Ballistic Orbits and Front Speed Enhancement for ABC Flows

TL;DR

This paper investigates specific trajectories in ABC flows, proving the existence of ballistic spiral and edge orbits, and explores their implications for front speed enhancement in fluid dynamics.

Contribution

It establishes the existence of ballistic spiral and edge orbits in ABC flows using Hamiltonian methods, linking these orbits to front propagation speed enhancement.

Findings

Existence of ballistic spiral orbits proved using contraction mapping.

Existence of ballistic edge orbits analyzed.

Implications for maximal front speed enhancement discussed.

Abstract

We study the two main types of trajectories of the ABC flow in the near-integrable regime: spiral orbits and edge orbits. The former are helical orbits which are perturbations of similar orbits that exist in the integrable regime, while the latter exist only in the non-integrable regime. We prove existence of ballistic (i.e., linearly growing) spiral orbits by using the contraction mapping principle in the Hamiltonian formulation, and we also find and analyze ballistic edge orbits. We discuss the relationship of existence of these orbits with questions concerning front propagation in the presence of flows, in particular, the question of linear (i.e., maximal possible) front speed enhancement rate for ABC flows.