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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/npg-2019-12
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-2019-12
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 26 Apr 2019

Research article | 26 Apr 2019

Review status
This discussion paper is a preprint. A revision of the manuscript is under review for the journal Nonlinear Processes in Geophysics (NPG).

On the nonlinear and Solar-forced nature of the Chandler wobble in the Earth's pole motion

Dmitry M. Sonechkin Dmitry M. Sonechkin
  • Shirshov Oceanology Institute, RAS, Moscow, Russia

Abstract. About 250 years ago L. Euler has derived a system of three quadratic-nonlinear differential equations to depict the rotation of the Earth as a rigid body. Neglecting a small distinction between the equatorial inertia moments, he reduced this system to much simpler linear one, and concluded that the Earth's pole must experience a harmonic oscillation of the 304-day period. Astronomers could not find this oscillation, but instead, S.C Chandler has found two powerful wobbles with the 12- and ~ 14-month periods in reality. Adhering to the Euler's linearization, astronomers can not explain the nature of the later wobble up to now. I indicate that the neglect by the above small distinction (“a small parameter” of the Euler's primary nonlinear equations) is not admissible because the effect of this parameter is singular. Analysing the primary equations by an asymptotic technique, I demonstrate that the Chandler wobble tones are formed from combinational harmonics of the Euler's 304-day oscillation, long-term Luni-Solar tides as well as the 22-year cycle of the heliomagnetic activity. Correlating simultaneous variations of the wobble and a solar activity index, I corroborate that the Chandler wobble is really affected by the Sun.

Dmitry M. Sonechkin
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Dmitry M. Sonechkin
Dmitry M. Sonechkin
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Latest update: 22 Jul 2019
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Short summary
I look for a combination of some external periodicities, which period coincides with Chandler's period. My predecessors considered a model of the linear oscillator with a viscosity and several periodic external forces. Necessary and sufficient condition for emergence of a peak in power spectrum at Chandler's period is nonlinearity of the oscillator being considered. The main achievement of my work is the proof that it is necessary to consider the raw nonlinear equations of L. Euler.
I look for a combination of some external periodicities, which period coincides with Chandler's...
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