In the case that the flow is incompressible, or equivalently that , the enstrophy can be described as the integral of the square of the vorticity :
or, in terms of the flow velocity:
In the context of the incompressible Navier-Stokes equations, enstrophy appears in the following useful result:
The quantity in parentheses on the left is the kinetic energy in the flow, so the result says that energy declines proportional to the kinematic viscosity  times the enstrophy.