- A parameter of two-dimensional, nondivergent flow, with a value that is constant along each streamline.

*x*,

*y*) plane, the streamfunction ψ is related to the respective coordinate velocities

*u*and

*v*by the equations

In meteorology the most common application of the streamfunction is in the assumption of geostrophic equilibrium. If variations in the Coriolis parameter

*f*are ignored, the streamfunction in a constant-pressure surface is proportional to the geopotential

*gz*, that is, ψ =

*gz*/

*f*; in an isentropic surface, it is ψ = (

*gz*+

*c*

_{p}

*T*)/

*f*, called the Montgomery streamfunction, where

*c*

_{p}is the specific heat at constant pressure and

*T*the Kelvin temperature.

- Stokes's streamfunction (
*also called*current function): If the flow is three-dimensional but is axisymmetric (i.e., the same in every plane containing the axis of symmetry), a Stokes's streamfunction ψ will exist such that

where*v*_{s}is the speed in an arbitrary direction*s*,*r*is the distance from the axis of symmetry, and*n*is normal to the direction*s*, increasing to the left.

Note that Stokes's streamfunction has dimensions of volume per time. Streamfunctions can also be defined for more complex three-dimensional flows.