. supplementary movie 4

Helicity isosurface of LCa (Po=-0.4).

Download Lopez et al. supplementary movie 4(Video)
Video 3.8 MB

Lopez et al. supplementary movie 5

Helicity isosurface of SC (Po=-0.3745).

Download Lopez et al. supplementary movie 5(Video)
Video 15.7 MB