Latitudinal libration driven flows in triaxial ellipsoids

S. Vantieghem, D. Cébron, J. Noir

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Motivated by understanding the liquid core dynamics of tidally deformed planets and moons, we present a study of incompressible flow driven by latitudinal libration within rigid triaxial ellipsoids. We first derive a laminar solution for the inviscid equations of motion under the assumption of uniform vorticity flow. This solution exhibits a res- onance if the libration frequency matches the frequency of the spin-over inertial mode. Furthermore, we extend our model by introducing a reduced model of the effect of viscous Ekman layers in the limit of low Ekman number (Noir and C\'ebron 2013). This theoretical approach is consistent with the results of Chan et al. (2011) and Zhang et al. (2012) for spheroidal geometries. Our results are validated against systematic three-dimensional numerical simulations. In the second part of the paper, we present the first linear sta- bility analysis of this uniform vorticity flow. To this end, we adopt different methods (Lifschitz and Hameiri 1991; Gledzer and Ponomarev 1977) that allow to deduce upper and lower bounds for the growth rate of an instability. Our analysis shows that the uniform vorticity base flow is prone to inertial instabilities caused by a parametric resonance mechanism. This is confirmed by a set of direct numerical simulations. Applying our results to planetary settings, we find that neither a spin-over resonance nor an inertial instability can exist within the liquid core of the Moon, Io and Mercury.
Original languageEnglish
Pages (from-to)193-228
Number of pages36
JournalJ. Fluid Mech.
Volume771
DOIs
Publication statusPublished - May 2015

Fingerprint

libration
ellipsoids
Vorticity
Moon
vorticity
Linear stability analysis
Incompressible flow
Direct numerical simulation
Ekman layer
Liquids
Planets
base flow
Io
Equations of motion
incompressible flow
natural satellites
liquids
moon
direct numerical simulation
planets

Keywords

  • physics.flu-dyn

Cite this

Latitudinal libration driven flows in triaxial ellipsoids. / Vantieghem, S.; Cébron, D.; Noir, J.

In: J. Fluid Mech., Vol. 771, 05.2015, p. 193-228.

Research output: Contribution to journalArticle

Vantieghem, S. ; Cébron, D. ; Noir, J. / Latitudinal libration driven flows in triaxial ellipsoids. In: J. Fluid Mech. 2015 ; Vol. 771. pp. 193-228.
@article{684c15cbd05c4c7f838e45f953f76edb,
title = "Latitudinal libration driven flows in triaxial ellipsoids",
abstract = "Motivated by understanding the liquid core dynamics of tidally deformed planets and moons, we present a study of incompressible flow driven by latitudinal libration within rigid triaxial ellipsoids. We first derive a laminar solution for the inviscid equations of motion under the assumption of uniform vorticity flow. This solution exhibits a res- onance if the libration frequency matches the frequency of the spin-over inertial mode. Furthermore, we extend our model by introducing a reduced model of the effect of viscous Ekman layers in the limit of low Ekman number (Noir and C\'ebron 2013). This theoretical approach is consistent with the results of Chan et al. (2011) and Zhang et al. (2012) for spheroidal geometries. Our results are validated against systematic three-dimensional numerical simulations. In the second part of the paper, we present the first linear sta- bility analysis of this uniform vorticity flow. To this end, we adopt different methods (Lifschitz and Hameiri 1991; Gledzer and Ponomarev 1977) that allow to deduce upper and lower bounds for the growth rate of an instability. Our analysis shows that the uniform vorticity base flow is prone to inertial instabilities caused by a parametric resonance mechanism. This is confirmed by a set of direct numerical simulations. Applying our results to planetary settings, we find that neither a spin-over resonance nor an inertial instability can exist within the liquid core of the Moon, Io and Mercury.",
keywords = "physics.flu-dyn",
author = "S. Vantieghem and D. C{\'e}bron and J. Noir",
year = "2015",
month = "5",
doi = "10.1017/jfm.2015.130",
language = "English",
volume = "771",
pages = "193--228",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",

}

TY - JOUR

T1 - Latitudinal libration driven flows in triaxial ellipsoids

AU - Vantieghem, S.

AU - Cébron, D.

AU - Noir, J.

PY - 2015/5

Y1 - 2015/5

N2 - Motivated by understanding the liquid core dynamics of tidally deformed planets and moons, we present a study of incompressible flow driven by latitudinal libration within rigid triaxial ellipsoids. We first derive a laminar solution for the inviscid equations of motion under the assumption of uniform vorticity flow. This solution exhibits a res- onance if the libration frequency matches the frequency of the spin-over inertial mode. Furthermore, we extend our model by introducing a reduced model of the effect of viscous Ekman layers in the limit of low Ekman number (Noir and C\'ebron 2013). This theoretical approach is consistent with the results of Chan et al. (2011) and Zhang et al. (2012) for spheroidal geometries. Our results are validated against systematic three-dimensional numerical simulations. In the second part of the paper, we present the first linear sta- bility analysis of this uniform vorticity flow. To this end, we adopt different methods (Lifschitz and Hameiri 1991; Gledzer and Ponomarev 1977) that allow to deduce upper and lower bounds for the growth rate of an instability. Our analysis shows that the uniform vorticity base flow is prone to inertial instabilities caused by a parametric resonance mechanism. This is confirmed by a set of direct numerical simulations. Applying our results to planetary settings, we find that neither a spin-over resonance nor an inertial instability can exist within the liquid core of the Moon, Io and Mercury.

AB - Motivated by understanding the liquid core dynamics of tidally deformed planets and moons, we present a study of incompressible flow driven by latitudinal libration within rigid triaxial ellipsoids. We first derive a laminar solution for the inviscid equations of motion under the assumption of uniform vorticity flow. This solution exhibits a res- onance if the libration frequency matches the frequency of the spin-over inertial mode. Furthermore, we extend our model by introducing a reduced model of the effect of viscous Ekman layers in the limit of low Ekman number (Noir and C\'ebron 2013). This theoretical approach is consistent with the results of Chan et al. (2011) and Zhang et al. (2012) for spheroidal geometries. Our results are validated against systematic three-dimensional numerical simulations. In the second part of the paper, we present the first linear sta- bility analysis of this uniform vorticity flow. To this end, we adopt different methods (Lifschitz and Hameiri 1991; Gledzer and Ponomarev 1977) that allow to deduce upper and lower bounds for the growth rate of an instability. Our analysis shows that the uniform vorticity base flow is prone to inertial instabilities caused by a parametric resonance mechanism. This is confirmed by a set of direct numerical simulations. Applying our results to planetary settings, we find that neither a spin-over resonance nor an inertial instability can exist within the liquid core of the Moon, Io and Mercury.

KW - physics.flu-dyn

U2 - 10.1017/jfm.2015.130

DO - 10.1017/jfm.2015.130

M3 - Article

VL - 771

SP - 193

EP - 228

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -