A model for tectonic rotations about a vertical axis

The rotation of a rigid ellipsoidal inclusion within a highly viscous fluid, orientated so that two of the principal axes remain horizontal, is used as a model for the rotation of crustal inclusions in wide zones of continental deformation. This model is also applicable to other geological problems involving the rotation of inclusions in a matrix. The pattern of behaviour in such a model is shown to be complex. In general the rotation rate of the inclusion is a function of all components of the velocity field of the deforming medium and the horizontal aspect ratio of the inclusion. However, for a given velocity field, this aspect ratio must exceed a critical value before the inclusion can rotate continuously. Inclusions with lower aspect ratios will rotate, for a certain range of orientations, in an opposite direction to the sense of shear in the deforming zone. The possibility of the inclusion changing shape during rotation adds to the complexity of behaviour.