Saffman decay law
= Saffman decay law
{c}
{title2=$\mathcal E\propto(t-t_*)^{-6/5}$}
With nonzero invariant $L$, a self-preserving <integral scale of turbulence> gives $L\propto\mathcal E\ell^3$. Combining this with freely decaying high-Reynolds-number <viscous dissipation> $\epsilon\propto\mathcal E^{3/2}/\ell$ gives $\mathcal E\propto(t-t_*)^{-6/5}$ and $\ell\propto(t-t_*)^{2/5}$. The closure assumptions, not the invariant alone, determine this exponent.