Affine velocity field
= Affine velocity field
{title2=$\mathbf u(\mathbf x,t)=K(t)\mathbf x+\mathbf b(t)$}
A <velocity field> with spatially constant <velocity gradient> $K$. Differences of fluid <velocities> satisfy $\mathbf u(\mathbf x+\mathbf R)-\mathbf u(\mathbf x)=K\mathbf R$, even when the uniform translation $\mathbf b$ is nonzero. <Incompressibility> requires $\operatorname{tr}K=0$.