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Ω u · ω dx , which measures the swirliness about the local direction of flow. The enstrophy is not a conserved quadratic quantity since it can be amplified by the stretching of the vortex tubes, i.e. increased by the properly oriented velocity gradient. In two dimension, the vortex stretching mechanism is absent because the velocity gradient is always perpendicular to the vorticity. As the consequence, the enstrophy is a constant of motion.
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