THE ONE-DIMENSIONAL COMPLEX GINZBURG-LANDAU EQUATION IN THE LOW DISSIPATION LIMIT

Turbulent solutions of the one-dimensional complex Ginzburg-Landau equ ation when the dissipation is very small am considered. It is found th at probability distributions are strictly Gaussian, implying hard turb ulence does not occur. Also, no inertial range is observed in the wave number spectrum. As expected a linear relation between the attractor d imension and the domain length exists, but the results suggest that th e dimension of the inertial manifold is smaller than has been predicte d. Finally, universal behaviour in both the wavenumber and Lyapunov ex ponent spectra is demonstrated.