The coupling between inertial and rotational eigenmodes in planets with liquid cores

Triana, S. A.; Rekier, J.; Trinh, Antony; Déhant, V.

doi:10.1093/gji/ggz212

Cited by 20 publications

(27 citation statements)

References 20 publications

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“…Rather than solving equation directly for the flow velocity, v , we use the projections equations and presented in Appendix , there given in terms of their spherical harmonics components. We solve these equations numerically using a dedicated spectral solver described in some details in Rekier et al () and Triana et al (). The spherical harmonics components

P_{ℓ, m} false(r false)

and

T_{ℓ, m} false(r false)

are discretized in the radial direction by using a representation in terms of Chebyshev coefficients.…”

Section: Methodsmentioning

confidence: 99%

“…In a recent paper (Triana et al, ), we explained the difficulties of solving the equations of hydrodynamics at low Ekman number for geometries that are too far from the simple spherical symmetry. This is because the flow develops a very thin Ekman boundary layer that needs to be resolved numerically.…”

Section: Methodsmentioning

confidence: 99%

“…Thanks to the efficiency of our method and the fact that it is based on an algebraic representation in terms of sparse matrices, we are able to reach values of Ek ≲ 10 −10 . See Rekier et al (2018) and Triana et al (2019) for more details.…”

Section: Numerical Implementationmentioning

confidence: 99%

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Internal Energy Dissipation in Enceladus's Subsurface Ocean From Tides and Libration and the Role of Inertial Waves

et al. 2019

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Enceladus is characterized by a south polar hot spot associated with a large outflow of heat, the source of which remains unclear. We compute the heat generated via viscous dissipation resulting from tidal and (longitudinal) libration forcing in the moon's subsurface ocean using the linearized Navier‐Stokes equation in a three‐dimensional spherical model. We conclude that libration is the dominant cause of dissipation at the linear order, providing up to ∼0.001 GW of heat to the ocean, which remains insufficient to explain the ∼10 GW observed by Cassini. We also illustrate how resonances with inertial modes can significantly augment the dissipation. Our work is an extension to Rovira‐Navarro et al. (2019, https://doi.org/10.1016/j.icarus.2018.11.010) to include the effects of libration and the presence of the icy crust. The model developed here is readily applicable to the study of other moons with a subsurface ocean and planets with a liquid core.

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P_{ℓ, m} false(r false)

and

T_{ℓ, m} false(r false)

are discretized in the radial direction by using a representation in terms of Chebyshev coefficients.…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Internal Energy Dissipation in Enceladus's Subsurface Ocean From Tides and Libration and the Role of Inertial Waves

et al. 2019

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“…One can overcome this problem in homoeoidal shells by using the Poincaré transformation (i.e., the ellipsoidal volume is remapped onto a computational spherical domain in which distorted equations must be solved, see in Tilgner 2001, 2003;Ivers 2017a)). For arbitrary shells, one could use non-orthogonal spherical-like coordinates to solve (Rogister and Rochester 2004;Rochester et al 2014), or Taylor-expand the non-spherical BC (Rekier et al 2019;Triana et al 2019). Non-spectral flexible methods could also be considered (e.g., finite elements (Su et al 2020)).…”

Section: Numerical Methods For the Fluid Modesmentioning

confidence: 99%

Core Eigenmodes and their Impact on the Earth’s Rotation

et al. 2021

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Changes in the Earth’s rotation are deeply connected to fluid dynamical processes in the outer core. This connection can be explored by studying the associated Earth eigenmodes with periods ranging from nearly diurnal to multi-decadal. It is essential to understand how the rotational and fluid core eigenmodes mutually interact, as well as their dependence on a host of diverse factors, such as magnetic effects, density stratification, fluid instabilities or turbulence. It is feasible to build detailed models including many of these features, and doing so will in turn allow us to extract more (indirect) information about the Earth’s interior. In this article, we present a review of some of the current models, the numerical techniques, their advantages and limitations and the challenges on the road ahead.

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“…This assumption does not necessarily always hold because other eigenmodes might interact with uniform vorticity flows as demonstrated by Triana et al. (2019) (see also Rogister & Valette (2009) and Schmitt (2006)). The resulting flow in the interior can thus deviate considerably from solid body rotation.…”

Section: Introductionmentioning

confidence: 99%

The Viscous and Ohmic Damping of the Earth's Free Core Nutation

et al. 2021

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The cause for the damping of the Earth's free core nutation (FCN) and the free inner core nutation eigenmodes has been a matter of debate since the earliest reliable estimations from nutation observations were made available. Numerical studies are difficult given the extreme values of some of the parameters associated with the Earth's fluid outer core, where important energy dissipation mechanisms can take place. We present a fully 3D numerical model for the FCN capable of describing accurately viscous and Ohmic dissipation processes taking place in the bulk of the fluid core as well as in the boundary layers. We find an asymptotic regime, appropriate for Earth's parameters, where viscous and Ohmic processes contribute to the total damping, with the dissipation taking place almost exclusively in the boundary layers. By matching the observed nutational damping, we infer an enhanced effective viscosity matching and validating methods from previous studies. We suggest that turbulence caused by the Earth's precession can be a source for the enhanced viscosity.

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The coupling between inertial and rotational eigenmodes in planets with liquid cores

Cited by 20 publications

References 20 publications

Internal Energy Dissipation in Enceladus's Subsurface Ocean From Tides and Libration and the Role of Inertial Waves

Internal Energy Dissipation in Enceladus's Subsurface Ocean From Tides and Libration and the Role of Inertial Waves

Core Eigenmodes and their Impact on the Earth’s Rotation

The Viscous and Ohmic Damping of the Earth's Free Core Nutation

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