When two scalar functions (stream functions) $\psi_{i}$ are are producing two surfaces, $\nabla\psi_{i}$. The surfaces are intersecting in a line given by $\alpha\vec{v}=\nabla\psi_{1}\times\nabla\psi_{2}$. This leads to $\nabla\vec{v}=0$.
I have found $\nabla\vec{v}=0$ can be shown by a direct calculation. Is there a more elegant proof?