From Glossary of Meteorology
Exact solution of the Navier–Stokes equations for a steady vortex in which the diffusion of vorticity is balanced by vortex stretching in an external strain field.
The vortex has a Gaussian shape. For example, for a vertical axisymmetric vortex in an external velocity field given by
the vorticity is
in which ν is the kinematic viscosity.