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

Nobili, Clement; Meunier, Patrice; Favier, Benjamin; Bars, Michaël Le

doi:10.1017/jfm.2020.938

Cited by 12 publications

(13 citation statements)

References 45 publications

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“…Spheroidal cavities exhibit hysteresis cycles of turbulence with respect to the precession rate Po near the resonance with the FCN. As first evidenced by Malkus (1968) and more recently by Nobili et al (2021), it is closely related to the hysteresis of the differential rotation well known theoretically in spheroids (Cébron 2015). Starting from a laminar regime at low Po the differential rotation jumps to a much larger value (decoupled core-mantle) as the precession rate approaches the FCN frequency, leading to turbulent flows.…”

Section: Flows Driven By Precessionsupporting

confidence: 53%

“…Theoretical progress, experiments with improved measurements, and the increase in performance of numerical simulations in the last 10 years, shed light on the nature of the instabilities witnessed by Malkus, Vanyo, and Noir and helped to provide scaling laws for the onset of the different regimes. One can distinguish essentially three instability mechanisms: parametric instabilities in non-spherical cavities (Kerswell 1993), shear-driven bulk parametric instabilities (CSI) (Lin et al 2015;Nobili et al 2021), and boundary layer turbulence (Sous et al 2013;Cébron et al 2019).…”

Section: Flows Driven By Precessionmentioning

confidence: 99%

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Fluid Dynamics Experiments for Planetary Interiors

et al. 2021

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Understanding fluid flows in planetary cores and subsurface oceans, as well as their signatures in available observational data (gravity, magnetism, rotation, etc.), is a tremendous interdisciplinary challenge. In particular, it requires understanding the fundamental fluid dynamics involving turbulence and rotation at typical scales well beyond our day-to-day experience. To do so, laboratory experiments are fully complementary to numerical simulations, especially in systematically exploring extreme flow regimes for long duration. In this review article, we present some illustrative examples where experimental approaches, complemented by theoretical and numerical studies, have been key for a better understanding of planetary interior flows driven by some type of mechanical forcing. We successively address the dynamics of flows driven by precession, by libration, by differential rotation, and by boundary topography.

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Section: Flows Driven By Precessionsupporting

confidence: 53%

Section: Flows Driven By Precessionmentioning

confidence: 99%

Fluid Dynamics Experiments for Planetary Interiors

et al. 2021

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“…After characterizing its amplitude, we now aim at shedding light on the dynamical nature of the non-uniform vorticity flow. Three instability mechanisms have been identified in precessing fluid cavities: parametric resonances (Kerswell 1993;Goto et al 2007;Lin et al 2015), viscous boundary layer instabilities (Tilgner & Busse 2001;Cébron et al 2019;Nobili et al 2020;Buffett 2021) and, more recently, experiments and numerical simulations suggest that centrifugal instabilities may occur in precessing cylinders leading to space filling turbulence (Giesecke et al 2018(Giesecke et al , 2019. Our spatially limited UDV measurements may not allow us to completely disentangle these mechanisms, for example we cannot get access to the radial profile of the angular momentum that plays a crucial role in the identification of the centrifugal instability reported by Giesecke et al (2018).…”

Section: Instabilitiesmentioning

confidence: 99%

“…Vanyo et al 1995;Noir et al 2001a;Noir, Jault & Cardin 2001b;Tilgner & Busse 2001;Noir et al 2003). While the viscous solution in the sphere is always unique, in spheroids two stable solutions may be found over a finite range of precession rates, leading to a hysteresis cycle (Noir et al 2003;Cébron 2015;Nobili et al 2020).…”

Section: Introductionmentioning

confidence: 99%

Experimental study of the flows in a non-axisymmetric ellipsoid under precession

Burmann

Noir

2021

J. Fluid Mech.

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Precession driven flows are of great interest for both, industrial and geophysical applications. While cylindrical, spherical and spheroidal geometries have been investigated in great detail, the numerically and theoretically more challenging case of a non-axisymmetric cavity has received less attention. We report experimental results on the flows in a precessing triaxial ellipsoid, with a focus on the base flow of uniform vorticity, which we show to be in good agreement with existing theoretical models. As predicted, the uniform vorticity component exhibits two branches of solutions leading to a hysteresis cycle as a function of the Poincaré number. The first branch is observed at low forcing and characterized by large amplitude of the total fluid rotation and a moderate tilt angle of the fluid rotation axis. In contrast, the second branch displays only a moderate fluid rotation and a large tilt angle of the fluid rotation axis, which tends to align with the precession axis. In addition, we observe the occurrence of parametric instabilities early in the first branch, which saturate in the second branch, where we observe the same order of the kinetic energy in the base flow and instabilities.

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“…Busse (1968) then considered the viscous torque generated by the boundary layers to predict the slowdown of the solid body rotation (see also Hollerbach & Kerswell 1995;Kerswell 1995). This nonlinear theory, which has been validated experimentally (Noir, Jault & Cardin 2001;Horimoto et al 2018;Nobili et al 2021), predicts a hysteresis cycle between two solutions for strong ellipticity or large tilt angles. In these studies, the zonal flow plays a crucial role.…”

Section: Introductionmentioning

confidence: 99%