Dynamic spectral analysis of phase turbulence

We analyze the time fluctuations associated to the power spectrum of a finite system governed by the complex Ginzburg–Landau equation (CGLE) in the phase turbulence region. It is shown that, for any given value of the parameters of the CGLE, these fluctuations follow an exponential law with the wavenumber. The exponent, α, is such that α→0 indicating a critical behavior when the system is approaching the defect turbulence region. On the contrary α→∞ near the Benjamin–Feir line.