We carried out a computational study of propagation speeds of
reaction-diffusion-advection fronts in three dimensional (3D) cellular and
Arnold-Beltrami-Childress (ABC) flows with Kolmogorov-Petrovsky-Piskunov(KPP)
nonlinearity. The variational principle of front speeds reduces the problem to a principal
eigenvalue calculation. An adaptive streamline diffusion finite element method is used in
the advection dominated regime. Numerical results showed that the front speeds are
enhanced in cellular flows according to sublinear power law
O(δp),
p ≈ 0.13, δ the flow intensity. In ABC flows however,
the enhancement is O(δ) which can be attributed to the
presence of principal vortex tubes in the streamlines. Poincaré sections are used to
visualize and quantify the chaotic fractions of ABC flows in the phase space. The effect
of chaotic streamlines of ABC flows on front speeds is studied by varying the three
parameters (a,b,c) of the ABC flows. Speed enhancement along
x direction is reduced as b (the parameter controling
the flow variation along x) increases at fixed
(a,c) > 0, more rapidly as the corresponding ABC streamlines become
more chaotic.