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Precessing cube: resonant excitation of modes and triadic resonance

Published online by Cambridge University Press:  21 January 2020

Ke Wu ,
Bruno D. Welfert Open the ORCID record for Bruno D. Welfert [Opens in a new window]  and
Juan M. Lopez Open the ORCID record for Juan M. Lopez [Opens in a new window]
Ke Wu
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe AZ 85287, USA
Bruno D. Welfert
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe AZ 85287, USA
Juan M. Lopez*
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe AZ 85287, USA
*
†Email address for correspondence: [email protected]
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Abstract

Numerical simulations of the response flow in a fluid-filled rotating cube that is subjected to precessional forcing are examined over a wide range of rotation, precession and forcing frequencies. The responses are shown to correspond to resonantly excited inertial modes of the rotating cube that have the same spatio-temporal symmetry as the precessional forcing and, under certain conditions, the response flow loses stability via symmetry breaking that is intricately associated with a triadic resonance between the forced flow and two free inertial modes whose spatio-temporal symmetries do not coincide with that of the precessional forcing.

JFM classification

Instability: Parametric instability Geophysical and Geological Flows: Rotating flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 887 , 25 March 2020 , A6
Copyright
© 2020 Cambridge University Press

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Wu et al. supplementary movie 1

Animations of the forced response flows at half-frequencies as indicated, and the corresponding inertial eigenmodes. Shown are the components of vorticity orthogonal to the planes indicated.

Download Wu et al. supplementary movie 1(Video)
Video 2.9 MB

Wu et al. supplementary movie 2

Animations of the forced response flows at half-frequencies as indicated, and the corresponding inertial eigenmodes. Shown are the components of vorticity orthogonal to the planes indicated.

Download Wu et al. supplementary movie 2(Video)
Video 6.9 MB

Wu et al. supplementary movie 3

Animations of the three inertial eigenmodes involved in the triadic resonance. Shown are the components of vorticity orthogonal to the planes indicated.

Download Wu et al. supplementary movie 3(Video)
Video 20.8 MB

Wu et al. supplementary movie 4

Animation over 20 forcing periods of the response flow that results from the triadic resonance. Shown are the components of vorticity orthogonal to the planes indicated.

Download Wu et al. supplementary movie 4(Video)
Video 31.4 MB