Axial strain rate ($E=\partial w/\partial z$)

The axial strain rate is the axial component of the rate-of-strain tensor. For axial velocity $w(z)$ it is $E=\partial w/\partial z$. In a uniform uniaxial extensional flow, $w=Ez$ and incompressible flow requires $u_r=-Er/2$; positive $E$ stretches the axial direction and contracts the transverse directions.