# Streamfunction

From AMS Glossary

## streamfunction

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

For flow in the (*x*,*y*) plane, the streamfunction ψ is related to the respective coordinate velocities*u*and*v*by the equationsIn 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 thatwhere*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.