Stream function

For three-dimensional flows with axisymmetry, see Stokes stream function.

For an incompressible-flow velocity vector field (red, top), its streamlines (dashed) can be computed as the contours of the stream function (bottom).

In fluid dynamics, two types of stream function (or streamfunction) are defined:

• The two-dimensional (or Lagrange) stream function, introduced by Joseph Louis Lagrange in 1781, is defined for incompressible (divergence-free), two-dimensional flows.
• The Stokes stream function, named after George Gabriel Stokes, is defined for incompressible, three-dimensional flows with axisymmetry.

The properties of stream functions make them useful for analyzing and graphically illustrating flows.

The remainder of this article describes the two-dimensional stream function.