TY - JOUR
T1 - Rapidly rotating precessing cylinder flows
T2 - Forced triadic resonances
AU - Lopez, Juan
AU - Marques, Francisco
N1 - Funding Information:
This work was supported by the National Science Foundation grant CBET-1336410, and the Spanish Ministry of Education and Science/FEDER grant FIS2013-40880-P.
Publisher Copyright:
© 2018 Cambridge University Press.
PY - 2018/3/25
Y1 - 2018/3/25
N2 - 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.
AB - 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.
KW - nonlinear dynamical systems
KW - nonlinear instability
KW - waves in rotating fluids
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U2 - 10.1017/jfm.2017.922
DO - 10.1017/jfm.2017.922
M3 - Article
AN - SCOPUS:85042725775
SN - 0022-1120
VL - 839
SP - 239
EP - 270
JO - journal of fluid mechanics
JF - journal of fluid mechanics
ER -