Order, Disorder, and Phase Turbulence

Phase turbulence---a phenomenon associated with the time evolution of extended spatial patterns---is investigated on the basis of the Kuramoto-Sivashinsky equation. The turbulent behavior may be thought of as disorder of a primary cellular pattern and described by hydrodynamic analysis of slow modes. Such an approach explains qualitatively the spatial fluctuation spectrum. It also suggests that the ordering of the system into a linearly stable cellular state is inhibited and the lifetime of the turbulent state grows exponentially with the size of the system. This anomalous glasslike relaxation was observed in a numerical simulation.