Scientific Applications of Lunar Laser Ranging pp 131-132 | Cite as

# Core-Resonance Effects on the Earth’s Angular Momentum Vector and Rotation Axis—A Generalized Model

## Abstract

It is well-known that, compared to other geophysical phenomena, transverse (ie. non-radial) flow relative to the mantle within a fluid core is theoretically able to generate a large amount of relative angular momentum. What does not seem to have been previously noted is the large clockwise angular separation between the Earth’s rotation axis \(\vec \omega \) and its total angular momentum vector \(\vec H\) that would necessarily be induced by transverse meridianal core-flow relative to the mantle. It is shown here that a \( 0\mathop .\limits^ 20\) separation, with a period of approximately 347 days as viewed from space, could be caused by the free diurnal “wobble” mode, even assuming Rochester, Jensen and Smylie’s observational upper limit of \( 0\mathop .\limits^ 0006\) on the free diurnal wobble’s amplitude. Resonant response to the ψ_{1} tide is shown to introduce a forced separation between \(\vec \omega \) and \(\vec H\) with amplitude \( 0\mathop .\limits^ 06\) and a period of exactly 1 year as viewed from space. In the generalization of Poincaré’s model developed here, the main inertial-coupling and damping effects due to a fluid core are represented by lumped parameters. The general inertial-coupling parameter is a first step toward providing the flexibility needed to account for a variable-density core fluid. The shell is assumed to be rigid. Coefficients to account for shell elasticity can be introduced at a later stage as can time-varying surface-density-layer coefficients set up to model the oceantidal excitation. In view of the large predicted angular separation between \(\vec \omega \) and \(\vec H\), it may be that the past observational studies confirming the existence of a \( 0\mathop .\limits^ 01\) to \( 0\mathop .\limits^ 02\) free diurnal wobble, as well as more recent studies denying its existence will need to beredone with care taken not to assume at any stage that \(\vec \omega \) and \(\vec H\) are collinear.