Dynamical behaviors and invariant recurrent patterns of Kuramoto-Sivashinsky equation with time-periodic forces

In this study, we perform an extensive numerical study of the one-dimensional Kuramoto-Sivashinsky equation under time-periodic forces. We examine the statistics of chaotic solutions and the behaviors from turbulent solutions to steady periodic solutions as the period of the forces increases. When the period is small, global turbulent characteristics associated with local oscillations are found, and the forces are considered not to influence the turbulent dynamics. Long periodic orbits are found to capture the dynamics of the turbulent solutions. On the other hand, if the strength is large enough and the period is large, only regular periodic motions are found and their spatial structures are like viscous shocks.