Vorticity determination, distribution, partitioning and the heterogeneity and non-steadiness of natural deformations

Abstract

An investigation on vorticity in general heterogeneous and non-steady flows is presented. The bulk vorticity of a flow is solely determined by the imposed boundary conditions and it exerts no constraints on local flow. The distribution of bulk vorticity in different rheological domains and the partitioning of the distributed vorticity into shear-induced vorticity and spin are both time dependent. This indicates that heterogeneous flows are inevitably non-steady. In a quantitative example, it is demonstrated that even though the imposed boundary movement is a constant simple shear, local flow can be non-steady, spinning and non-coaxial. Super-simple shear flow with internal kinematic vorticity number greater than I occurs, but the finite strain does not necessarily pulsate. The geological implications of this investigation are discussed. The significance of heterogeneity and non-steadiness in natural deformations are emphasized. It is concluded that vorticity distribution and partitioning is the link between different scale structures. The internal kinematic vorticity number is not a criterion of finite strain oscillation.