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

Turbulent solutions of the one-dimensional complex Ginzburg-Landau equation when the dissipation is very small am considered. It is found that probability distributions are strictly Gaussian, implying hard turbulence does not occur. Also, no inertial range is observed in the wavenumber spectrum. As expected a linear relation between the attractor dimension and the domain length exists, but the results suggest that the dimension of the inertial manifold is smaller than has been predicted. Finally, universal behaviour in both the wavenumber and Lyapunov exponent spectra is demonstrated.