Numerical simulations of bistable flows in precessing spheroidal shells

Vormann, Jan; Hansen, Ulrich

doi:10.1093/gji/ggy024

Cited by 4 publications

(9 citation statements)

References 26 publications

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“…Here, the resulting solution depended on the starting condition for a small thermal forcing Ra = 0.1. This behaviour is very similar to the purely precession driven flows reported in Vormann & Hansen (2018). For an increased thermal forcing of Ra = 1, the simulation switches to a different branch by itself, showing that an external influence can change a precessing flow in the bistable parameter range.…”

Section: Discussionsupporting

confidence: 80%

“…Most importantly, we look at flows in spheroidal shells, were theoretical models (Busse 1968; Precessing flow under the influence of a temperature field 891 A15-3 2013; Cébron 2015) have shown that the assumption of a linear, rigid-rotation-like bulk flow leads to multiple stable solutions at certain parameters, particularly low Ekman numbers or strong deformation of the boundary. This behaviour has been recreated in laboratory (Malkus 1968) and numerical experiments (Lorenzani & Tilgner 2003;Goepfert & Tilgner 2016;Vormann & Hansen 2018). We conduct a range of numerical simulations at a moderate Ekman number Ek = 10 −4 and show that this bistable behaviour persists when a temperature field is present.…”

Section: Introductionmentioning

confidence: 89%

“…We perform the direct numerical simulations with the spectral element code Nek5000 developed at Argonne National Laboratory (nek5000.mcs.anl.gov), in which the variables are represented in a weak formulation by high-order Lagrange polynomials defined on the Gauss-Lobatto-Legendre points in each element of a grid. The method combines high accuracy with geometric flexibility and very good parallel scaling capabilities and has been used for fluid mechanics problems both with mechanical forcings (Favier et al 2015;Lemasquerier et al 2017;Reddy, Favier & Bars 2018;Vormann & Hansen 2018) and convection (Scheel & Schumacher 2014. The equations are integrated forward in time with a third-order accurate backward differentiation formula.…”

Section: Methodsmentioning

confidence: 99%

“…The equations are solved on a cubed spheroidal grid as in Vormann & Hansen (2018). We project a Cartesian grid with points (x i ,ỹ i ,z i ) from each surface of a cube in the radial directionr onto a spherical shell.…”

Section: Methodsmentioning

confidence: 99%

“…We conduct a range of numerical simulations at a moderate Ekman number Ek = 10 −4 and show that this bistable behaviour persists when a temperature field is present. A jump to the second stable solution can not only be realized through a hysteresis, as for the purely mechanical forcing (Vormann & Hansen 2018), but also by the influence of thermal convection. Further, we show which of the two flow types described above dominates dependent on the parameters and point out how they can be distinguished by decomposing the flow field into symmetric and asymmetric components.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Characteristics of a precessing flow under the influence of a convecting temperature field in a spheroidal shell

Vormann

Hansen

2020

J. Fluid Mech.

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Section: Discussionsupporting

confidence: 80%

Section: Introductionmentioning

confidence: 89%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Characteristics of a precessing flow under the influence of a convecting temperature field in a spheroidal shell

Vormann

Hansen

2020

J. Fluid Mech.

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Precession-driven flows in stress-free ellipsoids

Vidal

Cébron

2022

J. Fluid Mech.

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Motivated by modelling rotating turbulence in planetary fluid layers, we investigate precession-driven flows in ellipsoids subject to stress-free boundary conditions (SF-BC). The SF-BC could indeed unlock numerical constraints associated with the no-slip boundary conditions (NS-BC), but are also relevant for some astrophysical applications. Although SF-BC have been employed in the pioneering work of Lorenzani & Tilgner (J. Fluid Mech., vol. 492, 2003, pp. 363–379), they have scarcely been used due to the discovery of some specific mathematical issues associated with angular momentum conservation. We revisit the problem using asymptotic analysis in the low-viscosity regime, which is validated with numerical simulations. First, we extend the reduced model of uniform-vorticity flows in ellipsoids to account for SF-BC. We show that the long-term evolution of angular momentum is affected by viscosity in triaxial geometries, but also in axisymmetric ellipsoids when the mean rotation axis of the fluid is not the symmetry axis. In a regime relevant to planets, we analytically obtain the primary forced flow in triaxial geometries, which exhibits a second inviscid resonance. Then, we investigate the bulk instabilities existing in precessing ellipsoids. We show that using SF-BC would be useful to explore the non-viscous instabilities (e.g. Kerswell, Geophys. Astrophys. Fluid Dyn., vol. 72, 1993, pp. 107–144), which are presumably relevant for planetary applications but are often hampered in experiments or simulations with NS-BC.

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Precessing cylinder as high-shear-rate mixer: Application to emulsification

et al. 2023

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Through laboratory experiments of oil-in-water emulsification, we show that we can construct a high-shear-rate mixer (precession mixer) by using the precession of a cylindrical container without any mixing blades. For high-shear-rate mixing, a container with a larger diameter and its faster spin are preferable so that the wall velocity becomes large enough. Then, the emulsification is most efficient when we set the Poincar\'e number $Po=\Omega_p/\Omega_s$, which is the ratio of the spin and precession rotation speeds, about $0.2$--$0.3$. When $Po$ is smaller than these values, shear rates in the mixer get much lower, though mixing in the bulk of the container is enhanced. On the other hand, when $Po$ is larger, shear rates near the cylindrical wall get higher but mixing in the bulk drastically declines. Through our systematic parameter survey for efficient emulsification by the precession mixer, we have also discovered an experimental law describing the maximum shear rate in the mixer. Since we can use it to appropriately choose the driving conditions of the mixer according to the properties of the materials to be mixed, this experimental law gives useful information for the practical use of the mixer.

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Numerical simulations of bistable flows in precessing spheroidal shells

Cited by 4 publications

References 26 publications

Characteristics of a precessing flow under the influence of a convecting temperature field in a spheroidal shell

Characteristics of a precessing flow under the influence of a convecting temperature field in a spheroidal shell

Precession-driven flows in stress-free ellipsoids

Precessing cylinder as high-shear-rate mixer: Application to emulsification

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