The self-consistent dynamic pole tide in global oceans

Fluid dynamic theories of the pole tide are in conflict with pole tide observations. The former predict that the oceanic response to the Chandler wobble should be nearly static; while the latter reveal the tide to possess significant non-equilibrium characteristics. Resolution of the conflict would determine whether mantle anelasticity or non-equilibrium oceans is responsible for a measurable contribution to the Chandler period. It is possible that resolution might be achieved through a more exact mathematical investigation of pole tide fluid dynamics than theories have carried out to date. The theories have also neglected to consider a unique property of the pole tide, its ability to lengthen the period of its own forcing function; this property implies that the pole tide characteristics and effects on wobble cannot be correctly determined unless the tide and wobble equations are jointly solved. This work constitutes a first attempt to determine, accurately and self-consistently, the nature of the pole tide and its effects on the Chandler wobble. The Laplace tidal equations, modified by the addition of bottom friction but with no simplifying approximations, are employed together with the Liouville equations to elucidate pole tide characteristics. This work is a first attempt because the earth model chosen is a crude one, consisting of global oceans of uniform depth overlying a rigid mantle with a fluid core. Results for this model suggest that departures of the pole tide from equilibrium may indeed be minimal. The relevance of these results to the actual pole tide, however, must await the application of our self-consistent and more exact dynamical theory to the situation of realistic oceans.