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There are two types of motion in continuum mechanics: translation and rotation.

  1. \frac{1}{2}mv^2 gives us the energy of translation
  2. \frac{1}{2} \omega^2 is related to the rotational energy, and we call this the enstrophy density (and sometimes just enstrophy, but that could also mean the volume integral of this quantity, so context really matters).

Two dimensional turbulence was studied intensively when we didn’t have the computing power to do three dimensions. Researchers found that enstrophy goes to smaller and smaller scales by vortex stretching. This is why it was used so much.