Analysis of the polar form of the von Mises transformation

摘要

The implementation of the classical form of the von Mises transformation in the study of fluid flow in two-dimensional curvilinear domains gives rise to an infinite Jacobian of transformation when viscous fluid flow is considered and when the streamlines of the flow become vertical at any point in the flow domain. In this work, it will be shown that in special cases the infinite nature of the Jacobian can be eliminated when the streamlines are vertical by utilizing the polar form of the transformation.