Filament turbulence in oscillatory media

Experiments and theoretical studies show that filament turbulence in bounded three-dimensional media can arise due to a number of different mechanisms or instabilities. In this paper, we show that in oscillatory media, as described by the complex Ginzburg-Landau equation, these different instabilities generate different turbulent filament behaviors that are reflected in the statistical properties on the surface of the medium. We find in particular that the specific filament dynamics in the regime of negative line tension and in the regime of amplitude turbulence can be unambiguously identified by the differing forms for the creation rates of filaments attached to the surface of the medium, as long as the system size is sufficiently large to ensure extensive turbulence. This implies that it is sufficient to study the dynamics on the surface, which allows one to make predictions even if the bulk dynamics is inaccessible. We also find that in the regime of amplitude turbulence the statistical properties of the turbulent dynamics on the surface of a three-dimensional medium are identical to that of a two-dimensional medium.