Spiral Waves, Edge Transport, and Front Speed Enhancement for ABC Flows

We show that trajectories of the ABC flow in the near-integrable regime are typically of two distinct types: spiral waves and edge transport orbits. We prove existence of special helical orbits (spiral waves), which belong to the Kolmogorov-Arnold-Moser (KAM) regime, by using the contraction mapping principle in the Hamiltonian formulation. In the non-integrable regime we also find and analyze non-KAM spiral-like orbits (edge transport), which consist of one linearly growing component and two oscillating components. These non-KAM spirals do not exist in the integrable regime. We discuss the relationship of existence of such flow trajectories with questions concerning front propagation, in particular, the question of linear (i.e., maximal possible) front speed enhancement rate for ABC flows.