Spatio-temporal patterns in excitable media with non-solenoidal flow straining

Abstract

The propagation of spiral waves in excitable media with the Belousov–Zhabotinsky reactions in a non-solenoidal, time-independent velocity field is studied numerically as a function of the amplitude and frequency of the velocity. It is shown that the spiral wave is slightly distorted for small amplitudes and low frequencies, whereas it breaks-up into new spiral waves which merge and form periodic, cusped fronts at moderate amplitudes and small frequencies. For larger amplitudes but still small frequencies, the spiral wave undergoes a second transition to thick fronts characterized by small curvature, and the radius of curvature increases as the amplitude of the velocity field is increased. It is also shown that an increase in the frequency of the velocity field results in front distorsion and corrugations which are due to the increase in the number of stagnation points as the frequency is increased, straining of the front at stagnation points and the non-solenoidal velocity field employed in the paper. An explanation of these corrugations in terms of the straining, gradient of the transverse velocity along the normal to the front and compressibility is provided.