Stable positions of rigid objects in non-coaxial flow—a study in vorticity analysis

Abstract

Distortions of a homogeneous fabric, which occur around rigid objects in rocks deformed by non-coaxial ductile flow are useful to determine the sense of shear, but also contain information on other aspects of the flow. Rigid objects in a non-coaxial flow fall into two categories: those which are permanently rotating and those which can reach stable positions at high finite strain. The orientation of such immobilized objects with respect to eigenvectors of instantaneous flow is a function of the vorticity number of the flow, the ratio of instantaneous stretches and the axial ratio of the object. In naturally deformed rocks, immobilized rigid objects may be recognized from the geometry of the surrounding fabric. Tails of recrystallized material around porphyroclasts in a mylonite rotate towards parallellism with the extensional eigenvector of the flow, and the shape of tails reflects the rotational behaviour of the porphyroclast. The axial ratio of immobilized porphyroclasts and their orientation with respect to the tails can theoretically be used to determine the vorticity number of the flow and deviations from isochoric plane strain. In practice such an analysis is as yet difficult, but a tentative example is given of the way in which the vorticity number can be calculated from a population of feldspar porphyroclasts in a quartzite mylonite from the French Pyrenees.