Stream functions and complex potentials: implications for development of rock fabric and the continuum assumption

Abstract

Stream functions may be applied to study the development of ductile deformation patterns in rocks. It is demonstrated how to derive the stream function and the associated complex potential from the velocity field of any particular flow. Finite deformation patterns are subsequently modelled analytically from this mathematical description of flow. Basic examples discussed are rigid body translation, pure shear and composite flows due to simultaneous pure and simple shear. A general stream function is obtained to describe the flow regime within a ductile deformation zone deforming by homogeneous plane strain by superposed pure and simple shear components. The deformation patterns are visualized, using analytical methods only. The results are discussed in terms of fabric formation. Progressive deformation in a simple continuum, modelled here mathematically using principles of fluid mechanics, is compared with crystalline creep in rocks. The validity of the continuum assumption is briefly outlined in view of recent experiments on particular synthetic, monocrystalline aggregates (octochloropropane, ocp) deformable at room conditions. This provides a method for testing how crystalline deformation compares with an isotropic continuum.