Statistics of phase turbulence II

The system described by the Kuramoto–Sivashinsky equation (SKSE) is shown to have a short- and a long-time regimes. The probability distribution function (PDF) for the absolute value of the solution is subjected to different scaling laws in the two time regimes. The local expansion rate (LER) and its two-time correlation function are calculated. The time regime where the correlation for the LER remains is shorter than the one for the absolute value of the solution for the SKSE. The fluctuation in the LER becomes small as the damping constant is increased. The PDF for the LER is also given in this paper.