We study the reaction dynamics of active particles that are advected passively by 2D incompressible open flows, whose motion is nonhyperbolic. This nonhyperbolicity is associated with the presence of persistent vortices near the wake, wherein fluid is trapped. We show that the fractal equilibrium distribution of the reactants is described by an effective dimension $d_{\mathit{eff}}$, which is a finite resolution approximation to the fractal dimension. Furthermore, $d_{\mathit{eff}}$ depends on the resolution $ϵ$ and on the reaction rate $1∕\tau$. As $\tau$ is increased, the equilibrium distribution goes through a series of transitions where the effective dimension increases abruptly. These transitions are determined by the complex structure of Cantori surrounding the Kolmogorov-Arnold-Moser (KAM) islands.

• Received 9 April 2003

DOI:https://doi.org/10.1103/PhysRevE.70.036216