Symmetrical double rotor spiral waves on spherical surfaces

Abstract

Chemical waves are influenced by the geometry of the medium on which they propagate and may form different complex spatiotemporal structures in specific cases. Chemical waves on a sphere, chemical pinwheels and the interactions of waves with obstacles are examples of such structures. In this paper, experimental and theoretical studies on the shape of chemical waves on spherical surfaces are described. The chemical composition of a medium dictates the velocity of chemical waves. Geometric constraints for a sphere require that waves moving parallel to the equator travel different distances depending on the latitudinal position. The propagation of waves must, therefore, adjust to changing curvature or the direction of propagation. An equation describing the shape of the chemical wave is obtained which shows agreement with the experimental data although additional effects due to the meandering of the spiral cores also become evident.