Vortex glass and vortex liquid in oscillatory media

Abstract

We study the disordered, multispiral solutions of two-dimensional oscillatory media for parameter values at which the single-spiral/vortex solution is fully stable. Using the complex Ginzburg-Landau (CGLE) equation, we show that these states, heretofore believed to be static, actually evolve extremely slowly. This is achieved via a reduction of the CGLE to the evolution of the sole vortex coordinates. This true defect-mediated turbulence occurs in two distinct phases, a vortex liquid characterized by normal diffusion of spirals, and a slowly relaxing, intermittent, ‘‘vortex glass.’’