Libration-driven multipolar instabilities

David Cébron, Stijn Vantieghem, Wietze Herreman

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We consider rotating flows in non-axisymmetric enclosures that are driven by libration, i.e. by a small periodic modulation of the rotation rate. Thanks to its simplicity, this model is relevant to various contexts, from industrial containers (with small oscillations of the rotation rate) to fluid layers of terrestial planets (with length-of-day variations). Assuming a multipolar $n$-fold boundary deformation, we first obtain the two-dimensional basic flow. We then perform a short-wavelength local stability analysis of the basic flow, showing that an instability may occur in three dimensions. We christen it the Libration Driven Multipolar Instability (LDMI). The growth rates of the LDMI are computed by a Floquet analysis in a systematic way, and compared to analytical expressions obtained by perturbation methods. We then focus on the simplest geometry allowing the LDMI, a librating deformed cylinder. To take into account viscous and confinement effects, we perform a global stability analysis, which shows that the LDMI results from a parametric resonance of inertial modes. Performing numerical simulations of this librating cylinder, we confirm that the basic flow is indeed established and report the first numerical evidence of the LDMI. Numerical results, in excellent agreement with the stability results, are used to explore the non-linear regime of the instability (amplitude and viscous dissipation of the driven flow). We finally provide an example of LDMI in a deformed spherical container to show that the instability mechanism is generic. Our results show that the previously studied libration driven elliptical instability simply corresponds to the particular case $n=2$ of a wider class of instabilities. Summarizing, this work shows that any oscillating non-axisymmetric container in rotation may excite intermittent, space-filling LDMI flows, and this instability should thus be easy to observe experimentally.
Original languageEnglish
Pages (from-to)502-543
Number of pages42
JournalJournal of Fluid Mechanics
Volume739
Early online date2 Jan 2014
DOIs
Publication statusPublished - 25 Jan 2014
Externally publishedYes

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libration
containers
Containers
Planets
enclosure
Enclosures

Keywords

  • Parametric instability
  • Rotating flows
  • Topographic effects

Cite this

Cébron, D., Vantieghem, S., & Herreman, W. (2014). Libration-driven multipolar instabilities. Journal of Fluid Mechanics, 739, 502-543. https://doi.org/10.1017/jfm.2013.623

Libration-driven multipolar instabilities. / Cébron, David; Vantieghem, Stijn; Herreman, Wietze.

In: Journal of Fluid Mechanics, Vol. 739, 25.01.2014, p. 502-543.

Research output: Contribution to journalArticle

Cébron, D, Vantieghem, S & Herreman, W 2014, 'Libration-driven multipolar instabilities' Journal of Fluid Mechanics, vol. 739, pp. 502-543. https://doi.org/10.1017/jfm.2013.623
Cébron, David ; Vantieghem, Stijn ; Herreman, Wietze. / Libration-driven multipolar instabilities. In: Journal of Fluid Mechanics. 2014 ; Vol. 739. pp. 502-543.
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