Variational calculation of the free core nutation mode

• Published in: Physics of the earth and planetary interiors Vol. 94; no. 3; pp. 159 - 182
• Main Authors: Jiang, Xianhua, Smylie, D.E.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-04-1996
• ISSN: 0031-9201; 1872-7395
• DOI: 10.1016/0031-9201(95)03104-9

Estimates of the period of the free core nutation (FCN) mode from observations of both Earth tides and nutations consistently show a difference of about 25–30 solar days from the period predicted by theoretical models. Reconciliation of this discrepancy has been the focus of some recent research in both analyses of observations and theoretical modelling.
In this paper, we present numerical calculations of eigenperiod of the FCN mode based upon a variational principle of the liquid outer core of the Earth. This variational principle is numerically implemented by a finite element approach. This numerical implementation of the variational principle then leads to a nonlinear eigenvalue-eigenvector problem. Solutions to this eigenvalue-eigenvector system will deliver eigenperiods of free core nutation modes and eigenperiods of associated wobble modes.
The eigenperiod of the FCN mode obtained in our numerical calculations is approximately 450 solar day which is 10 days shorter than the period predicted by previous theoretical models. One of the possible reasons for this difference may lie in different approaches to the dynamics of the liquid outer core.