Function for incompressible divergence-free flows in two dimensions
For three-dimensional flows with axisymmetry, see Stokes stream function.
Streamlines – lines with a constant value of the stream function – for the incompressible potential flow around a circular cylinder in a uniform onflow.
In fluid dynamics, two types of stream function are defined:
The two-dimensional (or Lagrange) stream function, introduced by Joseph Louis Lagrange in 1781,[1] is defined for incompressible (divergence-free), two-dimensional flows.
The Stokes stream function, named after George Gabriel Stokes,[2] 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.
^Lagrange, J.-L. (1868), "Mémoire sur la théorie du mouvement des fluides (in: Nouveaux Mémoires de l'Académie Royale des Sciences et Belles-Lettres de Berlin, année 1781)", Oevres de Lagrange, vol. Tome IV, pp. 695–748
^Stokes, G.G. (1842), "On the steady motion of incompressible fluids", Transactions of the Cambridge Philosophical Society, 7: 439–453, Bibcode:1848TCaPS...7..439S Reprinted in: Stokes, G.G. (1880), Mathematical and Physical Papers, Volume I, Cambridge University Press, pp. 1–16
In fluid dynamics, two types of streamfunction are defined: The two-dimensional (or Lagrange) streamfunction, introduced by Joseph Louis Lagrange in...
In fluid dynamics, the Stokes streamfunction is used to describe the streamlines and flow velocity in a three-dimensional incompressible flow with axisymmetry...
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