Editing Stream function (section)

{{Short description|Function for incompressible divergence-free flows in two dimensions}}
{{for|three-dimensional flows with [[axisymmetry]]|Stokes stream function}}
[[File:Stream function.png|thumb|For an incompressible-flow velocity vector field (red, top), its [[Streamlines, streaklines, and pathlines|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,<ref>{{citation |first=J.-L. |last=Lagrange |author-link=Joseph-Louis Lagrange |url=http://gallica.bnf.fr/ark:/12148/bpt6k229223s/f697.image |contribution=Mémoire sur la théorie du mouvement des fluides (in: Nouveaux Mémoires de l'Académie Royale des Sciences et Belles-Lettres de Berlin, année 1781) |title=Oevres de Lagrange |year=1868 |volume=Tome IV |pages=695–748 }}</ref> is defined for [[incompressible flow|incompressible]] ([[divergence-free]]), two-dimensional [[fluid flow|flows]].
* The [[Stokes stream function]], named after [[George Gabriel Stokes]],<ref>{{citation | first=G.G. | last=Stokes | authorlink=George Gabriel Stokes | year= 1842 | title= On the steady motion of incompressible fluids | journal= Transactions of the Cambridge Philosophical Society | volume= 7 | pages= 439–453 | bibcode=1848TCaPS...7..439S }}<br>Reprinted in: {{citation | first= G.G. | last=Stokes | year= 1880 | title= Mathematical and Physical Papers, Volume I | publisher= Cambridge University Press | pages= 1–16 | url= https://archive.org/details/mathphyspapers01stokrich }} </ref> 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.