INTRODUCTION

Rotating fluid dynamics is of primary importance in the understanding of the origin of planetary magnetic fields which are generated by dynamo processes in the rotating fluid interiors of planets. There are two important but traditionally separate branches in the subject of rotating fluid dynamics: inertial oscillation and convection. Both have been extensively investigated. Inertial oscillation in rotating systems is governed by the Poincare equation; it was also shown by Malkus (1967) that the problem of hydromagnetic inertial oscillation can be changed to the Poincaré problem with a special form of the basic field. A classic introduction and most of the earlier research results concerning this problem can be found in Greenspan's monograph (1969). The important application to the dynamics of the Earth's fluid core was discussed by Aldridge & Lumb (1987).