Stream function

Summary

A stream function is a scalar function $\psi$ that encodes a two-dimensional incompressible flow through $u = \partial \psi / \partial y$ and $v = -\partial \psi / \partial x$. The curves of constant $\psi$ are the streamlines of the flow. The difference of $\psi$ between two points is the volume flux through any curve that joins them. It reduces the two unknown velocity components to one scalar unknown.