Enstrophy measures squared vorticity: a local density is , and its spatial integral or ensemble mean gives a global measure. In homogeneous incompressible flow, viscous dissipation satisfies . Vortex stretching can produce enstrophy in three dimensions; kinematic viscosity destroys it.
For unforced homogeneous incompressible flow, the vorticity equation gives . Curl and full-gradient squared averages agree because the vorticity is divergence free and boundary divergences average to zero. In established high-Reynolds-number turbulence, slow integral-time evolution makes production and destruction nearly balance.
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Enstrophy is a concept used in fluid dynamics and turbulence theory to quantify the intensity of vorticity in a fluid. It is defined mathematically as the integral of the square of the vorticity over a given volume. The vorticity itself is a vector field that represents the local rotation of the fluid, and is defined as the curl of the velocity vector field.