Chandler wobble: Stochastic and deterministic dynamics
Abstract
We propose a model of the Earth's torqueless precession, the "Chandler wobble", as a self-oscillation driven by positive feedback between the wobble and the centrifugal deformation of the portion of the Earth's mass contained in circulating fluids. The wobble may thus run like a heat engine, extracting energy from heat-powered geophysical circulations whose natural periods would otherwise be unrelated to the wobble's observed period of about fourteen months. This can explain, more plausibly than previous models based on stochastic perturbations or forced resonance, how the wobble is maintained against viscous dissipation. The self-oscillation is a deterministic process, but stochastic variations in the magnitude and distribution of the circulations may turn off the positive feedback (a Hopf bifurcation), accounting for the occasional extinctions, followed by random phase jumps, seen in the data. This model may have implications for broader questions about the relation between stochastic and deterministic dynamics in complex systems, and the statistical analysis thereof.
Cite
@article{arxiv.1506.02810,
title = {Chandler wobble: Stochastic and deterministic dynamics},
author = {Alejandro Jenkins},
journal= {arXiv preprint arXiv:1506.02810},
year = {2016}
}
Comments
10 pages, 3 figures. v2: Briefly clarified incompatibility of forced resonance model with estimated quality factor, improved references, adjustments to title and abstract, change of format. Presented at the 13th International Conference, Dynamical Systems - Theory and Applications (DSTA '2015), {\L}\'od\'z, Poland, 7-10 Dec. 2015