Numerical modeling of heterogeneous flow fields around rigid objects with special reference to particle paths, strain shadows and foliation drag

With the help of two-dimensional numerical models this paper investigates three aspects of heterogeneous deformation around rigid objects: (1) the nature of particle paths; (2) the development of strain shadow zones; and (3) the drag patterns of passive markers. In simple shear, spherical objects develop typically a concentric vortex motion, showing particle paths with an eye (double-bulge)-shaped separatrix. The separatrix has no finite dimension along the central line, parallel to the shear direction. Under a combination of pure shear and simple shear, the particle paths assume a pattern with a bow-tie shaped separatrix. With increase in the ratio of pure shear to simple shear (S_r), the separatrix around the object shrinks in size. The axial ratio of the object (R) is another important factor that controls the geometry of particle paths. When R<1.5, the loci of a particle close to the object form an elliptical shell with the long axis lying along the central line. With increase in axial ratio R, the loci form a doublet elliptical shell structure. Objects with R>3 do not show closed particle paths, but give rise to elliptical or circular spiral particle paths.

The development of strain shadow zones against equant rigid bodies depends strongly on the strain ratio S_r. When S_r=0 (simple shear), they develop opposite to the extensional faces of the object, forming a typical σ-type tail. The structure has a tendency to die out with an increase in the pure shear component of the bulk deformation (S_r). The initial angle of the long axis of the object with the shear direction (φ) and the axial ratio of the object (R) determine the development of strain shadow zones near inequant rigid objects. Objects with large R and φ between 60 and 120° form pronounced zones of low finite strain, giving rise to strain shadow structures. A geometrical classification of diverse drag patterns of passive markers around rigid objects is presented along with their conditions of formation.