= Mean enstrophy balance
{title2=$\dot Z=\langle\omega_i\omega_jS_{ij}\rangle-\nu\langle|\nabla\times\boldsymbol\omega|^2\rangle$}
For unforced homogeneous <incompressible flow>, the <vorticity equation> gives $\dot Z=\langle\omega_i\omega_jS_{ij}\rangle-\nu\langle|\nabla\times\boldsymbol\omega|^2\rangle$. <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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