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Hysteresis and instabilities in a spheroid in precession near the resonance with the tilt-over mode

Published online by Cambridge University Press:  23 December 2020

C. Nobili ,
P. Meunier Open the ORCID record for P. Meunier [Opens in a new window] ,
B. Favier Open the ORCID record for B. Favier [Opens in a new window]  and
M. Le Bars Open the ORCID record for M. Le Bars [Opens in a new window]
C. Nobili
Affiliation:
IRPHE, UMR 7342, CNRS, Aix-Marseille Université, Centrale Marseille, 49 rue Joliot-Curie, 13013Marseille, France
P. Meunier*
Affiliation:
IRPHE, UMR 7342, CNRS, Aix-Marseille Université, Centrale Marseille, 49 rue Joliot-Curie, 13013Marseille, France
B. Favier
Affiliation:
IRPHE, UMR 7342, CNRS, Aix-Marseille Université, Centrale Marseille, 49 rue Joliot-Curie, 13013Marseille, France
M. Le Bars
Affiliation:
IRPHE, UMR 7342, CNRS, Aix-Marseille Université, Centrale Marseille, 49 rue Joliot-Curie, 13013Marseille, France
*
†Email address for correspondence: meunier@irphe.univ-mrs.fr
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Abstract

This study explores experimentally the flows driven by precession in an oblate spheroid, in the vicinity of the possible resonance with the tilt-over mode. Two main phenomena are reported, combining observations and velocity measurements. First, a hysteretic cycle is quantitatively described between two uniform vorticity solutions, in good agreement with the historical analytical study of Busse (J. Fluid Mech., vol. 33, 1968, pp. 739–752). We then address the destabilization of each branch at low enough Ekman number. We confirm the possible presence of a so-called conical shear instability, recently depicted in the sphere by Lin et al. (Phys. Fluids, vol. 27, 2015, 046601) and in the spheroid by Horimoto et al. (Phys. Rev. Fluids, vol. 5, 2020, 063901). However, available measurements in the accessible parameter range are not sufficient to definitively discard an elliptical or shear origin of the excited instabilities in the spheroid, as first introduced by Kerswell (Geophys. Astrophys. Fluid Dyn., vol. 72, 1993, pp. 107–144).

JFM classification

Geophysical and Geological Flows: Rotating flows Instability: Transition to turbulence Geophysical and Geological Flows: Waves in rotating fluids
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 909 , 25 February 2021 , A17
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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Nobili et al. supplementary movie 1

Visualisation of the transition from the first to the second Busse solution, when the Poincaré number decreases from Po=-0.087 to Po=-0.091.

Download Nobili et al. supplementary movie 1(Video)
Video 6.6 MB

Nobili et al. supplementary movie 2

Visualisation of the transition from the first to the second Busse solution, when the Poincaré number decreases from Po=-0.087 to Po=-0.091.

Download Nobili et al. supplementary movie 2(Video)
Video 10 MB

Nobili et al. supplementary movie 3

Visualisation of the transition from the second to the first Busse solution, when the Poincaré number increases from Po=-0.063 to Po=-0.061.

Download Nobili et al. supplementary movie 3(Video)
Video 10 MB