Complex patterns in three-dimensional excitable media with advection

Wave propagation in three-dimensional excitable media subject to homogeneous Neumann boundary conditions and subject to irrotational or rotational advective fields which satisfy the no-penetration condition is studied numerically. It is shown that the velocity field annihilates spiral waves and results in complex periodic spatio-temporal patterns which are characterized by either planar or curved fronts depending on the flow compressibility, number and location of stagnation points, rotation and straining. For sinusoidal velocity fields with a frequency equal to one, almost planar fronts which resemble those found in two-dimensional excitable media are found, whereas, when the frequency is increased, several curved fronts propagate at about the same speed and surround each other when they approach an edge of the domain. It is also shown that the main effect of increasing the frequency of the velocity field on the concentrations at fixed monitor locations is to decrease the period of the spikes of the activator's concentration