= Kolmogorov decay law
{c}
{title2=$u^2\propto(t-t_*)^{-10/7},\quad\ell\propto(t-t_*)^{2/7}$}
Assume a nonzero invariant <Loitsyansky integral>, self-preserving large-scale correlations, and high-<Reynolds number> freely decaying <isotropic turbulence>. Then $I\propto u^2\ell^5$ and $-d(u^2)/dt\propto u^3/\ell$ imply the displayed decay and growth laws. The assumptions on correlation shape and the dissipation coefficient are needed in addition to conservation of the integral.
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