PHASE TURBULENCE IN THE 2-DIMENSIONAL COMPLEX GINZBURG-LANDAU EQUATION

Turbulence arising from the phase instability of planewaves in the com plex Ginzburg-Landau equation is studied by means of numerical simulat ions of two-dimensional domains of linear size L ranging from 80 to 51 20. It is shown that, although phase turbulence can be considered as s ustained and statistically stationary in a finite region of parameter space for systems of finite size studied over a limited time period, i t is likely to break down towards amplitude turbulence at the infinite -size infinite-time ''thermodynamic limit.'' As long as it persists, h owever, the statistical properties of phase turbulence are well descri bed within the framework of fluctuating interfaces. Parameters of an e ffective Kardar-Parisi-Zhang equation governing the large-scale phase fluctuations are evaluated. The logarithmic behavior predicted for the linear regime in two dimensions is observed. The crossover to the non trivial scaling regime is estimated to take place at L several orders of magnitude larger than the largest size considered here.