Inertial instabilities of fluid flow in precessing spheroidal shells

Lorenzani, Silvia; Tilgner, A.

doi:10.1017/s002211200300572x

Cited by 55 publications

(59 citation statements)

References 17 publications

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“…Theoretical investigation is not possible in this geometry due to the ill-posed Cauchy problem inherent to the spherical shell 16 . At large enough precession rate, the uniform vorticity flow becomes unstable through the parametric coupling of two inertial waves leading to a growth and collapse to small scales [17][18][19][20] .…”

Section: Introductionmentioning

confidence: 99%

Experimental study of fluid flows in a precessing cylindrical annulus

2014

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The flow inside a precessing fluid cavity has been given particular attention since the end of the 19th century in geophysical and industrial contexts. The present study aims at shedding light on the underlying mechanism by which the flow inside a precessing cylindrical annulus transitions from laminar to multiple scale complex structures. We address this problem experimentally using ultrasonic Doppler velocimetry to diagnose the fluid velocity in a rotating and precessing cylindrical annulus. When precession is weak, the flow can be described as a superposition of forced inertial modes. Above a critical value of the precession rate, the forced flow couples with two free inertial modes satisfying triadic resonance conditions, leading to the classical growth and collapse. Using a Bayesian approach, we extract the wavenumber, frequency, growth rate and amplitude of each mode involved in the instability. In some cases, we observe for the first time ever experimentally two pairs of free modes coexisting with the forced flow. At larger precession rates, we do not observe triadic resonance any more, instead we observe several harmonics whose frequencies are integer multiples of the rotation frequency.

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Section: Introductionmentioning

confidence: 99%

Experimental study of fluid flows in a precessing cylindrical annulus

2014

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“…Such an approach has been used for studying kinematic dynamo models in a spheroidal galaxy (Walker & Barenghi, 1994). More recently, a spheroidal symmetry has been considered for some geophysical applications (Lorenzani & Tilgner, 2001;2003;Tilgner, 1999). In the latter approach, a coordinate transformation was performed in order to replace the ellipsoidal volume by a spherical one, for which a distorted equation of motion was used.…”

Section: Introductionmentioning

confidence: 99%

Numerical study of viscous modes in a rotating spheroid

Schmitt¹

2006

J. Fluid Mech.

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The motion of an incompressible, viscous rotating fluid contained in an oblate spheroidal container is studied by a direct numerical simulation in an appropriate spheroidal coordinate system and in the linear approximation. The behaviour of a few eigenmodes is investigated as a function of the eccentricity e of the container, for aEkman number E = 10 -5 . Viscous effects are evidenced through internal shear layers, the spatial structure of which strongly depends on the eccentricity. In particular, for the spin-over mode, a resonance occurs around a critical value e c ≈ 0.50, where the decay rate strongly deviates from the predicted theoretical variation. This resonance is discussed in relation with the accidental coincidence between the spin-over frequency and two other frequencies corresponding to the (8,1,5) and (14,1,9) inertial eigenmodes.

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“…In particular the occurrence of this 'tidal' instability together with thermal or compositional convection in the molten cores of planets, such as the Earth, might be of prime importance in the generation or in the dynamics of the geomagnetic fields (Kerswell, 1994;Kerswell and Malkus, 1998). Recent measurements of magnetic fields around relatively small planets such as the Jovian moons Io and Ganymède (Kivelson et al, 1996a,b) may reinforce the interest in the study of inertial instabilities such as the elliptical or the precessional ones (Malkus, 1968;Busse, 1968;Noir et al, 2001;Kerswell, 1993;Lorenzani and Tilgner, 2003). Aldridge et al (1997), and Seyed-Mahmoud et al (2000 have performed computations and built as already mentioned, a rotating deformable shell where they observed the presence of the elliptical instability.…”

Section: Introductionmentioning

confidence: 99%

Elliptical instability of the flow in a rotating shell

Lacaze¹,

Gal²,

Dizès³

2005

Physics of the Earth and Planetary Interiors

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A theoretical and experimental study of the spin-over mode induced by the elliptical instability of a flow contained in a slightly deformed rotating spherical shell is presented. This geometrical configuration mimics the liquid rotating cores of planets when deformed by tides coming from neighboring gravitational bodies. Theoretical estimations for the growth rates and for the non linear amplitude saturations of the unstable mode are obtained and compared to experimental data obtained from Laser Döppler anemometry measurements. Visualizations and descriptions of the various characteristics of the instability are given as functions of the flow parameters.

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Inertial instabilities of fluid flow in precessing spheroidal shells

Cited by 55 publications

References 17 publications

Experimental study of fluid flows in a precessing cylindrical annulus

Experimental study of fluid flows in a precessing cylindrical annulus

Numerical study of viscous modes in a rotating spheroid

Elliptical instability of the flow in a rotating shell

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