In fluid dynamics, the enstrophy  can be interpreted as another type of potential density; or, more concretely, the quantity directly related to the kinetic energy in the flow model that corresponds to dissipation effects in the fluid. It is particularly useful in the study of turbulent flows, and is often identified in the study of thrusters as well as in combustion theory and meteorology.
Given a domain  and a once-weakly differentiable vector field  which represents a fluid flow, such as a solution to the Navier-Stokes equations, its enstrophy is given by:where . This quantity is the same as the squared seminorm of the solution in the Sobolev space .