= Kolmogorov first similarity hypothesis
{c}
{title2=$S_2(r)=v_\eta^2F(r/\eta)$}
In the locally isotropic <equilibrium range>, the small-scale <velocity increment> statistics depend on the separation, mean <viscous dissipation> and <kinematic viscosity>, independently of large-scale forcing details. <Dimensional analysis> leaves the <Kolmogorov microscales> as normalization scales and gives the displayed second-order <longitudinal structure function>. Universality of $F$ is part of the hypothesis, not something proved by <dimensional analysis>.
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