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In this paper, we prove that the ODE system $$ \begin{align*} \dot x &=\sinz+\cos y\\ \dot y &= \sin x+\cos z\\ \dot z &=\sin y + \cos x, \end{align*} $$whose right-hand side is the Arnold-Beltrami-Childress (ABC) flow withparameters $A=B=C=1$, has periodic orbits on $(2\pi\mathbb T)^3$ with rotationvectors parallel to $(1,0,0)$, $(0,1,0)$, and $(0,0,1)$. An application of thisresult is that the well-known G-equation model for turbulent combustion withthis ABC flow on $\mathbb R^3$ has a linear (i.e., maximal possible) flamespeed enhancement rate as the amplitude of the flow grows.

Periodic orbits of the ABC flow with $A=B=C=1$