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.

The Problem of Engines in Statistical Physics

“…A further complication is introduced by the fact that the fluctuations may, in some cases, make the active dynamics intermittent by pushing the dynamical system through Hopf bifurcations; see, e.g., [80,81]. Such intermittency may be relevant not just in biophysics and microengineering but also in turbulence [82] and even very large active systems, such as geophysics [83] and macroeconomics [23,84]. The development of an adequate statistical treatment of such non-Gaussian systems remains a great intellectual challenge.…”

The problem of engines in statistical physics

“…A further complication is introduced by the fact that the fluctuations may, in some cases, make the active dynamics intermittent by pushing the dynamical system through Hopf bifurcations; see, e.g., [80,81]. Such intermittency may be relevant not just in biophysics and microengineering, but also in turbulence [82], and even in very large active systems such as geophysics [83] and macroeconomics [23,84]. The development of an adequate statistical treatment of such non-Gaussian systems remains a great intellectual challenge.…”