Flow-induced symmetry reduction in two-dimensional reaction–diffusion system

Abstract

The influence of uniform flow on the pattern formation is investigated in a two-dimensional reaction–diffusion system. It is found that the convective flow plays a key role on pattern modulation. Both traveling and stationary periodic patterns are obtained. At moderate flow rates, the perfect hexagon, phase-shifted hexagon and stable square, which are essentially unstable in unperturbed reaction–diffusion systems, are obtained. These patterns move downstream. If the flow rate is increased further, the stationary flow-oriented stripes develop and compete with the spots. If the flow rate exceeds some critical value, the system is convectively unstable and the stationary stripes prevail against the traveling spots. The above patterns all have the same critical wavenumber associated with Turing bifurcation, which indicates that Turing instability produces the patterns while the flow induces the symmetry reduction, i.e., from six-fold symmetry to four-fold one, and to two-fold one ultimately.