Numerical modeling of the motion of rigid ellipsoidal objects in slow viscous flows: A new approach

A simple algorithm for modeling the rotation of rigid ellipsoidal objects in viscous flows based on Jeffery's (1922, Proceedings of the Royal Society of London A102, 161–179) theory is presented and is implemented in a fully graphic mathematics application Mathcad® (http://www.mathsoft.com). The orientation of ellipsoidal objects is specified in terms of polar coordinate angles that can be easily converted to the trend and plunge angles of the three principal axes rather than the Euler angles. With the Mathcad worksheets presented in the supplementary data associated with this paper, modeling the rotation paths of individual rigid objects, the development of inclusion trail geometry within syn-kinematic porphyroblasts, and the development of preferred orientation and shape fabrics for a population of rigid objects becomes as easy a task as using a spreadsheet. The shape and preferred orientation fabrics for a population of rigid objects can be presented in both a three-dimensional form and a two-dimensional form, allowing easy comparison between field data and model predictions. The modeler can customize the type and format of the output to best fit the purpose of the investigation and to facilitate the comparison of model predictions with geological observations. Application examples are presented for various types of modeling involving rigid objects.