Efficient use of the velocity gradients tensor in flow modelling

Abstract

For models of fabric development in rocks, with vorticity as a variable parameter, the choice of an unsuitable reference frame for instantaneous flow can hamper clear presentation of results. The orientation of most fabric elements which develop in deforming rocks is attached to some principal direction of instantaneous flow: syntaxial fibres, crystallographic preferred orientation patterns, steady state foliations and immobilised rigid objects seem to orient themselves in a fixed position relative to instantaneous stretching axes (d¡), while shape fabric elements and mica preferred orientation approach parallelism with the extensional apophysis (l₁) of the flow. Models for development of such fabric elements benefit from a choice of reference frame attached to either d¡, or l₁.