Velocity increment
= Velocity increment
{title2=$\delta\mathbf u(\mathbf r)=\mathbf u(\mathbf x+\mathbf r)-\mathbf u(\mathbf x)$}
A velocity increment is the difference of a <velocity field> between two positions. Its longitudinal component is the projection onto their separation direction. Moments of increments define <longitudinal structure functions>; the <Kolmogorov 1941 theory> estimates a typical inertial-range magnitude as $(\epsilon r)^{1/3}$.