Rotational dynamics of tidally deformed planetary bodies and validity of fluid limit and quasi-fluid approximation

Hu, Haiyang; Wal, Wouter van der; Vermeersen, L. L. A.

doi:10.1016/j.icarus.2018.08.013

Cited by 4 publications

(6 citation statements)

References 22 publications

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“…Such approximation is commonly referred to as the "quasi-fluid" approach (Lefftz et al, 1991;Ricard et al, 1993). Recently, Hu et al (2017aHu et al ( , 2019 analyzed the quasi-fluid approximation and by comparing the traditional solutions to their full-Maxwell approach they showed that the prediction of TPW speed on Earth and Mars were underestimated in previous studies.…”

Section: Introductionmentioning

confidence: 99%

“…Its estimate should be included within geological interpretations of planetary reorientation, demanding a general and user friendly tool for TPW rate assessment. Recently, Hu et al (2019) provided a link between the TPW rate and the applicability of the fluid limit solution of Matsuyama and Nimmo (2007), but estimates for reorientation timescales are still very scarce in the literature.…”

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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True Polar Wander on Dynamic Planets: Approximative Methods vs. Full Solution

Patočka

2021

Preprint

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Almost three decades ago, the problem of long term polar wander on a dynamic planet was formulated and simplified within the framework of normal mode theory. The underlying simplifications have been debated ever since, recently in a series of papers by Hu et al. (2017bHu et al. ( , 2017aHu et al. ( , 2019, who clarify the role of neglecting short-term relaxation modes of the body. However, the authors still do not solve the governing equations in full, because they make approximations to the Liouville equation (LE). In this paper I use a time domain approach and for previously studied test loads I solve both the relaxation of the body and the LE in full. I also compute the energy balance of true polar wander (TPW) in order to analyze the existing LE approximations. For fast rotating bodies such as the Earth, I show that the rotation axis is always aligned with the maximum principal axis of inertia (ω||MMOI) once free oscillations are damped. The ω||MMOI assumption is also re-derived theoretically. Contrary to previous beliefs, I demonstrate that it is not necessarily linked to the quasi-fluid simplification of the body's viscoelastic response to loading and rotation, but that it is an expression of neglecting the Coriolis and Euler forces in the equation of motion. For slowly rotating bodies such as Venus, the full LE together with energy analysis indicate that previous estimates of TPW in the normal direction need to be revisited. The numerical code LIOUSHELL is made freely available.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…

…”

mentioning

confidence: 99%

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True Polar Wander on Dynamic Planets: Approximative Methods vs. Full Solution

Patočka

2021

Preprint

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“…Recently, Hu et al. (2017b, 2019) analyzed the quasi‐fluid approximation, and by comparing the traditional solutions to their full‐Maxwell approach they showed that the prediction of the TPW speed on Earth and Mars were underestimated in previous literature.…”

Section: Introductionmentioning

confidence: 99%

“…Such an approximation is commonly referred to as the "quasi-fluid" approach (Lefftz et al, 1991;Ricard et al, 1993). Recently, Hu et al (2017bHu et al ( , 2019 analyzed the quasi-fluid approximation, and by comparing the traditional solutions to their full-Maxwell approach they showed that the prediction of the TPW speed on Earth and Mars were underestimated in previous literature.…”

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confidence: 99%

True Polar Wander on Dynamic Planets: Approximative Methods Versus Full Solution

Patočka

2021

JGR Planets

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Internal and external planetary processes such as mantle convection, deglaciation, or large meteorite impacts cause bodies to move as a whole relative to their rotation axis. The rotation poles of planets and moons thus wander on their surfaces, as shown by paleomagnetic, astrometric, and geodetic measurements (e.g., Mitrovica & Wahr, 2011). Such reorientation in space is commonly referred to as true polar wander (TPW).The TPW mechanism can be described as follows. Let us assume that a rotating planet in hydrostatic equilibrium is subject to a sudden loading with a positive geoid anomaly, shifting the principal directions of the planet's inertia tensor in effect (the principal direction that has the largest associated moment of inertia is hereafter referred to as the main inertia axis, MIA). When viewed by an observer on the surface of the planet, the rotation axis will start a circular motion, known as free oscillations, around the new MIA. As soon as free oscillations dampen out (Nakada & Karato, 2012), the resulting position of the rotation pole will be closer to the principal axis of the load than in the initial state. Such motion of the rotation axis misaligns it with the hydrostatic rotational bulge, which effectively prevents the rotation axis from moving further toward the load axis (see figure 1 in Matsuyama et al., 2014). Gold (1955) argued that the stabilization is only transient, because the rotational bulge will eventually adjust to the new direction of rotation. The planet is then free to reorient further, and the process gradually

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Large true polar wander in a sea level model with application to the Neoproterozoic snowball Earth events

Liu

2019

Earth and Planetary Science Letters

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Rotational dynamics of tidally deformed planetary bodies and validity of fluid limit and quasi-fluid approximation

Cited by 4 publications

References 22 publications

True Polar Wander on Dynamic Planets: Approximative Methods vs. Full Solution

True Polar Wander on Dynamic Planets: Approximative Methods vs. Full Solution

True Polar Wander on Dynamic Planets: Approximative Methods Versus Full Solution

Large true polar wander in a sea level model with application to the Neoproterozoic snowball Earth events

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