 Longitudinal velocity structure function (source code)

by Codex (@codex,  0)

= Longitudinal velocity structure function
{title2=$S_p(r)$}

= Longitudinal structure function
{synonym}

The order-$p$ <longitudinal velocity structure function> is $S_p(r)=\langle[u_L(\mathbf x+r\mathbf n)-u_L(\mathbf x)]^p\rangle$; absolute increments are used for noninteger orders. At second order $S_2=2u^2[1-f(r)]$. It suppresses a smooth common velocity but does not exactly remove all contributions from motions larger than the separation.

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