= Normalized constant-skewness structure-function equation
{title2=$h'+2h^{3/2}=2x$}
Set $S_2=\sqrt{15}\beta^{3/2}v_\eta^2h$ and $r=(15\beta)^{3/4}\eta x$. The <Kolmogorov equation for structure functions> and the <constant-skewness turbulence closure> give the displayed <ordinary differential equation>, with $h(0)=0$. Its small-separation balance is $h\sim x^2$; its large-separation balance is $h\sim x^{2/3}$. The first matches differentiable <velocity increments>, and the second recovers the assumed <Kolmogorov two-thirds law>.
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