Nucleation and transients at the onset of vortex turbulence

Abstract

We present analytical and numerical results that explain the transient turbulent dynamics observed in the complex Ginzburg-Landau equation. Just below the transition to turbulence, we observe that metastable turbulent states break down by the nucleation and growth of single-vortex droplets, leading to a ``frozen'' state with a low (but finite) density of stationary vortices. We derive the relation between nucleation time and radius, and determine their dependence on the distance to the turbulence transition line.