From AMS Glossary
One-half the square of the relative vorticity.
The term was popularized by C. Leith and is based on the modern Greek στρωφη, meaning "act of turning." Enstrophy is a conservative quantity in two-dimensional inviscid flow. However, when viscosity is finite, enstrophy tends to be selectively decayed relative to more rugged integrals such as energy and angular momentum.
Leith, C. E. 1968. Diffusion approximation for two-dimensional turbulence. Phys. Fluids. 11. 671–673.