Chandler wobble: Stochastic and deterministic dynamics

TL;DR

This paper presents a self-oscillation model for the Earth's Chandler wobble driven by feedback between the wobble and fluid circulations, explaining its maintenance and irregularities through deterministic and stochastic dynamics.

Contribution

It introduces a novel self-oscillation model based on positive feedback, contrasting with previous stochastic or forced resonance explanations.

Findings

The wobble can be sustained by a feedback-driven heat engine mechanism.

Stochastic variations can cause the wobble to cease temporarily and produce phase jumps.

The model links deterministic self-oscillation with stochastic perturbations in Earth's fluid circulations.

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.