The one-dimensional complex Ginzburg-Landau equation in the low dissipation limit

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

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