TY - JOUR
T1 - Triadic resonances in precessing rapidly rotating cylinder flows
AU - Albrecht, T.
AU - Blackburn, H. M.
AU - Lopez, Juan
AU - Manasseh, R.
AU - Meunier, P.
N1 - Publisher Copyright:
© © 2015 Cambridge University Press.
PY - 2015/7/30
Y1 - 2015/7/30
N2 - Direct numerical simulations of flows in cylinders subjected to both rapid rotation and axial precession are presented and analysed in the context of a stability theory based on the triadic resonance of Kelvin modes. For a case that was chosen to provide a finely tuned resonant instability with a small nutation angle, the simulations are in good agreement with the theory and previous experiments in terms of mode shapes and dynamics, including long-time-scale regularization of the flow and recurrent collapses. Cases not tuned to the most unstable triad, but with the nutation angle still small, are also in quite good agreement with theoretical predictions, showing that the presence of viscosity makes the physics of the triadic-resonance model robust to detuning. Finally, for a case with nutation angle for which it has been suggested that resonance does not occur, the simulations show that a slowly growing triadic resonance predicted by theory is in fact observed if sufficient evolution time is allowed.
AB - Direct numerical simulations of flows in cylinders subjected to both rapid rotation and axial precession are presented and analysed in the context of a stability theory based on the triadic resonance of Kelvin modes. For a case that was chosen to provide a finely tuned resonant instability with a small nutation angle, the simulations are in good agreement with the theory and previous experiments in terms of mode shapes and dynamics, including long-time-scale regularization of the flow and recurrent collapses. Cases not tuned to the most unstable triad, but with the nutation angle still small, are also in quite good agreement with theoretical predictions, showing that the presence of viscosity makes the physics of the triadic-resonance model robust to detuning. Finally, for a case with nutation angle for which it has been suggested that resonance does not occur, the simulations show that a slowly growing triadic resonance predicted by theory is in fact observed if sufficient evolution time is allowed.
KW - geophysical and geological flows
KW - nonlinear instability
KW - waves in rotating fluids
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U2 - 10.1017/jfm.2015.377
DO - 10.1017/jfm.2015.377
M3 - Article
AN - SCOPUS:84938398594
SN - 0022-1120
VL - 778
SP - R11-R112
JO - journal of fluid mechanics
JF - journal of fluid mechanics
ER -