Vortex line

A vortex line is an integral curve of the vorticity vector field: its tangent is parallel to $\mathbf{\omega }=\nabla \times \mathbf{u}$. In a two-dimensional incompressible flow, these lines are perpendicular to the flow plane and the vorticity equation gives $D\omega /Dt=0$. Since material cross-sectional area is preserved, the flux of vorticity through a material vortex tube, equal to its circulation, is constant.