Critical points and manifolds of the Lamb vector field in swirling jets

The Lamb vector field in a swirling jet flow at a Reynolds number in the transitional regime is computed for kinematic analysis. The vector lines for the Lamb vector and streamlines and vortex lines are analyzed in detail. The main result is that the set of critical points of the Lamb vector field contains stable and unstable manifolds characterizing high shear regions. Lamb surfaces do not exist in these regions.