Tile patterns in excitable media subject to non-solenoidal flow fields

The propagation of spiral waves in excitable media subject to a non-solenoidal advective field which satisfies the no-penetration condition on the boundaries of the domain is studied numerically, and it is shown that, depending on the amplitude and spatial frequencies of the velocity field, the spiral wave may be distorted highly, break up into a number of smaller spiral waves, or exhibit polygonal shapes or tile patterns. These patterns reflect the symmetry/asymmetry of the velocity field and are characterized by thick regions of high concentration at stagnation points where the velocity gradient is largest, and thin ones which are parallel to the velocity vector. It is also shown that the advective field distorts the spiral wave by decreasing its thickness where the velocity is largest due to the stretching of the wave, and by increasing it at the stagnation points where the curvature of the wave is largest.