Longitudinal velocity correlation
= Longitudinal velocity correlation
{title2=$Q_{LL}=u^2f(r)$}
For a separation parallel to a unit vector $\mathbf n$, the <longitudinal velocity correlation> is $Q_{LL}=\langle u_L(\mathbf x)u_L(\mathbf x+r\mathbf n)\rangle=u^2f(r)$. In isotropic incompressible <turbulence> the transverse normalized correlation is $g=f+rf\prime/2$ and the trace is $C=u^2(3f+rf\prime)$.