Vortex line
= Vortex line
A <vortex line> is an <integral> curve of the <vorticity> vector field: its tangent is parallel to $\boldsymbol\omega=\nabla\times\mathbf u$. 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.