= Long-range pressure correlations in turbulence
{title2=$\langle u_x^2p'\rangle=O(r^{-3})$}
The quadrupolar kernel of the <pressure Poisson equation for incompressible flow> allows mixed pressure-velocity correlations with an $r^{-3}$ tail. Its derivative in the evolution of a longitudinal triple correlation allows an $r^{-4}$ tail, potentially changing the <Loitsyansky integral>. The existence of a nonlocal kernel does not fix the tail coefficient or prevent cancellations. An isotropic mean pressure multipole can vanish while a mixed higher-order correlation remains nonzero.
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