ZERO-HELICITY LAGRANGIAN KINEMATICS OF 3-DIMENSIONAL ADVECTION

The toroidal-poloidal decomposition for divergenceless vector fields in three dimensions is used to classify incompressible steady velocity fields in three dimensions according to whether they have zero, or nonzero helicity, and whether they are integrable, or nonintegrable as dynamical systems. Linearized steady Rayleigh-Benard convection flows provide examples from each class. Computational techniques that preserve volume and helicity are developed and used to visualize the Lagrangian particle trajectories of three-dimensional advection for two Rayleigh-Benard flows having zero helicity in a periodic domain.