Nonlinear analysis of stationary patterns in convection-reaction-diffusion systems

Stationary spatially inhomogeneous patterns which appear due to the interaction of reaction and convection in a packed-bed cross-flow reactor are observed and analyzed. A linear stability analysis was performed for the case of unbounded system, and an analytical expression for the amplification threshold was determined. Above this threshold stationary patterns could be sustained in bounded systems. A weakly nonlinear analysis is used in order to derive the governing amplitude equation. The results of linear and nonlinear analyses were verified by direct numerical simulations.