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Wound-up phase turbulence in the Complex Ginzburg-Landau Equation

Montagne, R.; Hernández-García, E.; Amengual, A.; San Miguel, M.
Physical Review E 56, 151-167 (1997)

We consider phase turbulent regimes with nonzero winding number
in the one-dimensional Complex Ginzburg-Landau equation. We find that
phase turbulent states
with winding number larger than a critical one are only transients and decay to
states within a range of allowed winding numbers. The analogy with the Eckhaus
instability for non-turbulent waves is stressed. The transition
from phase to defect turbulence is interpreted as an ergodicity breaking
transition which occurs when the
range of allowed winding numbers vanishes. We explain the states reached at long
times in terms of three basic states, namely {sl quasiperiodic} states, {sl
frozen turbulence} states, and {sl riding turbulence} states. Justification and
some insight into
them is obtained from an analysis of a phase equation for nonzero winding
number: rigidly moving solutions of this equation, which correspond to
quasiperiodic and frozen turbulence states, are understood in terms
of periodic and chaotic solutions of an associated system of ordinary
differential equations. A short
report of some of our results has been published in [{sl Montagne et al.,
Phys. Rev. Lett. {f 77}, 267 (1996)}].

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