# Chandler Wobble according to Na

In Chapter 13 of the book, we have a description of the mechanism forcing the Chandler Wobble in the Earth’s rotation. As a counter to a recent GeoenergyMath post suggesting there is little consensus behind this mechanism, a recent paper by Na et al provides a foundation to understand how the lunar forcing works.

Chandler wobble and free core nutation are two major modes of perturbation in the Earth rotation. Earth rotation status needs to be known for the coordinate conversion between celestial reference frame and terrestrial reference frame. Due mainly to the tidal torque exerted by the moon and the sun on the Earth’s equatorial bulge, the Earth undergoes precession and nutation.

Na, S.-H. et al. Chandler Wobble and Free Core Nutation: Theory and Features. Journal of Astronomy and Space Sciences 36, 11–20 (2019).

The tidal torque of the earth and sun are sufficient, and the non-spherical bulge is essential to start any kind of precession — as a perfectly-uniform rotating spherical object can’t be influenced by an external torque, explained by symmetry arguments alone.

Na et al estimate the Chandler Wobble cycle from the empirical time-series to be 432.2 days, compared to our estimate of 432.4 days based on the lunar nodal cycle synchronized to a semi-annual cycle.

They continue with a further rationale and formulate a precession matrix that one can apply.

For precession, one may assume the lunar and solar masses as circularly distributed around the Earth like donuts. In fact, the moon and the sun give periodic torques as oscillatory perturbations and lead Earth nutation. By analogy of harmonic oscillator to periodic forces, amplitude of long period nutation is larger than short period one.

Na, S.-H. et al. Chandler Wobble and Free Core Nutation: Theory and Features. Journal of Astronomy and Space Sciences 36, 11–20 (2019).

So the foundation is in place but they have yet to make an association of the ~432 day cycle to the known simultaneous nodal crossing period.

Another finding that they make is the apparent measured decrease in the amplitude of the Chandler wobble over time.

This may be related to the Earth’s spin axis drift over recent years, perhaps revealing a change in the moment of inertia — caused by redistribution of mass such as in glaciers, glacial rebound, and/or mantle convection. Less likely, but perhaps coincidental, could this decrease be related to the QBO anomaly of 2016, which also is synchronized to the nodal crossing cycle?

In any case, it will be interesting if the cycle period remains constant with further reduction in wobble amplitude.

## 7 thoughts on “Chandler Wobble according to Na”

1. This study correlates the 6.4 year envelope of Chandler Wobble with magma eruptions on Mt. Etna
https://phys.org/news/2019-12-earth-earthquakes-volcanic-eruptions-mount.html

Lambert, S. & Sottili, G. Is there an influence of the pole tide on volcanism? Insights from Mount Etna recent activity. Geophysical Research Letters (2019) doi:10.1029/2019GL085525.

“The tide from polar motion causes the crust to deform over the span of seasons or years. This distortion is strongest at 45 degrees latitude, where the crust moves by about 1 centimeter (0.4 inches) per year.”

And from earlier in the year, Tamino found this correlation of Chandler Wobble with sea-level rise oscillations at mid-latitudes along the USA east cost:

https://tamino.wordpress.com/2019/01/12/wobbly-sea-level-rise-u-s-east-coast-vi/

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2. Pingback: EGU 2020 Notes | GeoEnergy Math

3. https://sci-hub.tw/10.1142/S012918312050117X

International Journal of Modern Physics C
Article Title: Model discrepancy of Earth polar motion using topological data analysis
and convolutional neural network analysis
Author(s): Dongjin Lee, Christopher Bresten, Kookhyoun Youm, Ki-Weon Seo, JaeHun Jung
DOI: 10.1142/S012918312050117X

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4. https://sci-hub.tw/10.1007/978-981-15-2600-8

In this chapter, the dynamic effects of the Earth pole motion in the celestial-mechanical problem statement as the “deformable Earth–Moon problem in the gravitational field of the Sun” are discussed. The orbits of the Moon and the Earth–Moon barycenter are assumed as known and given ones. Combination harmonics in the Earth pole motion are found and their connection with perturbations caused by the Moon’s orbit precession is shown. Applying a numerical–analytical approach, the additional components of the Earth pole motion model were determined in an explicit form.

Krylov S.S., Perepelkin V.V., Filippova A.S. (2020)
Long-Period Lunar Perturbations in Earth Pole Oscillatory Process: Theory and Observations.
In: Jain L., Favorskaya M., Nikitin I., Reviznikov D. (eds) Advances in Theory and Practice of Computational Mechanics. Smart Innovation, Systems and Technologies, vol 173. Springer, Singapore. https://doi.org/10.1007/978-981-15-2600-8_22

No idea if they are saying what drives the frequency, even though Fig 22-2 pins down the 18.6 year period

22.4 Conclusions

The developed celestial-mechanical model that takes into account the gravitationaltidal lunar–solar perturbations allows to assume the presence of a specific oscillatory process in the Earth pole motion. The perturbation from the Moon leads to the additional combinational harmonics modulated by a harmonic at a frequency close to the lunar orbit precession frequency, and the perturbation from the Sun makes this process nonstationary. More precisely, it can be said that the process will be quasistationary until the ratio of the amplitudes of the Chandler and annual components goes through 1 (becomes more than one or, on the contrary, less). Using the data processing of IERS observations over the Earth pole trajectory, a method is proposed for identifying the discovered oscillations.

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