Velocity correlation tensor
= Velocity correlation tensor
{title2=$Q_{ij}(\mathbf r)$}
The <velocity correlation tensor> is $Q_{ij}(\mathbf r)=\langle u_i(\mathbf x)u_j(\mathbf x+\mathbf r)\rangle$. For <isotropic turbulence> it splits into longitudinal and transverse parts. Incompressibility constrains them, while the <Fourier transform> gives the <turbulent energy spectrum>. Its trace is the scalar velocity-dot-product correlation.