Editing Polar motion (section)

===Chandler wobble===
{{main|Chandler wobble}}

It is improbable that the internal parameters of the Earth responsible for the Chandler wobble would be time dependent on such short time intervals. Moreover, the observed stability of the annual component argues against any hypothesis of a variable Chandler resonance frequency. One possible explanation for the observed frequency-amplitude behavior would be a forced, but slowly changing quasi-periodic excitation by interannually varying atmospheric dynamics. Indeed, a quasi-14 month period has been found in coupled ocean-atmosphere general circulation models,<ref>{{cite journal | last1 = Hameed | first1 = S. | last2 = Currie | first2 = R.G. | year = 1989 | title = Simulation of the 14-month Chandler wobble in a global climatic model | journal = Geophys. Res. Lett. | volume = 16 | issue = 3| page = 247 | doi=10.1029/gl016i003p00247 | bibcode=1989GeoRL..16..247H}}</ref> and a regional 14-month signal in regional [[sea surface temperature]] has been observed.<ref>Kikuchi, I., and I. Naito 1982 Sea surface temperature analysis near the Chandler period, Proceedings of the International Latitude Observatory of Mizusawa, '''21 K''', 64</ref>

To describe such behavior theoretically, one starts with the Euler equation with pressure loading as in eq.(3), however now with a slowly changing frequency ν, and replaces the frequency ν by a complex frequency {{nowrap|ν + iν<sub>D</sub>}}, where ν<sub>D</sub> simulates dissipation due to the elastic reaction of the Earth's interior. As in Figure 2, the result is the sum of a prograde and a retrograde circular polarized wave. For frequencies ν < 0.9 the retrograde wave can be neglected, and there remains the circular propagating prograde wave where the vector of polar motion moves on a circle in anti-clockwise direction. The magnitude of '''m''' becomes:<ref name=VollandAR/>

(6) {{pad|4em}} m = 14.5 p<sub>0</sub> ν<sub>C</sub>/[(ν − ν<sub>C</sub>)<sup>2</sup> + ν<sub>D</sub><sup>2</sup>]<sup>{{frac|1|2}}</sup> {{pad|5em}} (for ν < 0.9)

It is a resonance curve which can be approximated at its flanks by

(7) {{pad|4em}} m ≈ 14.5 p<sub>0</sub> ν<sub>C</sub>/|ν − ν<sub>C</sub>| {{pad|5em}} (for (ν − ν<sub>C</sub>)<sup>2</sup> ≫ ν<sub>D</sub><sup>2</sup>)

The maximum amplitude of m at {{nowrap|ν {{=}} ν<sub>C</sub>}} becomes

(8) {{pad|4em}} m<sub>max</sub> = 14.5 p<sub>0</sub> ν<sub>C</sub>/ν<sub>D</sub>

In the range of validity of the empirical formula eq.(2), there is reasonable agreement with eq.(7). From eqs.(2) and (7), one finds the number {{nowrap|p<sub>0</sub> ∼ 0.2 hPa}}. The observed maximum value of m yields {{nowrap|m<sub>max</sub> ≥ 230 mas}}. Together with eq.(8), one obtains

(9) {{pad|4em}} τ<sub>D</sub> = 1/ν<sub>D</sub> ≥ 100 years

The number of the maximum pressure amplitude is tiny, indeed. It clearly indicates the resonance amplification of Chandler wobble in the environment of the Chandler resonance frequency.