Dynamics of phase turbulence

The state vector is defined for the phase turbulence described by the Kuramoto–Sivashinsky equation. Then the two-time correlation function (TTCF) for the state vector is calculated numerically. In the case when the damping constant is zero, the TTCF decays like Lorentzian. The TTCF changes its shape as we increase the value of the damping constant from zero. In addition, the local expansion rate is calculated and it is shown that the local expansion rate fluctuates around at zero