Turing pattern formation for reaction–convection–diffusion systems in fixed domains submitted to toroidal velocity fields

Abstract

We have studied the effect of advection on reaction–diffusion equations by using toroidal velocity fields. Turing patterns formation in diffusion–advection–reaction problems was studied specifically, considering the Schnackenberg and glycolysis reaction kinetics models. Four cases were analyzed and solved numerically using finite elements. For glycolysis models, the advective effect modified the form of Turing patterns obtained with diffusion–reaction; whereas for Schnackenberg problems, the original patterns distorted themselves slightly, making them rotate in direction of the velocity field. We have also determined that the advective effect surpassed the diffusive one for high values of velocity and instability driven by diffusion was eliminated. On the other hand the advective effect is not considerable for very low values in the velocity field, and there was no modification in the original Turing pattern.