Spatial Variation of Correlation Times for 1D Phase Turbulence

For one-dimensional phase-turbulent solutions of the Kuramoto-Sivashinsky equation with rigid boundary conditions, we show that there is a substantial variation of the correlation time~${\tau }_c(x)$ with spatial position $x$ in moderately large systems of size $L$. These results suggest that some time-averaged properties of spatiotemporal chaos do not become homogeneous away from boundaries for large systems and for long times.