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 by 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.
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References
L. Euler, Theoria motus corporum solidorum seu rigidorum (A. F. Rose, Rostock & Greifswald, 1765)
L. D. Landau, E. M. Lifshitz, Mechanics, 3rd edn. (Elsevier, Oxford, 1976)
F. Klein, A. Sommerfeld, The Theory of the Top, vol. III (Birkhäuser, New York, 2012 [1903])
S. C. Chandler, “On the variation of latitude, I”, Astron. J. 11 (1891), 59–61
S. C. Chandler, “On the variation of latitude, II”, Astron. J. 11 (1891), 65–70
W. E. Carter, M. S. Carter, “Seth Carlo Chandler, Jr. 1846–1913”, in Biographical Memoirs 66 (National Academy of Sciences, Washington, D.C., 1995), 44–79
C. R. Wilson, R. O. Vicente, “Maximum likelihood estimates of polar motion parameters”, in Variations in Earth Rotation, eds. D. D. McCarthy and W. E. Carter (American Geophysical Union, Geophysical Monograph Series 59, 1990), 151–155
S. Newcomb, “On the dynamics of the Earth’s rotation, with respect to the periodic variations of latitude”, Mon. Not. R. Astron. Soc. 52 (1892), 336–341
H. Jeffreys, “The variation of latitude”, Mon. Not. R. Astron. Soc. 100 (1940), 139–155
H. Jeffreys, “The variation of latitude”, Mon. Not. R. Astron. Soc. 141 (1968), 255–268
H.-P. Plag, “Chandler wobble and pole tide in relation to interannual atmosphere-ocean dynamics”, in Tidal Phenomena (Springer, Lecture Notes on Earth Sciences 66, 1997), 183–218
R. S. Gross, “The excitation of the Chandler wobble”, Geophys. Res. Lett. 27 (2000), 2329–2332
Y. Aoyama, I. Naito, “Atmospheric excitation of the Chandler wobble, 1983–1998”, J. Geophys. Res. 106 (2001), 8941–8954
Y. Aoyama et al., “Atmospheric quasi-14 month fluctuation and excitation of the Chandler wobble”, Earth Planets Space 55 (2003), e25–e28
A. A. Andronov, A. A. Vitt, S. È. Khaĭkin, Theory of Oscillators (Dover, Mineola, 1987 [1966])
A. Jenkins, “Self-oscillation”, Phys. Rep. 525 (2013), 167–222
S. H. Strogatz et al., “Theoretical mechanics: Crowd synchrony on the Millennium Bridge”, Nature 403 (2005) 43–44
G. B. Airy, “On certain Conditions under which a Perpetual Motion is possible”, Trans. Cambridge Phil. Soc. 3 (1830), 369–372
R. Willis, “On the Mechanism of the Larynx”, Trans. Cambridge Phil. Soc. 4 (1833), 323–352. This work was originally presented in May 1829.
Z. Malkin, N. Miller, “Chandler wobble: two more large phase jumps revealed”, Earth Planets Space 62 (2010), 943–947
K. Lambeck, The Earth’s Variable Rotation (Cambridge U. P., Cambridge 1980)
F. D. Stacey, P. M. Davis, Physics of the Earth, 4th edn. (Cambridge U. P., Cambridge, 2008)
A. Souriau, “The influence of earthquakes on the polar motion”, in Earth Rotation: Solved and Unsolved Problems, ed. A. Cazenave (Reidel, Dordrecht, 1986), 229–249
B. F. Chao, R. S. Gross, “Changes in the Earth’s rotation and low-degree gravitational field induced by earthquakes”, Geophys. J. Roy. Astr. S. 91 (1987), 569–596
V. Frède, P. Mazzega, “Detectability of deterministic non-linear processes in Earth rotation time-series I. Embedding”, Geophys. J. Int. 137 (1999), 551–564
V. Frède, P. Mazzega, “Detectability of deterministic non-linear processes in Earth rotation time-series II. Dynamics”, Geophys. J. Int. 137 (1999), 565–579
V. Frède, P. Mazzega. “A preliminary nonlinear analysis of the Earth’s Chandler wobble”, Discrete Dyn. Nat. Soc. 4 (2000), 39–53
B. B. Mandelbrot, K. McCamy, “On the Secular Pole Motion and the Chandler Wobble”, Geophys. J. R. astro. Soc. 21 (1970), 217–232
D. J. Tritton, Physical Fluid Dynamics, 2nd edn. (Oxford U. P., Oxford, 1998)
H. Georgi, The Physics of Waves (Prentice Hall, Englewood Cliffs, 1993)
D. Volchenkov, T. Krüger, P. Blanchard, “Heavy-tailed Distributions In Some Stochastic Dynamical Models", Discontinuity Nonlinearity Complexity 1 (2012), 1–40
Acknowledgments
The author thanks Eric Alfaro, Jorge Amador, and Paul O’Gorman for discussions on meteorological issues, as well as Howard Georgi and José Gracia-Bondía for encouragement and advice on this project.
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Jenkins, A. (2016). Chandler Wobble: Stochastic and Deterministic Dynamics. In: Awrejcewicz, J. (eds) Dynamical Systems: Theoretical and Experimental Analysis. Springer Proceedings in Mathematics & Statistics, vol 182. Springer, Cham. https://doi.org/10.1007/978-3-319-42408-8_15
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DOI: https://doi.org/10.1007/978-3-319-42408-8_15
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