The kinematics of stretching and alignment of material elements in general flow fields

Abstract

A rigorous, kinematic description of the stretching and alignment of infinitesimal material elements in general flow fields is presented. An evolution equation is derived, in the Lagrangian frame, for the alignment angles between a material element and the principal axes of strain. The equation identifies the precise roles played by the local angular velocity and the rotation of the strain axes in the alignment process and provides the framework in which to investigate the extent to which the straining field is ‘persistent’. This general kinematical picture is specialized to study line and vortex stretching in fluid flows and analytically predicts the numerically observed alignment of the vorticity vector with the intermediate strain axis. The alignment equations are solved exactly for a number of special flow fields and investigated numerically for the ABC and STF flows. The kinematic formalism and numerical phenomenology suggests the use of new criteria to analyse the material element stretching properties of large-scale numerical simulations.