Pathline
= Pathline
{title2=$\dot{\mathbf x}=\mathbf u(\mathbf x,t)$}
A <pathline> is a fluid particle's material trajectory through a time-dependent velocity field. Unlike a <streamline>, which follows the velocity field at one frozen time, a <pathline> solves the displayed ODE. The two curves coincide in a steady flow but generally differ in an unsteady one.