Enstrophy

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. ${\frac {1}{2}}m\omega ^{2}$ gives the energy of rotation, and we call this Enstrophy (density).

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 in the way thermodynamics predicts, but other measures of energy do not. This is why it was used so much.