ORDER-PARAMETER FOR THE TRANSITION FROM PHASE TO AMPLITUDE TURBULENCE

The maximal conserved phase gradient is introduced as an order paramet er to characterize the transition from phase to defect turbulence in t he complex Ginzburg-Landau equation. It has a finite value in the phas e-turbulent regime and decreases to zero when the transition to defect turbulence is approached. Solutions with a nonzero phase gradient are studied via a Lyapunov analysis. The, degree of ''chaoticity'' decrea ses for increasing values of the phase gradient and finally leads to s table traveling wave solutions. A modified Kuramoto-Sivashinsky equati on for the phase dynamics is able to reproduce the main features of th e stable waves and to explain their origin.