= Pressure Poisson equation for incompressible flow
{title2=$\nabla^2(p/\rho)=-\partial_i\partial_j(u_iu_j)$}
Taking the divergence of the constant-density <Navier-Stokes equation> and using <incompressibility> gives the displayed elliptic <Poisson equation> for pressure. Its <Green function> is nonlocal. For an isolated eddy, the far pressure has a quadrupolar contribution proportional to $r^{-3}$, obtained by differentiating the kernel $1/r$ twice. Boundary conditions can contribute additional pressure fields.
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